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Magnetism Molecules to Materials V

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					Magnetism:
Molecules
to Materials V
Edited by Joel S. Miller and Marc Drillon
Magnetism: Molecules to Materials V




Edited by J.S. Miller and M. Drillon
Further Titles of Interest:


J.S. Miller, M. Drillon (Eds.)
Magnetism: Molecules to Materials IV
2003, ISBN 3-527-30429-0

J.S. Miller, M. Drillon (Eds.)
Magnetism: Molecules to Materials III
Nanosized Magnetic Materials
2002, ISBN 3-527-30302-2

J.S. Miller, M. Drillon (Eds.)
Magnetism: Molecules to Materials II
Molecule-Based Materials
2001, ISBN 3-527-30301-4

J.S. Miller, M. Drillon (Eds.)
Magnetism: Molecules to Materials
Models and Experiments
2001, ISBN 3-527-29772-3

F. Schüth, K.S.W. Sing, J. Weitkamp (Eds.)
Handbook of Porous Solids
2002, ISBN 3-527-30246-8

F. Laeri, F. Schüth, U. Simon, M. Wark (Eds.)
Host-Guest-Systems Based on Nanoporous Crystals
2003, ISBN 3-527-30501-7
Magnetism:
Molecules
to Materials V
Edited by Joel S. Miller and Marc Drillon
Prof. Dr. Joel S. Miller
Department of Chemistry
University of Utah
Salt Lake City
UT 84112-0850
USA

Prof. Dr. Marc Drillon
CNRS
Institut de Physique et Chimie
des Matériaux de Strasbourg
23 Rue du Loess
67037 Strasbourg Cedex
France

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Contents




Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI

1   Metallocenium Salts
   of Radical Anion Bis(Dichalcogenate) Metalates
   Vasco Gama and Maria Teresa Duarte . . . . . . . . . . . . . . . . . . .              1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       1
1.2 Basic Structural Motifs . . . . . . . . . . . . . . . . . . . . . . . . . .          4
      1.2.1 ET Salts Based on Decamethylmetallocenium Donors . . . . .                   4
      1.2.2 ET Salts Based on Other Metallocenium Donors . . . . . . . .                 6
1.3 Solid-state Structures and Magnetic Behavior . . . . . . . . . . . . . .             7
      1.3.1 Type I Mixed Chain Salts . . . . . . . . . . . . . . . . . . . . .           7
      1.3.2 Type II Mixed Chain [M(Cp*)2 ][M (L)2 ] Salts . . . . . . . . .             21
      1.3.3 Type III Mixed Chain [M(Cp*)2 ][M (L)2 ] Salts . . . . . . . .              23
      1.3.4 Type IV Mixed Chain [M(Cp*)2 ][M (L)2 ] Salts . . . . . . . .               30
      1.3.5 Salts with Segregated Stacks not 1D Structures . . . . . . . . .            36
1.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . .             37
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    39
2     Chiral Molecule-Based Magnets
      Katsuya Inoue, Shin-ichi Ohkoshi, and Hiroyuki Imai . . . . . . . . . . .         41
2.1    Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   41
2.2    Physical and Optical Properties of Chiral or Noncentrosymmetric
       Magnetic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     41
       2.2.1 Magnetic Structure and Anisotropy . . . . . . . . . . . . . . .            42
       2.2.2 Nonlinear Magneto-optical Effects . . . . . . . . . . . . . . . .          43
       2.2.3 Magneto-chiral Optical Effects . . . . . . . . . . . . . . . . . .         48
2.3    Nitroxide-manganese Based Chiral Magnets . . . . . . . . . . . . . .             49
       2.3.1 Crystal Structures . . . . . . . . . . . . . . . . . . . . . . . . .       49
       2.3.2 Magnetic Properties . . . . . . . . . . . . . . . . . . . . . . . .        51
2.4    Two- and Three-dimensional Cyanide Bridged Chiral Magnets . . . .                53
       2.4.1 Crystal Design . . . . . . . . . . . . . . . . . . . . . . . . . . .       54
       2.4.2 Two-dimensional Chiral Magnet [39] . . . . . . . . . . . . . .             54
       2.4.3 Three-dimensional Chiral Magnet [40] . . . . . . . . . . . . .             57
VI      Contents

      2.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . .       .   .   .   .   .   .   60
2.5 SHG-active Prussian Blue Magnetic Films . . . . . . . . .              .   .   .   .   .   .   60
      2.5.1 Magnetic Properties and the Magneto-optical Effect             .   .   .   .   .   .   60
      2.5.2 Nonlinear Magneto-optical Effect . . . . . . . . . .           .   .   .   .   .   .   64
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . .       .   .   .   .   .   .   68
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   .   .   .   .   .   .   69

3   Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes
   Jamie L. Manson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                   71
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                 71
3.2 “Binary” α-M(dca)2 Magnets . . . . . . . . . . . . . . . . . . . . . . .                       73
      3.2.1 Structural Aspects . . . . . . . . . . . . . . . . . . . . . . . . .                   73
      3.2.2 Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . .                     76
      3.2.3 Canted Antiferromagnetism . . . . . . . . . . . . . . . . . . . .                      79
      3.2.4 Mechanism for Magnetic Ordering . . . . . . . . . . . . . . . .                        81
      3.2.5 Pressure-dependent Susceptibility . . . . . . . . . . . . . . . .                      82
3.3 β-M(dca)2 Magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . .                      82
      3.3.1 Structural Evidence . . . . . . . . . . . . . . . . . . . . . . . .                    82
      3.3.2 Magnetic Behavior of α-Co(dca)2 . . . . . . . . . . . . . . . .                        84
      3.3.3 Comparison of Lattice and Spin Dimensionality in α-
             and β-Co(dca)2 . . . . . . . . . . . . . . . . . . . . . . . . . . .                   85
3.4 Mixed-anion M(dca)(tcm) . . . . . . . . . . . . . . . . . . . . . . . . .                       85
      3.4.1 Crystal Structure . . . . . . . . . . . . . . . . . . . . . . . . . .                   85
      3.4.2 Magnetic Properties . . . . . . . . . . . . . . . . . . . . . . . .                     86
3.5 Polymeric 2D (cat)M(dca)3 cat = Ph4 As, Fe(bipy)3 . . . . . . . . . .                           87
      3.5.1 (Ph4 As)[Ni(dca)3 ] . . . . . . . . . . . . . . . . . . . . . . . . .                   87
      3.5.2 [Fe(bipy)3 ][M(dca)3 ]2 {M = Mn, Fe} . . . . . . . . . . . . . .                        88
3.6 Heteroleptic M(dca)2 L Magnets . . . . . . . . . . . . . . . . . . . . .                        88
      3.6.1 Mn(dca)2 (pyz) . . . . . . . . . . . . . . . . . . . . . . . . . . .                    89
      3.6.2 Mn(dca)2 (2,5-Me2 pyz)2 (H2 O)2 . . . . . . . . . . . . . . . . . .                     95
      3.6.3 Mn(dca)2 (H2 O) . . . . . . . . . . . . . . . . . . . . . . . . . . .                   96
      3.6.4 Fe(dca)2 (pym)·EtOH . . . . . . . . . . . . . . . . . . . . . . .                       97
      3.6.5 Fe(dca)2 (abpt)2 . . . . . . . . . . . . . . . . . . . . . . . . . . .                  98
3.7 Dicyanophosphide: A Phosphorus-containing Analog
      of Dicyanamide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                  99
3.8 Conclusions and Future Prospects . . . . . . . . . . . . . . . . . . . .                       100
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .               101

4  Molecular Materials Combining Magnetic
   and Conducting Properties
   Peter Day and Eugenio Coronado . . . . . . . . . . . . . . . . . . . . . 105
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.2 Interest of Conducting Molecular-based Magnets . . . . . . . . . . . . 106
                                                                           Contents                VII

      4.2.1 Superconductivity and Magnetism . . . . . . . . . .            . . . . . . 107
      4.2.2 Exchange Interaction between Localised Moments
            and Conduction Electrons . . . . . . . . . . . . . . .         .   .   .   .   .   .   108
4.3 Magnetic Ions in Molecular Charge Transfer Salts . . . . .             .   .   .   .   .   .   111
      4.3.1 Isolated Magnetic Anions . . . . . . . . . . . . . . .         .   .   .   .   .   .   111
      4.3.2 Metal Cluster Anions . . . . . . . . . . . . . . . . .         .   .   .   .   .   .   131
      4.3.3 Chain Anions: Maleonitriledithiolates . . . . . . . .          .   .   .   .   .   .   143
      4.3.4 Layer Anions: Tris-oxalatometallates . . . . . . . .           .   .   .   .   .   .   146
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . .      .   .   .   .   .   .   153
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   .   .   .   .   .   .   155

5   Lanthanide Ions in Molecular Exchange Coupled Systems
   Jean-Pascal Sutter and Myrtil L. Kahn . . . . . . . . . . . . . . . . . . .                     161
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                 161
      5.1.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                 161
5.2 Molecular Compounds Involving Gd(III) . . . . . . . . . . . . . . . .                          164
      5.2.1 Gd(III)–Cu(II) Systems . . . . . . . . . . . . . . . . . . . . . .                     164
      5.2.2 Systems with Other Paramagnetic Metal Ions . . . . . . . . . .                         165
      5.2.3 Gd(III)-organic Radical Compounds . . . . . . . . . . . . . . .                        165
5.3 Superexchange Mediated by Ln(III) Ions . . . . . . . . . . . . . . . .                         170
5.4 Exchange Coupled Compounds Involving Ln(III) Ions
      with a First-order Orbital Momentum . . . . . . . . . . . . . . . . . .                      174
      5.4.1 Qualitative Insight into the Exchange Interaction . . . . . . . .                      174
      5.4.2 Quantitative Insight into the Exchange Interaction . . . . . . .                       180
      5.4.3 The Exchange Interaction . . . . . . . . . . . . . . . . . . . . .                     181
5.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . .                     185
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .               185

6     Monte Carlo Simulation: A Tool to Analyse Magnetic Properties
      Joan Cano and Yves Journaux . . . . . . . . . . . . . . . . . . . . . . .                    189
6.1     Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             189
6.2     Monte Carlo Method . . . . . . . . . . . . . . . . . . . . . . . . . . . .                 190
        6.2.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . .               190
        6.2.2 Metropolis Algorithm . . . . . . . . . . . . . . . . . . . . . . .                   192
        6.2.3 Thermalization Process . . . . . . . . . . . . . . . . . . . . . .                   193
        6.2.4 Size of Model and Periodic Boundary Conditions . . . . . . .                         194
        6.2.5 Random Number Generators . . . . . . . . . . . . . . . . . . .                       196
        6.2.6 Magnetic Models . . . . . . . . . . . . . . . . . . . . . . . . . .                  196
        6.2.7 Structure of a Monte Carlo Program . . . . . . . . . . . . . . .                     197
6.3     Regular Infinite Networks . . . . . . . . . . . . . . . . . . . . . . . . .                199
6.4     Alternating Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . .               203
6.5     Finite Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .               206
6.6     Exact Laws versus MC Simulations . . . . . . . . . . . . . . . . . . .                     208
VIII    Contents

      6.6.1 A Method to Obtain an ECS Law for a Regular 1D System:
            Fisher’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . .       209
      6.6.2 Small Molecules . . . . . . . . . . . . . . . . . . . . . . . . . .        211
      6.6.3 Extended Systems . . . . . . . . . . . . . . . . . . . . . . . . .         213
6.7 Some Complex Examples . . . . . . . . . . . . . . . . . . . . . . . . .            217
6.8 Conclusions and Future Prospects . . . . . . . . . . . . . . . . . . . .           220
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   220
7   Metallocene-based Magnets
    Gordon T. Yee and Joel S. Miller . . . . . . . . . . . . . . . . . . . . . .       223
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     223
7.2 Electrochemical and Magnetic Properties of Neutral
     Decamethylmetallocenes and Decamethylmetallocenium
     Cations Paired with Diamagnetic Anions . . . . . . . . . . . . . . . .            224
7.3 Preparation of Magnetic Electron Transfer Salts . . . . . . . . . . . .            226
     7.3.1 Electron Transfer Routes . . . . . . . . . . . . . . . . . . . . .          226
     7.3.2 Metathetical Routes . . . . . . . . . . . . . . . . . . . . . . . .         226
7.4 Crystal Structures of Magnetic ET Salts . . . . . . . . . . . . . . . . .          227
7.5 Tetracyanoethylene Salts (Scheme 7.2) . . . . . . . . . . . . . . . . .            230
     7.5.1 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      230
     7.5.2 Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         232
     7.5.3 Chromium . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          232
     7.5.4 Other Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . .        232
7.6 Dimethyl Dicyanofumarate
     and Diethyl Dicyanofumarate Salts . . . . . . . . . . . . . . . . . . . .         233
     7.6.1 Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         233
     7.6.2 Chromium . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          234
7.7 2,3-Dichloro-5,6-dicyanoquinone Salts
     and Related Compounds . . . . . . . . . . . . . . . . . . . . . . . . . .         235
7.8 2,3-Dicyano-1,4-naphthoquinone Salts . . . . . . . . . . . . . . . . . .           236
     7.8.1 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      236
     7.8.2 Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         237
     7.8.3 Chromium . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          238
7.9 7,7,8,8-Tetracyano-p-quinodimethane Salts . . . . . . . . . . . . . . .            238
     7.9.1 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      238
     7.9.2 Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         239
     7.9.3 Chromium . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          239
7.10 2,5-Dimethyl-N, N -dicyanoquinodiimine Salts . . . . . . . . . . . .              239
     7.10.1 Iron and Manganese . . . . . . . . . . . . . . . . . . . . . . . .         239
7.11 1,4,9,10-Anthracenetetrone Salts . . . . . . . . . . . . . . . . . . . . .        240
7.12 Cyano and Perfluoromethyl Ethylenedithiolato Metalate Salts . . . .               240
     7.12.1 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     241
     7.12.2 Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        241
                                                                               Contents                 IX

7.13  Benzenedithiolates and Ethylenedithiolates . . . . . . .         . . . . . . . . 244
7.14  Additional Dithiolate Examples . . . . . . . . . . . . . .       . . . . . . . . 245
7.15  Bis(trifluoromethyl)ethylenediselenato Nickelate Salts           . . . . . . . . 246
7.16  Other Acceptors that Support Ferromagnetic Coupling,
      but not Long-range Order above ∼2 K . . . . . . . . . .          .   .   .   .   .   .   .   .   246
7.17 Other Metallocenes and Related Species as Donors . .              .   .   .   .   .   .   .   .   249
7.18 Muon Spin Relaxation Spectroscopy . . . . . . . . . . .           .   .   .   .   .   .   .   .   251
7.19 Mössbauer Spectroscopy . . . . . . . . . . . . . . . . .          .   .   .   .   .   .   .   .   251
7.20 Spin Density Distribution from Calculations
      and Neutron Diffraction Data . . . . . . . . . . . . . . .       . . . . . . . . 253
7.21 Dimensionality of the Magnetic System
      and Additional Evidence for a Phase Transition . . . . .         . . . . . . . . 253
7.22 The Controversy Around the Mechanism
      of Magnetic Coupling in ET Salts . . . . . . . . . . . .         .   .   .   .   .   .   .   .   254
7.23 Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . .    .   .   .   .   .   .   .   .   255
7.24 Research Opportunities . . . . . . . . . . . . . . . . . .        .   .   .   .   .   .   .   .   256
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   .   .   .   .   .   .   .   .   257

8   Magnetic Nanoporous Molecular Materials
   Daniel Maspoch, Daniel Ruiz-Molina, and Jaume Veciana . . . . . . . .                               261
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                     261
8.2 Inorganic and Molecular Hybrid Magnetic Nanoporous Materials . .                                   263
8.3 Magnetic Nanoporous Coordination Polymers . . . . . . . . . . . . .                                266
      8.3.1 Carboxylic Ligands . . . . . . . . . . . . . . . . . . . . . . . .                         266
      8.3.2 Nitrogen-based Ligands . . . . . . . . . . . . . . . . . . . . . .                         271
      8.3.3 Paramagnetic Organic Polytopic Ligands . . . . . . . . . . . .                             273
8.4 Summary and Perspectives . . . . . . . . . . . . . . . . . . . . . . . .                           278
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                   280

9     Magnetic Prussian Blue Analogs
      Michel Verdaguer and Gregory S. Girolami . . . . . . . . . . . . . . . .                         283
9.1    Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                  283
9.2    Prussian Blue Analogs (PBA), Brief History, Synthesis
       and Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                   284
       9.2.1 Formulation and Structure . . . . . . . . . . . . . . . . . . . .                         285
       9.2.2 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                     288
9.3    Magnetic Prussian Blues (MPB) . . . . . . . . . . . . . . . . . . . . .                         290
       9.3.1 Brief Historical Survey of Magnetic Prussian Blues . . . . . .                            291
       9.3.2 Interplay between Models and Experiments . . . . . . . . . . .                            293
       9.3.3 Quantum Calculations . . . . . . . . . . . . . . . . . . . . . . .                        306
9.4    High TC Prussian Blues (the Experimental Race
       to High Curie Temperatures) . . . . . . . . . . . . . . . . . . . . . . .                       322
       9.4.1 Chromium(II)–Chromium(III) Derivatives . . . . . . . . . . .                              323
X       Contents

      9.4.2 Manganese(II) –Vanadium(III) Derivatives . . . . . . . . .             .   .   324
      9.4.3 The Vanadium(II) –Chromium(III) Derivatives . . . . . . .              .   .   325
      9.4.4 Prospects in High-TC Magnetic Prussian Blues . . . . . . .             .   .   334
9.5 Prospects and New Trends . . . . . . . . . . . . . . . . . . . . . . .         .   .   338
      9.5.1 Photomagnetism: Light-induced Magnetisation . . . . . .                .   .   338
      9.5.2 Fine Tuning of the Magnetisation . . . . . . . . . . . . . .           .   .   339
      9.5.3 Dynamics in Magnetic and Photomagnetic Prussian Blues                  .   .   339
      9.5.4 Nanomagnetism . . . . . . . . . . . . . . . . . . . . . . . .          .   .   339
      9.5.5 Blossoming of Cyanide Coordination Chemistry . . . . . .               .   .   340
9.6 Conclusion: a 300 Years Old “Inorganic Evergreen” . . . . . . . .              .   .   341
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   .   .   341
10   Scaling Theory Applied to Low Dimensional Magnetic Systems
     Jean Souletie, Pierre Rabu, and Marc Drillon . . . . . . . . . . . . . .              347
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        347
10.2 Non-critical-scaling: the Other Solutions of the Scaling Model . . . .                348
10.3 Universality Classes and Lower Critical Dimensionality . . . . . . . .                351
10.4 Phase Transition in Layered Compounds . . . . . . . . . . . . . . . .                 352
10.5 Description of Ferromagnetic Heisenberg Chains . . . . . . . . . . . .                363
      10.5.1 Application to Ferromagnetic S = 1 Chains . . . . . . . . . .                 366
10.6 Application to the Spin-1 Haldane Chain . . . . . . . . . . . . . . . .               368
10.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          375
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       375

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
Preface




The development, characterization, and technological exploitation of new materi-
als, particularly as components in ‘smart’ systems, are key challenges for chem-
istry and physics in the next millennium. New substances and composites in-
cluding nanostructured materials are envisioned for innumerable areas including
magnets for the communication and information sector of our economy. Mag-
nets are already an important component of the economy with worldwide sales
exceeding $30 billion per annum. Hence, research groups worldwide are target-
ing the preparation and study of new magnets especially in combination with
other technologically important properties, e. g., electrical and optical proper-
ties.
    In the past few years our understanding of magnetism and magnetic materials,
thought to be mature, has enjoyed a renaissance as it is being expanded by con-
tributions from many diverse areas of science and engineering. These include (i)
the discovery of bulk ferro- and ferrimagnets based on organic/molecular com-
ponents with critical temperature exceeding room temperature, (ii) the discovery
that clusters in high, but not necessarily the highest, spin states due to a large
magnetic anisotropy or zero field splitting have a significant relaxation barrier
that traps magnetic flux enabling a single molecule/ion (cluster) to act as a mag-
net at low temperature; (iii) the discovery of materials exhibiting large, negative
magnetization; (iv) spin-crossover materials that can show large hysteretic effects
above room temperature; (v) photomagnetic and (vi) electrochemical modulation
of the magnetic behavior; (vii) the Haldane conjecture and its experimental real-
ization; (viii) quantum tunneling of magnetization in high spin organic molecules;
(viii) giant and (ix) colossal magnetoresistance effects observed for 3-D network
solids; (x) the realization of nanosize materials, such as self organized metal-
based clusters, dots and wires; (xi) the development of metallic multilayers and
the spin electronics for the applications. This important contribution to magnetism
and more importantly to science in general will lead us into the next millen-
nium.
    Documentation of the status of research, ever since William Gilbert’s de Magnete
in 1600, provides the foundation for future discoveries to thrive. As this millen-
nium begins the time is appropriate to pool our growing knowledge and assess
many aspects of magnetism. This series entitled Magnetism: Molecules to Mate-
XII

rials provides a forum for comprehensive yet critical reviews on many aspects of
magnetism that are on the forefront of science today.

Joel S. Miller                                                     Marc Drillon
Salt Lake City                                               Strasbourg, France
List of Contributors




Joan Cano                                Maria Teresa Duarté
Laboratoire de Chimie Moléculaire        Centro de Química Estrutural
Universtité de Paris-Sud                 Instituto Superior Técnico
91405 Orsay                              Av. Rovisco Pais
France                                   1049-001 Lisboa
                                         Portugal
Eugenio Coronado
Instituto de Ciencia Molecular           Gregory S. Girolami
Universitat de Valencia                  Department of Chemistry
C/ Doctor Moliner 50                     University of Illinois
46100 Burjassot                          Urbana-Champaign 61801
Spain                                    USA
                                         Hiroyuki Imai
Vasco Pires Silva da Gama                Institute for Molecular Science
Instituto Technológico e Nuclear         Okazaki National Institutes
Estrada Nacional 10                      38 Nishigounaka
2686-953 Sacavém                         Myoudaiji
Portugal                                 Okazaki 444-8585
                                         Japan
Peter Day
Davy Faraday Research Laboratory         Katsuya Inoue
The Royal Institution of Great Britain   Institute for Molecular Science
21 Albemarle Street                      Okazaki National Institutes
London W1S 4BS                           38 Nishigounaka
United Kingdom                           Myoudaiji
                                         Okazaki 444-8585
Marc Drillon                             Japan
Institut de Physique et Chimie           Yves Journaux
des Matériaux de Strasbourg              Laboratoire de Chimie Inorganique,
UMR 7504 du CNRS                         URA 420
23 Rue du Loess                          Université de Paris-Sud
67037 Strasbourg                         CNRS, BAT 420
France                                   91405 Orsay
                                         France
XIV    List of Contributors

Myrtil L. Kahn                         Pierre Rabu
Institut de Chimie                     Institut de Physique et Chimie
de la Matière Condensée                des Matériaux de Strasbourg
de Boreaux – CNRS                      UMR 75040 du CNRS
Avenue Dr. Schweitzer                  23 rue du Loess
33608 Pessac                           67037 Strasbourg
France                                 France
Jamie L. Manson                        Jean Souletie
Department of Chemistry                Centre de Recherche sur les très
and Biochemistry                       basses températures, CNRS
Estern Washington University           25 Avenue des Martyrs
226 Science                            38042 Grenoble
526 5th St.                            France
Cheney, WA 99004
USA                                    Jean-Pascal Sutter
                                       Institut de Chimie
Daniel Maspoch                         de la Matière Condensée
Institut de Ciència de Materials       de Bordeaux – CNRS
de Barcelona (CSIC)                    Avenue Dr. Schweitzer
Campus Universitari de Bellaterra      33608 Pessac
08193 Cerdanyola                       France
Spain
                                       Jaume Veciana
Joel S. Miller                         Institut de Ciència de Materials
Department of Chemistry                de Barcelona (CSIC)
University of Utah                     Campus Universitari de Bellaterra
Salt Lake City, UT 84112-0850          08193 Cerdanyola
USA                                    Spain
Shin-ichi Ohkoshi                      Michel Verdaguer
Research Center for Advanced Science   Laboratoire de Chimie Inorganique
and Technology                         et Matériaux Moléculaires
The University of Tokyo                Unité associée au C.N.R.S. 7071
4-6-1 Komaba                           Université Pierre et Marie Curie
Meguro-ku                              4 place Jussieu
Tokyo 153-8904                         75252 Paris Cedex 05
Japan                                  France
Daniel Ruiz-Molina                     Gordon T. Yee
Institut de Ciència de Materials       Department of Chemistry
de Barcelona (CSIC)                    Virginia Polytechnic Institute
Campus Universitari de Bellaterra      and State University
08193 Cerdanyola                       Blacksburg, VA 24061
Spain                                  USA
1 Metallocenium Salts of Radical Anion
  Bis(Dichalcogenate) Metalates
     Vasco Pires Silva da Gama and Maria Teresa Duarté




1.1 Introduction

For the last 30 years metal-bis(1,2-dichalcogenate) anionic complexes have been
extensively used as building blocks for the preparation of both conducting and
magnetic molecular materials. Several of these materials show remarkable features
and have made a significant contribution to the development of molecular materials
science.
    It is worth mentioning some examples of the molecular materials based on metal-
bis(1,2-dichalcogenate) anionic complexes based that have made a significant con-
tribution to the field of molecular material science, in the last decades. A large
number of molecular conductors and even superconductors based on metal-bis(1,2-
dichalcogenate) anionic acceptors have been obtained [1] and Me4 N[Ni(dmit)2 ]2
(dmit = 1,3-dithiol-2-thione-4,5-dithiolate) was the first example of a π acceptor
superconductor with a closed-shell donor [2]. The spin-Peierls transition was ob-
served for the first time in the linear spin chain system TTF[Cu(tdt)2 ] [3] (TTF
= tetrathiafulvalene; tdt = 1,2-ditrifluoromethyl-1,2-ethylenedithioate). The co-
existence of linear spin chains and conducting electrons, was observed for the first
time in the compounds Per2 [M(mnt)2 ] (M = Ni, Pd, Pt) [4] (mnt = 1,2-dicyano-
1,2-ethylene-dithiolato), presenting competing spin-Peierls and Peierls instabili-
ties of the spin chains and 1D conducting electronic systems. A purely organic
system with a spin-ladder configuration was observed for the first time in the
compound DT-TTF2 [Au(mnt)2 ] [5] (DT-TTF = dithiophentetrathiafulvalene). A
spin transition was observed in the compound [Fe(mnt)2 rad] [6], where rad =
2-(p-N-methylpyridinium)4,4,5,5-tetramethylimidazoline-1-oxyl. Ferromagnetic
ordering was reported for NH4 [Ni(mnt)2 ]H2 O [7].
    The discovery of the first molecule-based material exhibiting ferromagnetic or-
dering, the electron-transfer (ET) salt [Fe(Cp*)2 ]TCNE (TCNE = tetracyanoethy-
lene), with TC = 4.8 K, in 1986 [8, 9], was a landmark in molecular magnetism and
gave a significant impulse to this field. Since then among the strategies followed to
obtain cooperative magnetic properties, considerable attention has been given to the
linear-chain electron-transfer salts based on metallocenium donors and on planar
acceptors. [10, 11]. Besides [Fe(Cp*)2 ]TCNE, bulk ferromagnetism was reported
2       1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates

for other ET salts based on decamethylmetallocenes and on the conjugated polyni-
triles TCNE [12] and TCNQ [13] (TCNQ = 7,7,8,8-tetracyano-p-quinodimethane).
An extensive study of these salts was made, covering a variety of aspects including
the structure-magnetic property relationship [10], and the effects of spin variation
and of spinless defects [10]. Furthermore they provided a valuable basis to test the
various models that were proposed in order to explain the magnetic coupling and
magnetic ordering in the molecule-based magnets [14, 15].




Fig. 1.1. Molecular structure of [Fe(Cp*)2 ][Ni(edt)2 ], showing the basic donor and acceptor
molecules studied in this review.




   Following the report of ferromagnetism for [Fe(Cp*)2 ]TCNE, metal bis-
dichalcogenate planar acceptors were also considered as suitable candidates for
use in the preparation of ET salts with the radical metallocenium donors, and in
the search for new molecular magnets the first metal bis-dichalcogenate based
compounds were reported in 1989 [16, 17]. In particular the monoanionic forms
of the metal bis-dichalcogenate (Ni, Pd, Pt) complexes seem particularly promis-
ing for ‘‘the synthesis of mixed-stack molecular charge-transfer salts that dis-
play cooperative magnetic phenomena due to (1) their planar structures, (2) de-
localized electronic states, S = 1/2 spin state for the monomeric species, and
(3) the possibility of extended magnetic interactions mediated by the chalcogen
atoms’’ [17].
   The work with ET salts based on metallocenium donors and on planar metal bis-
dichalcogenate radical anions is summarized in this chapter. Most of the materials
studied to date are decamethylmetallocenium based ET salts, other compounds
based on different metallocenium derivatives have also been reported and will be
                                                                   1.1 Introduction        3

              S       S
                  M                  [M(edt)2]
              S       S


    F3C    X          X   CF3
                                    [M(tdt)2] (X = S)
                  M
                                    [M(tds)2] (X = Se)
           X          X   CF3
    F3C


N                          N
          S       S
              M                       [M(mnt)2]
          S       S
N                          N


          X       X                 [M(bdt)2] (X = S)
              M
                                    [M(bds)2] (X = Se)
          X       X



      S       S       S    S
                                    [M(dmit)2] (X = S)
X                 M             X
                                    [M(dmio)2] (X = O)
      S       S       S    S



     S        S       S
                  M                 [M( -tpdt)2]
              S       S   S

Scheme 1.1 Schematic representation of the metal bis-dichalcogenate acceptors studied in this
chapter.


referred to. The metal bis-dichalcogenate complexes mentioned in this chapter are
represented in Scheme 1.1.
   As magnetic ordering is a bulk property, particular attention will be given to the
supramolecular arrangements which determine the magnetic behavior. The crystal
structure of the compounds will be correlated with the magnetic behavior of these
ET salts. The magnetic coupling in the ET salts based on decamethylmetallocenium
donors has been analyzed mainly through McConnell I [18] or McConnell II [19]
mechanisms, and this issue is still a subject of controversy [15, 20]. Of these models,
McConnell I has been most often used in the interpretation of the magnetic behavior
of these salts, as, in spite of its simplicity, it has shown good agreement with
the experimental observations. In this chapter the interpretation of the magnetic
coupling will be analyzed in the perspective of this model. However, it should be
mentioned that the validity of the McConnell I mechanism has been questioned
both theoretically [21] and experimentally [22].
4       1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates

1.2 Basic Structural Motifs

1.2.1    ET Salts Based on Decamethylmetallocenium Donors

In most of the ET salts based on decamethylmetallocenium donors, due to the pla-
nar configurations of both the C5 Me5 ligands and of the metal bis-dichalcogenate
acceptors the crystal structures are, with a few exceptions, based on linear chain
arrangements of alternating donor and acceptor molecules. In these salts four dis-
tinct types of linear chain arrangements have been observed and are represented
schematically in Figure 1.2. The type I chain arrangement corresponds to the most
simple case of an alternated linear chain motif ··A− D+ A− D+ A− D+ ··, similar to
that observed in several salts based on metallocenium donors and on acceptors such
as TCNE and TCNQ [10]. In the case of the type II chain, the donors alternate with
face-to-face pairs of acceptors, ··A− A− D+ A− A− D+ ··, as in this arrangement there
is a net charge (−) per repeat unit, A− A− D+ , charge compensation is required.
For the type III arrangement the linear chains consist of alternated face-to-face
pairs of acceptors with side-by-side pairs of donors, ··A− A− D+ D+ A− A− D+ D+ ··.
Finally in the type IV arrangement, the acceptors alternate with side-by-side pairs
of donors, ··A− D+ D+ A− D+ D+ ··, in this case there is a net charge (+) per repeat
unit, D+ D+ A− , which must be compensated. For most of the ET salts based on
types I and III arrangements (neutral chains), only one type of chain arrangement
was observed. However, in the case of compounds based on types II and IV ar-
rangements (charged chains), more complex crystal structures could be observed,
resulting from the required charge neutralization. Table 1.1 summarizes the unit
cell parameters, space group symmetry, and the type of observed linear chain ar-




Fig. 1.2. Representation of the basic types of mixed chain sequences observed in the ET salts
based on metallocene donors and on metal bis-dichalcogenate acceptors.
                                                                             1.2 Basic Structural Motifs                     5

Table 1.1. Unit cell parameters and chain type for the mixed chain salts.

Compound                       Chain Space          a, Å     b, Å     c, Å      α, ◦     β, ◦     γ , ◦ Vol., Z     T,     Ref.
                               Type Group                                                                Å3         ◦C

[Fe(Cp*)2 ][Ni(edt)2 ]               I   C2/m     13.319   13.699    8.719     90.00   125.06    90.00   1302   2     20   23
[Cr(Cp*)2 ][Ni(edt)2 ]               I   C2/m      13.44    13.66     8.96      90.0    124.2     90.0   1320   2     20   23
[Fe(Cp*)2 ][Ni(tdt)2 ]               I   C2/c     14.417   12.659   18.454     90.00    95.17    90.00   3354   4    -70   16
[Mn(Cp*)2 ][Ni(tdt)2 ]               I   C2/c     14.302   12.697   18.415     90.00    94.63    90.00   3333   4    (a)   24
[Fe(Cp*)2 ][Pt(tdt)2 ]               I    P1       8.490   10.278   10.936    106.79   103.95   101.98    846   1    -70   25
[Fe(Cp*)2 ][Ni(tds)2 ]               I    P1       8.581   10.464   11.132    107.96   103.65   101.82    881   1     20   26
[Mn(Cp*)2 ][Ni(tds)2 ]               I    P1       8.582   10.472   11.158    108.41   103.57   101.79    882   1     20   27
[Cr(Cp*)2 ][Ni(tds)2 ]               I    P1       8.580   10.547   11.138    109.49   103.20   101.76    881   1     20   28
[Fe(Cp*)2 ][Pt(tds)2 ]               I    P1       8.606   10.521   11.138    108.81   102.89   101.30    891   1     20   26
[Mn(Cp*)2 ][Pt(tds)2 ]               I    P1       8.618   10.560   11.239    109.49   102.78   101.30    899   1     20   28
[Cr(Cp*)2 ][Pt(tds)2 ]               I   C2/c     11.352   21.848   14.969     90.00   103.73    90.00   3607   4     20   28
α -[Fe(Cp*)2 ][Pt(mnt)2 ]           II   C2/m     16.802   21.095   12.942     90.00    94.52    90.00   4473   6     20   16
β -[Fe(Cp*)2 ][Pt(mnt)2 ]            I    P1      12.106   14.152   14.394    108.94    96.37    90.51   2312   3     23   16
[Fe(Cp*)2 ]2 [Cu(mnt)2 ]           IV     P1       9.713   11.407   11.958    100.90   113.20    92.66   1185   1     25   29
[Fe(Cp*)2 ][Ni(dmit)2 ]            III    P1      11.347   14.958   10.020     97.68    94.36   109.52   1575   2   -120   17
[Mn(Cp*)2 ][Ni(dmit)2 ]            III    P1      11.415   14.940   10.020     97.40    94.58   109.63   1582   2    (a)   30
α -[Fe(Cp*)2 ][Pd(dmit)2 ]         III    P1       9.907   12.104   14.464     82.44    85.80    82.73   1703   2     20   31
[Fe(Cp*)2 ][Pt(dmit)2 ]            III    P1       9.996   11.554   15.108    109.72    97.62    93.78   1616   2     20   31
[Fe(Cp*)2 ][Ni(dmio)2 ]MeCN        IV    C2/m     16.374    10.84   19.530     90.00    88.02    90.00   3431   4    (a)   32
[Fe(Cp*)2 ][Pd(dmio)2 ]            III    P1      14.133   14.620   16.055     88.43    80.25    86.38   3260   4     20   31
[Fe(Cp*)2 ][Pt(dmio)2 ]            III    P1      14.133   14.620   16.055     88.43    80.25    86.38   3260   4     20   31
[Fe(Cp*)2 ][Ni(dsit)2 ]            III    P1       9.650   11.439   16.643     71.14    73.24    89.72   1657   2     20   31
[Fe(Cp*)2 ][Ni(bdt)2 ]             IV     P1       9.731   19.044   35.677    105.22    94.91    97.99   6266   8     20   33
[Mn(Cp*)2 ][Ni(bdt)2 ]             IV     P1       9.760   19.101   35.606    105.02    94.72    98.15   6293   8     20   33
[Cr(Cp*)2 ][Ni(bdt)2 ]             IV     P1       9.782   17.885   19.163     74.84    81.58    82.91   3189   4     20   33
[Mn(Cp*)2 ][Co(bdt)2 ]             IV     P1       9.738   19.119   35.698    105.27    94.36    98.34   6298   8     20   33
[Cr(Cp*)2 ][Co(bdt)2 ]             IV     P1       9.772   17.896   19.198     75.12    81.45    82.09   3191   4     20   33
[Fe(Cp*)2 ][Pt(bdt)2 ]             IV     P1       7.763   19.126   35.564    104.50    95.26    97.87   6314   8     20   33
[Cr(Cp*)2 ][Pt(bdt)2 ]             IV     P1       9.787   19.241   35.587    103.98    94.69    98.31   6387   8     20   33
[Fe(Cp*)2 ][Ni(bds)2 ]MeCN         IV     P1      11.720   16.282    9.606    100.66   106.03    81.75   1723   2   -120   17
[Fe(Cp*)2 ][Ni(α -tpdt)2 ]           I   P21 /c   20.360   10.237   15.443     90.00   107.54    90.00   3069   4     20   34
[Cr(Cp*)2 ][Ni(α -tpdt)2 ]           I   P21 /c   10.053   10.281   15.577     90.00   104.89    90.00   1556   2     20   35
[Fe(C5 Me4 SCMe3 )2 ][Ni(mnt)2 ]     I    P1       9.619    9.622   11.253     79.72    78.66    76.62    984   1     22   36
[Fe(C5 Me4 SCMe3 )2 ][Pt(mnt)2 ]     I    P1       9.591    9.681   11.252     78.17    78.47    77.38    984   1     22   36

(a) Not given.

rangements for mixed chain ET salts based on metallocenium donors and metal
bis-dichalcogenate acceptors.
   While in the case of the cyano radical based salts, most of the observed structures
present a type I structural arrangement, in the case of the ET salts based on metal
bis-dichalcogenate acceptors a much larger variety of arrangements was observed,
as described above. The structural motifs in the [M(Cp*)2 ][M (L)2 ] ET salts are
primarily determined by factors such as the dimensions of the anionic metal bis-
dichalcogenate complexes, the tendency of the acceptors to associate as dimers, the
extent of the π system in the acceptor molecule, and the charge density distribution
on the ligands.
   In the case of the [M(edt)2 ]− based salts, with the smaller acceptor, the size
of the acceptor is similar to the size of the C5 Me5 ligand of the donor and only
type I structural motifs (DADA chains) were observed. For the intermediate size
6          1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates

anionic complexes, [M(tdx)2 ]− , [M(mnt)2 ] and [Ni(α-tpdt)2 ]− , the most common
structural motif obtained in ET salts based on those acceptors is also of type I. For
the larger anionic complexes, [M(bdx)2 ]− and [M(dmix)2 ]− , types III and IV chain
arrangements were observed, in both cases acceptor molecules (type IV) or face-
to-face pairs of acceptors (type III) alternate with side-by-side pairs of donors. The
complexes [M(mnt)2 ]− and [M(dmix)2 ]− , (M = Ni, Pd and Pt), frequently undergo
dimerization in the solid state [37], and they are the only acceptors where the chain
arrangements have face-to-face pairs of acceptors (structural motifs II and III). The
variety of structural arrangements observed in the [M(mnt)2 ]− based compounds
can be related to both the large extent of the π system and the high charge density
on the terminal nitrile groups [38], as well as to the tendency of these complexes
to form dimers.


1.2.2      ET Salts Based on Other Metallocenium Donors

Besides the decamethylmetallocenium based salts, in the compounds based on other
metallocenium derivatives, mixed linear chain arrangements were only observed in
the case of the salts [Fe(C5 Me4 SCMe3 )2 ][M(mnt)2 ], M = Ni and Pt, which present
type I structural motifs.
   Some ET salts based on other metallocenium derivatives and on the acceptors
[M(mnt)2 ]− and [M(dmit)2 ]− (M = Ni and Pt) have also been reported. In the case
of these compounds, the crystal structure consists of segregated stacks of donors,
··D+ D+ D+ D+ ··, and acceptors, ··A− A− A− A− ··, which is a common situation in
molecular materials, in particular in the case of molecular conductors. In spite of the
fact that for most salts the dominant magnetic interactions between the metal bis-
dichalcogenate units are antiferromagnetic, there are cases where the interactions
are known to be ferromagnetic, as in the case of the compounds n-Bu4 N[Ni(α-
tpdt)2 ] [34] and NH4 [Ni(mnt)2 ](H2 O, which was the first metal bis-dichalcogenate
based material to present ferromagnetic ordering, with TC = 4.5 K [7]. The unit
cell parameters of the ferrocenium derivative salts with crystal structures based on
segregated acceptor stacks are shown in Table 1.2.

Table 1.2. Unit cell parameters for the segregated stack salts.

Compound                             Space      a, Å     b, Å   c, Å   α, ◦   β, ◦   γ , ◦ Vol., Z T , Ref.
                                     Group                                                  Å3     ◦C


[Fe(Cp)2 ]2 [Ni(mnt)2 ]2 [Fe(Cp)2 ]   P1      12.030   13.652 15.462 87.91 77.62 72.56    2365   2   (a)   39
[Fe(C5 Me4 SMe)2 ][Ni(mnt)2 ]         P1       8.649   14.080 15.358 65.27 77.77 80.78    1654   2   22    36
[Fe(C5 H4 R)2 ][Ni(mnt)2 ] (b)       P21 /n    7.572   28.647 16.374 90.00 93.10 90.00    3547   4   22    40
[Fe(Cp)(C5 H4 CH2 NMe3 )][Ni(mnt)2 ] P21 /n   12.116   30.094 7.139 90.00 103.97 90.00    2531   4   20    41
[Fe(Cp)(C5 H4 CH2 NMe3 )][Pt(mnt)2 ] P21 /n   12.119   30.112 7.244 90.00 103.97 90.00    2565   4   20    41
[Co(Cp)2 ][Ni(dmit)2 ]                P1      19.347   25.289 9.698 100.60 96.02 76.01    4517   8   20    42
[Co(Cp)2 ][Ni(dmit)2 ]3 2MeCN         P1       8.913   21.370 7.413 99.19 91.06 101.40    1363   1   (a)   43

(a) Not given. (b) [Fe(C5 R)2 ]+ = 1,1 -bis[2-(4-(methylthio)-(E)-ethenyl]ferrocenium.
                               1.3 Solid-state Structures and Magnetic Behavior     7

1.3 Solid-state Structures and Magnetic Behavior

After listing the general characteristics of the crystal structures of ET salts based
on metallocenium donors and metal bis-dichalcogenate acceptors, we will dis-
cuss them based on the systematization proposed in Section 1.2 and correlate the
supramolecular crystal motifs with the magnetic properties.


1.3.1     Type I Mixed Chain Salts

The magnetic behavior of the salts based on type I chains shows a considerable
similarity, namely, in most cases, the dominant magnetic interactions are FM and
several of these salts exhibit metamagnetic behavior. Table 1.3 summarizes the key
magnetic properties of type I compounds.


1.3.1.1    [M(Cp*)2 ][Ni(edt)2 ]
The compounds [M(Cp*)2 ][Ni(edt)2 ], with M = Fe and Cr, are isostructural and
the crystal structure [23] consists of a parallel arrangement of 1D alternated type
I chains, ··A− D+ A− D+ A− D+ ··. In Figure 1.3(a) a view along the chain direction
([101]) is presented for [Fe(Cp*)2 ][Ni(edt)2 ]. The chains are regular and the Ni
atoms sit above the Cp fragments from the donors, intrachain DA contacts, d
(d = interatomic separation), shorter than the sum of the van der Waals radii (dW ),
QW = d/dW < 1, were observed. These contacts involve a Ni atom from the
acceptor and one of the C atoms from the C5 ring, with a Ni–C distance of 3.678 Å
(QW = 0.99). For this compound the shortest interchain interionic separation was
found in the in-registry pair II–IV, with AA C–C contacts of 3.507 Å (QW = 1.11),
as shown in Figure 1.3(b). The out-of-registry pairs I–II, II–III and I–IV present
a similar interchain arrangement, with DA C–S contacts (C from Me from the
donor and an S from the acceptor) of 3.812 Å (QW = 1.11), the II–III pairwise
arrangement is shown in Figure 1.3(c).
   At high temperatures, in the case of the [M(Cp*)2 ][Ni(edt)2 ] compounds, AFM
interactions apparently dominate the magnetic behavior of the compounds, as seen
by the negative θ value obtained from the Curie–Weiss fits, −5 and −6.7 for
M = Fe and Cr respectively. A considerable field dependence of the obtained
θ value for polycrystalline samples (free powder) was observed in the case of
[Fe(Cp*)2 ][Ni(edt)2 ], suggesting the existence of a strong anisotropy in the mag-
netic coupling for this compound [23]. This was confirmed by the metamagnetic
behavior observed at low temperatures, with TN = 4.2 K and HC = 14 kG at 2 K.
   A typical metamagnetic behavior was observed in single crystal magnetization
measurements at 2 K [23], shown in Figure 1.4. With the applied magnetic field
parallel to the chains a field induced transition from an AFM state to a high field FM
8        1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates

Table 1.3. Magnetic characterization of type I ET salts.

Compound                            SD ; SA     θ, K       Comments                  Ref.
[Fe(Cp*)2 ][Ni(edt)2 ]              1/2; 1/2     −5        MM (a); TN = 4.2 K;       23
                                                           HC = 14 kG (2 K)
[Cr(Cp*)2 ][Ni(edt)2 ]              3/2; 1/2    −6.7       (b)                       23
[Fe(Cp*)2 ][Ni(tdt)2 ]              1/2; 1/2     15        (b)                       16
[Mn(Cp*)2 ][Ni(tdt)2 ]               1; 1/2      2.6       MM (a); TN = 2.4 K        24
[Mn(Cp*)2 ][Pd(tdt)2 ]               1; 1/2      3.7       MM (a); TN = 2.8 K;       24
                                                           HC = 0.8 kG (1.85 K)
[Fe(Cp*)2 ][Pt(tdt)2 ]              1/2; 1/2     27        (b)                       10
[Mn(Cp*)2 ][Pt(tdt)2 ]               1; 1/2     1.9        MM (a) TN = 2.3 K;        24
[Fe(Cp*)2 ][Ni(tds)2 ]              1/2; 1/2    8.9        (b)                       26, 44
[Mn(Cp*)2 ][Ni(tds)2 ]               1; 1/2     12.8       MM (a); TN = 2.1 K;       28, 44
                                                           HC = 0.28 kG (1.6 K)
[Cr(Cp*)2 ][Ni(tds)2 ]              3/2; 1/2     4.0       (b)                       28
[Fe(Cp*)2 ][Pt(tds)2 ]              1/2; 1/2     9.3       MM (a); TN = 3.3 K;       26
                                                           HC = 3.95 kG (1.7 K)
[Mn(Cp*)2 ][Pt(tds)2 ]               1; 1/2     16.6       MM (a); TN = 5.7 K;       28
                                                           HC = 4.05 kG (1.7 K)
[Cr(Cp*)2 ][Pt(tds)2 ]              3/2; 1/2     9.8       MM (c); TN = 5.2 K;       28
                                                           HC1 = 5 kG,
                                                           HC2 = 16 kG, (1.7 K)
[Fe(Cp*)2 ][Ni(α-tpdt)2 ]           1/2; 1/2   −5.1 (d)    Tm ≈ 130 K (e);           34
                                                           MM (a); TN = 2.6 K;
                                                           HC = 0.6 kG (1.6 K)
[Mn(Cp*)2 ][Ni(α-tpdt)2 ] (f)        1; 1/2      7.3       FM (g); TC = 2.2 K        35
[Cr(Cp*)2 ][Ni(α-tpdt)2 ]           3/2; 1/2     6.1       (b)                       35
[Fe(C5 Me4 SCMe3 )2 ][Ni(mnt)2 ]    1/2; 1/2      3        (b)                       36
[Fe(C5 Me4 SCMe3 )2 ][Pt(mnt)2 ]    1/2; 1/2      3        (b)                       36
β-[Fe(Cp*)2 ][Pt(mnt)2 ]            1/2; 1/2     9.8       (b)                       16
(a) Metamagnetic transition. (b) No magnetic ordering observed down to 1.8 K. (c) Two field
induced transitions were observed at low temperatures. (d) Non-Curie-Weiss behavior the
given θ value relates to the high temperature region (T > Tm ). (e) Minimum inχT vs. T . (f)
Crystal structure not yet determined. (g) Ferromagnetic transition.

state occurs at a critical field of 14 kG. While for measurements with the applied
field perpendicular to the chains, no transition was observed and a linear field
dependence was observed for the magnetization, as expected for an AFM.
   The magnetic behavior of [Fe(Cp*)2 ][Ni(edt)2 ] is consistent with the coexis-
tence of FM intrachain interactions, due to DA intrachain short contacts, with
AFM interchain interactions, resulting from the AD and AA interchain contacts.
The nature of the intra and interchain magnetic interaction is in good agreement
with the predictions of the McConnell I mechanism [26]. In this case the interchain
interactions must be particularly large as they seem to be the dominant interactions
Fig. 1.3. (a) Perspective view of the crystal structure of [Fe(Cp*)2 ][Ni(edt)2 ] along the chain direction. (b) Interchain arrangement of the pair II–I
V, d1 corresponds to the DA closest intrachain contact (3.678 Å, QW = 0.99) and d2 to the closest interchain contact (3.507 Å, QW = 1.11). (c)
Interchain arrangement of the pair II–III, d3 is the closest interchain contact (3.812 Å, QW = 1.11). Hydrogen atoms were omitted for clarity.
                                                                                                                                                           1.3 Solid-state Structures and Magnetic Behavior
                                                                                                                                                           9
10                       1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates

                   2.0
B)


                   1.5
Magnetization (N




                   1.0
                                                                 Fig. 1.4. Magnetization field depen-
                                                                 dence at 2 K, for a single crystal of
                   0.5                                           [Fe(Cp*)2 ][Ni(edt)2 ], the closed sym-
                                                                 bols refer to measurements with applied
                                                                 field parallel to the DADA chains and
                   0.0                                           the open symbols to the measurements
                         0     10    20   30   40    50    60    with the applied field perpendicular to
                                      Field (kG)                 the chains.


at high temperatures, and they also lead to a quite high value for the critical field
in the metamagnetic transition.



1.3.1.2                      [M(Cp*)2 ][M (tdx)2 ]
The [Fe(Cp*)2 ][Ni(tdt)2 ] and [Mn(Cp*)2 ][M (tdt)2 ] with M = Ni, Pd and Pt are
isostructural, and, as in the case of the [M(Cp*)2 ][Ni(edt)2 ] salts, a crystal structure
based on an arrangement of parallel alternating DA linear chains [16] is observed,
but with differences in the intra and interchain arrangements. A view normal to
the chains of [Fe(Cp*)2 ][Ni(tdt)2 ] is shown in Figure 1.5(a). In these compounds
the chains have a zigzag arrangement and the Cp sits above one of the NiS2 C2
fragments of the acceptor, as shown for [Fe(Cp*)2 ][Ni(tdt)2 ] in Figure 1.5(b). In this
compound, no intrachain DA short contacts were found and the closest interatomic
separation between the acceptor and the Cp ring corresponds to Ni–C contacts of
4.120 Å (QW = 1.11). In this salt the most relevant interchain contacts concern the
out-of registry pairs I–II and I–IV, these arrangements are similar and the first one
is shown in Figure 1.5(b). These pairs show interchain DA C–S contacts, involving
C atoms of the Me groups of the donors and S atoms of the acceptors, with a
separation of 3.728 Å (QW = 1.08).
    The magnetic behavior of the compounds [Fe(Cp*)2 ][Ni(tdt)2 ] and
[Mn(Cp*)2 ][M (tdt)2 ], with M = Ni, Pd and Pt, is dominated by the intrachain
DA FM interactions, as seen by the positive θ values obtained from the Curie-
Weiss fits (Table 1.3). At low temperatures the [Mn(Cp*)2 ][M (tdt)2 ] salts exhibit
metamagnetic transitions, with TN = 2.4, 2.8 and 2.3 K for M = Ni, Pd and Pt
respectively, HC = 600 G for M = Pd [24]. This behavior is attributed to the
coexistence of FM intrachain interactions with interchain AFM interactions.
                                    1.3 Solid-state Structures and Magnetic Behavior            11




Fig. 1.5. (a) View of the crystal structure of [Fe(Cp*)2 ][Ni(tdt)2 ] along the chain direction (Me
groups were omitted for clarity). (b) Interchain arrangement of the pair I–II, d1 corresponds
to the DA closest intrachain contact (4.120 Å, QW = 1.11) and d2 to the closest interchain
contact (3.728 Å, QW = 1.08). Hydrogen atoms were omitted for clarity.


   The compounds [Fe(Cp*)2 ][Pt(tdt)2 ], [M(Cp*)2 ][Ni(tds)2 ], with M = Fe, Mn
and Cr, [25–28] and [M(Cp*)2 ][Pt(tds)2 ], with M = Fe and Mn, [26, 28] are
isostructural and the crystal structure consists of a parallel arrangement of alternated
type I chains. The intrachain arrangement is similar to that of [Fe(Cp*)2 ][Ni(edt)2 ],
with the Cp sitting above the Ni or Pt atoms from the acceptor, but distinct interchain
arrangements were observed in these compounds. A view normal to the chains is
shown in Figure 1.6(a) for [Fe(Cp*)2 ][Pt(tds)2 ]. Short intrachain DA contacts were
observed in most of these salts, involving M (Ni or Pt) and carbons from the Cp
rings from the donors, for the Pt–C contact in [Fe(Cp*)2 ][Pt(tds)2 ] the interatomic
separation is 3.826 Å (QW = 0.98). For this series of compounds the shortest in-
terchain interionic separation was found in the in-registry pair I–II, shown in Fig-
ure 1.6(b), and it corresponds to an AA Se–Se contact, with a distance of 4.348 Å
(QW = 1.09). In the other interchain arrangements the interchain contacts are con-
siderably larger and the closest separations occur for the I–IV pair (Figure 1.6(c))
involving two C atoms from the donor Me groups, with a separation of 4.263 Å
(QW = 1.33) in the case of [Fe(Cp*)2 ][Pt(tds)2 ]. However [Cr(Cp*)2 ][Pt(tds)2 ] is
not isostructural with these compounds, the intra and interchain arrangements are
similar to those described above for [Fe(Cp*)2 ][Pt(tds)2 ] [28].
   The magnetic behavior of the compounds [Fe(Cp*)2 ][Pt(tdt)2 ],
[M(Cp*)2 ][Ni(tds)2 ] and [M(Cp*)2 ][Pt(tds)2 ] (M = Fe, Mn and Cr) is clearly
dominated by the strong intrachain DA FM coupling, as can be seen by the high
positive θ values (Table 1.3). The coexistence of an intrachain AFM interaction
is responsible for the metamagnetic transitions, which are observed in several
of those compounds, with TN = 2.1, 3.3, 5.7 K and HC = 0.28, 3.95, 4.05 kG
                                                                                                                                                      12




Fig. 1.6. (a) Perspective view of the crystal structure of [Fe(Cp*)2 ][Pt(tds)2 ] along the chain direction. (b) Interchain arrangement of the pair
I–II, d1 corresponds to the DA closest intrachain contact (3.826 Å, QW = 0.98) and d2 to the closest interchain contact (4.348 Å, QW = 1.09).
(c) Interchain arrangement of the pair I–IV, d3 is the closest interchain contact (4.263 Å, QW = 1.33). Hydrogen atoms were omitted for clarity.
                                                                                                                                                      1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates
                                                   1.3 Solid-state Structures and Magnetic Behavior   13



                           1.7K
B)
                                  2.6K
                                      3.2K
Magnetization (N



                                              2x105
                   2                                    8kG




                                      (emuG/mol)
                                          Mag
                                                       4kG


                                                    2kG
                                                   1kG
                                                   0     Temp (K)   10

                   0
                       0          5                      10          15
                                  Field (kG)
Fig. 1.7. Magnetization field dependence for [Fe(Cp*)2 ][Pt(tds)2 ], at 1.7, 2.6 and 3.2 K. The
inset shows the magnetization temperature dependence at 1, 2, 4 and 8 kG.


for [Mn(Cp*)2 ][Ni(tds)2 ], [M(Cp*)2 ][Pt(tds)2 ] (M = Fe, Pt) respectively. The
magnetization field dependence at 1.7, 2.6 and 3.2 K for [Fe(Cp*)2 ][Pt(tds)2 ] is
shown in Figure 1.7, a sigmoidal behavior typical of metamagnetic behavior is
observed for T < TN = 3.3 K [26]. For low applied magnetic fields (H < HC ),
a maximum in the magnetization temperature dependence can be observed,
corresponding to an AFM transition, which is suppressed with fields H > HC ,
as shown in the inset of Figure 1.7. The critical field temperature dependence
obtained from the isothermal (closed symbols) and isofield (open symbols)
measurements is shown in Figure 1.8.
   In the compounds [Fe(Cp*)2 ][Pt(tdt)2 ], [M(Cp*)2 ][Ni(tds)2 ] and
[M(Cp*)2 ][Pt(tds)2 ] (M = Fe, Mn and Cr) the Se–Se (or S–S) contacts, are
expected to give rise to strong AFM interchain interactions, as the contacts
are relatively short and there is a significant spin density on those atoms. The
intrachain DA contacts (along c) and the interchain AA (Se–Se or S–S) contacts
(along a) are expected to give rise to quasi-2D magnetic systems (ac plane), as
the other interchain contacts are expected to give rise to much weaker magnetic
interactions. The situation is quite distinct from that observed in the compounds
[M(Cp*)2 ][Ni(edt)2 ], [Fe(Cp*)2 ][Ni(tdt)2 ] and [Mn(Cp*)2 ][M (tdt)2 ], where the
interchain magnetic interactions are expected to be considerably more isotropic,
and for these compounds the magnetic systems can be described as quasi-1D. The
distinct dimensionality of the magnetic systems is reflected in the fast saturation
observed in the isothermals, just above HC , in the case of the salts with the
quasi-2D magnetic systems, unlike the compounds presenting quasi-1D magnetic
14            1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates

          6



                                        PM
          4
HC (kG)




          2
                   AFM
                                                     Fig. 1.8. Critical field dependence for
                                                     [Fe(Cp*)2 ][Pt(tds)2 ], where the closed
          0                                          and open symbols correspond to the data
              1          2          3           4    obtained with isothermal and isofield
                     Temperature (K)                 measurements respectively.


systems, where saturation occurs only at very high magnetic fields, when the
temperature is not much lower than TN [26].
    In the case of [Cr(Cp*)2 ][Pt(tds)2 ] metamagnetic behavior was also observed
(TN = 5.2 K), but a rather complicated phase diagram was obtained. Below TN ,
two field induced transitions were observed to occur, and at 1.7 K the critical fields
were 5 and 16 kG, respectively [28]. This is the first example of a metamagnetic
transition on a [Cr(Cp*)2 ] based ET salt and the low temperature phase diagram is
still under study [28].
    The analysis of the crystal structures, the magnetic behavior and atomic spin
density calculations of several ET salts based on decamethylferrocenium and on
metal-bis(dichalcogenate) acceptors with structures consisting of arrangements of
parallel alternating DA linear chains, allowed a systematic study of the intra and
interchain magnetic interactions [26]. In the case of these compounds a spin polar-
ization is observed in the metallocenium donors but not in the acceptors described
so far. The analysis of the intrachain contacts in the perspective of the McConnell I
mechanism suggests the existence of intrachain FM coupling, through the contacts
involving the metal or chalcogen atoms (positive spin density) from the acceptors
and the C atoms (negative spin density) from the Cp ring of the donors, which
shows good agreement with the experimental observations. A variety of interionic
interchain contacts were observed in these ET salts, AA (Se–Se, S–S and C–C),
DD (Me–Me) and DA (Me–S), and all these contacts were observed to lead to AFM
interchain coupling. A strict application of the McConnell I model was not pos-
sible in the case of the interchain contacts, as the shortest contacts would involve
mediation through H or F atoms, which are expected to present a very small spin
density [26]. However the results regarding the nature of the interchain magnetic
coupling would be compatible with that model if the contacts involving H or F
atoms were neglected, as all the atoms involved in these contacts present a posi-
                               1.3 Solid-state Structures and Magnetic Behavior     15

tive spin density. This study revealed that metamagnetism, which was observed in
several compounds presenting a crystal structure consisting of a parallel arrange-
ment of alternated 1D chains, is expected to occur in other compounds presenting
a similar solid state structure, in the case of the metal bis-dichalcogenate acceptors
no spin polarization effect is found.


1.3.1.3   [Fe(C5 Me4 SCMe3 )2 ][M(mnt)2 ], M = Ni, Pt
The compounds [Fe(C5 Me4 SCMe3 )2 ][M(mnt)2 ] (M = Ni, Pt) are the only cases
of salts based on metallocenium derivatives and [M(mnt)2 ]− complexes where the
crystal structure is based on a 1D alternated type I structural motif [36]. As in the
other salts described above, the crystal structure consists also of a parallel arrange-
ment of the chains. For [Fe(C5 Me4 SCMe3 )2 ][Pt(mnt)2 ] a view along the chains is
shown in Figure 1.9(a). In the chains the [Pt(mnt)2 ]− units are considerably tilted
in relation to the chain direction, as shown in Figure 1.9(b), and short interatomic
DA intrachain distances were observed, involving one C from the Cp and a S atom
from the acceptor, with a C–S distance of 3.501 Å (QW = 1.01). Relatively short
interchain interionic distances were observed in the out-of-registry pair I–IV (and
the similar II–III) and in the in-registry pair II–IV. For the I–IV pair arrangement,
shown in Figure 1.9(b), the shortest contact involves one S from the acceptor and a
C atom from a Me group of the donor, with a S–C distance of 3.787 Å (QW = 1.10).
While for the II–IV out-of-registry pair, shown in Figure 1.9(c), the shortest contact
concerns one N atom from the acceptor and a C from one of the donors Me groups,
with a N–C separation of 3.372 Å (QW = 1.09).
    The magnetic behavior of [Fe(C5 Me4 SCMe3 )2 ][M(mnt)2 ] (M = Ni, Pt) is dom-
inated by FM interactions (θ = 3 K, M = Ni and Pt), which can be attributed to the
DA intrachain interactions. The intrachain interactions are expected to be AFM. As
in the previous compounds exhibiting this type of structure metamagnetic behavior
is also expected to occur at low temperatures.


1.3.1.4   β-[Fe(Cp*)2 ][Pt(mnt)2 ]
The crystal structure of β-[Fe(Cp*)2 ][Pt(mnt)2 ] consists of parallel alternated
D+ A− D+ A− (type I) chains, which are isolated by chains of D+ [A2 ]2− D+ units.
A projection of the crystal structure along the stacking direction, [100], is shown
in Figure 1.10(a). In the DADA chains the [Pt(mnt)2 ]− are considerably tilted in
relation to the chain direction, sitting on top of the ethylenic C=C of the mnt2−
ligands from the acceptors. A pair of the closest DADA chains (I–II) is shown in
Figure 1.10(b) and they are considerably separated (16.576 Å). Short interatomic
DA intrachain distances were observed, involving one C from the Cp and a S atom
from the acceptor, with a C–S distance of 3.632 Å (QW = 1.05). A pair of the
closest DADA chains is shown in Figure 1.10(b). One of the D+ [A2 ]2− D+ chains
                                                                                                                                                         16




Fig. 1.9. (a) View of the structure along the chains for [Fe(C5 Me4 SCMe3 )2 ][Pt(mnt)2 ]. (b) Interchain arrangement of the pair I–IV, d1 corresponds
to the DA closest intrachain contact (3.501 Å, QW = 1.01) and d2 to the closest interchain contact (3.787 Å, QW = 1.10). (c) Interchain
arrangement of the pair II–IV, d3 is the closest interchain contact (3.372 Å, QW = 1.09). Hydrogen atoms were omitted for clarity.
                                                                                                                                                         1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates
Fig. 1.10. (a) Perspective view of the structure along the DADA chain direction. (b) Interchain arrangement of the pair I–II, d1 corresponds to
the DA closest intrachain contact (3.632 Å, QW = 1.01). (c) View of a D[A2 ]D chain. Hydrogen atoms were omitted for clarity.
                                                                                                                                                  1.3 Solid-state Structures and Magnetic Behavior
                                                                                                                                                  17
18        1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates

is shown in Figure 1.10(c), in the DAAD units the acceptors are strongly dimerized
with a Pt-Pt distance of 3.574 Å (QW = 0.78).
    The magnetic susceptibility of β-[Fe(Cp*)2 ][Pt(mnt)2 ] follows Curie–Weiss be-
havior with θ = 9.8 K. The dominant ferromagnetic interactions are assigned to
the magnetic intrachain DA interactions from the type I chains, as the contribution
from the D+ [A2 ]2− D+ unit chains is expected to be only from the donors due to
the strong dimerization of the acceptors, S = 0 for [A2 ]2− , and no intrachain close
contacts were observed to exist.



1.3.1.5     [M(Cp*)2 ][Ni(α-tpdt)2 ]
The crystal structure of [Fe(Cp*)2 ][Ni(α-tpdt)2 ], in spite of presenting the type I
structural chain motif, is considerably different from the structures presented so far
[34]. The crystal structure consists of alternate layers of donors, [Fe(Cp*)2 ]+ , and
acceptors, [Ni(α-tpdt)2 ]− , parallel to the ab plane (ab layers). A projection of the
crystal structure along a is shown in Figure 1.11(a) for [Fe(Cp*)2 ][Ni(α-tpdt)2 ]. In
the acceptor layers, relatively short interionic AA distances were found, involving S
atoms from the central NiS4 fragment and a C atom from the thiophenic fragment of
the ligand, as shown Figure 1.11(b). The S· · ·C separations are 3.723 and 3.751 Å,
exceeding the sum of the van der Waals radii (3.450 Å) by 8 and 9% respectively.
Short interlayer interionic DA distances were found, involving C atoms from the
Cp rings and the S atom from the thiophenic fragment from the acceptors, with
S· · ·C distances of 3.530 and 3.610 Å, exceeding the sum of the van der Waals radii
by 2 and 5% respectively. These contacts give rise to a set of layers (bc layers)
composed of parallel alternated DADA chains, as shown in Figure 1.11(c). The
chains in adjacent layers are almost perpendicular to each other, running along
directions alternating from 2b + c to 2b − c. Two chains from adjacent layers are
shown in Figure 1.11(d) along with two anionic ab layers.
    The chains in the bc layers present an out-of registry arrangement. Short in-
terionic DA interchain distances were observed, involving a S from the MS2 C2
fragment from the acceptor and a C from the Me groups in the donor, with S-C
separations exceeding the sum of the van der Waals radii by less than 8%, as shown
in Figure 1.11(c). The contacts between the chain in adjacent layers correspond to
the (S–C) AA contacts previously mentioned in the case of the acceptor ab layers.
    The compounds [M(Cp*)2 ][Ni(α-tpdt)2 ], M = Fe and Cr, although not isostruc-
tural, present a similar solid state structure. In the case of [Cr(Cp*)2 ][Ni(α-tpdt)2 ]
the crystal structure is more symetric than the analogue with M = Fe. The contacts
are of the same order and the most significant difference between the two structures
is the arrangement of the molecules in the acceptor ab layers, unlike the case of
[Fe(Cp*)2 ][Ni(α-tpdt)2 ], where there was only one type of relevant AA contact,
because of a short S–C distance, for [Cr(Cp*)2 ][Ni(α-tpdt)2 ], the S atom (from
the central NiS4 fragment) is close to two distinct C atoms from the thiophenic
                                  1.3 Solid-state Structures and Magnetic Behavior        19




Fig. 1.11. Projection of the structure along a for [Fe(Cp*)2 ][Ni(α-tpdt)2 ] (Me groups were
omitted for clarity). (b) View of an acceptor layer, showing the closest AA separations (S–C)
d1 and d2 (3.775 and 3.721 Å, QW = 1.09 and 1.08). (c) Partial view of the crystal structure
illustrating two consecutive anionic layers and two orthogonal DADA chains. (d) View of the
structure showing parallel DADA chains, the shortest interionic separations are shown, d3 and
d4 correspond to the intrachain contacts (3.519 and 3.622 Å, QW = 1.02 and 1.05) and d5-d7
are interchain DA (S–C) separations (3.671, 3.694, 3.722 Å, QW = 1.06, 1.06 and 1.08).
Hydrogen atoms were omitted for clarity.


fragment, with separations of the same order, 3.768 and 3.756 Å (QW = 1.09 and
1.08). However the closest contact involves the same C in both compounds.
   In the case of the compound [Fe(Cp*)2 ][Ni(α-tpdt)2 ] [34] a minimum is ob-
served in the temperature dependence of the χT product. at 130 K, which is con-
sistent either with ferrimagnetic behavior or with a change in the type of the dom-
inant magnetic interactions. A Curie–Weiss fit to the experimental data in the high
20      1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates

temperature regime gave a θ value of −5.1 K. At low temperatures metamagnetic
behavior was observed in the case of [Fe(Cp*)2 ][Ni(α-tpdt)2 ], with TN = 2.6 K and
HC = 600 G, at 1.7 K. The temperature dependence of HC is shown in Figure 1.12.
In the case of [M(Cp*)2 ][Ni(α-tpdt)2 ], with M = Mn and Cr [35], at high tempera-
tures, the magnetic susceptibility follows a Curie–Weiss behavior, with θ values of
7.3 and 6.1 K, showing dominant ferromagnetic interactions for these compounds.
A FM transition that was observed to occur in case of [Mn(Cp*)2 ][Ni(α-tpdt)2 ],
at 2.2 K, as denoted by a maximum observed in the real and imaginary contri-
butions of the ac susceptibility. No hysteresis was observed in the isothermals
below TC = 2.2 K, for low applied magnetic fields, the magnetization isothermals
showed a drastic increase and a very slow and nearly linear increase is observed
above 5 kG (M = 2.5 N µB ), reaching a value of 3.0 N µB at 120 kG, which is
consistent with the spin only (gA = gD = 2.0) value for the saturation magneti-
zation, Msat = gA SA + gD SD = 3.0 N µB . The poor quality of the crystals of this
compound has so far prevented crystal structure determination, however a crystal
structure similar to that observed for the Fe and Cr analogues, is expected for this
compound.
   Unlike the previously mentioned acceptors, calculations predict a spin polar-
ization effect in the case of [Ni(α-tpdt)2 ]− , and small negative spin densities are
expected in the S atom and in one of the carbons from the thiophenic ring [35]. As
a consequence a competition between FM and AFM (DA or AA) interactions is
expected. From the room temperature crystal structure analysis the stronger interi-
onic contact is expected to be AFM as it corresponds to the intrachain DA contact
involving two atoms with negative spin densities, a S from the thiophenic ring
of the acceptor and a C from the C5 ring of the donor. The shorter AA contacts
from the anionic layers are expected to give rise to FM interactions, as the spin
densities of the atoms do not have the same sign. The high temperature magnetic
behavior of the [M(Cp*)2 ][Ni(α-tpdt)2 ] salts indicates AFM dominant interactions,
which is consistent with the McConnell I model predictions for the DA interac-
tions. However the change in the nature of the magnetic interactions in the case of
[Fe(Cp*)2 ][Ni(α-tpdt)2 ], remains an open question. This change can be attributed
to small variations in the interionic contacts on cooling. In both intrachain DA and
interlayer AA arrangements, besides the shorter contacts referred to before, there
are also slightly longer interionic separations, which could lead to different types
of interactions for both the DA and AA contacts. As observed in the [Fe(Cp*)2 ]
based compound, in the case of [Cr(Cp*)2 ][Ni(α-tpdt)2 ], the shorter contacts in-
volve atoms with the same spin density parity (AFM coupling) and a competition
between AFM and FM interactions is expected. The experimental results indicate
that in this case the FM interactions dominate the magnetic behavior of this com-
pound. The distinct magnetic behavior found in [M(Cp*)2 ][Ni(α-tpdt)2 ], with M
= Fe, Mn and Cr, can be related to the competition between the FM and AFM
interactions and the small differences in the DA overlap observed in the DADA
chains. The poor quality of the crystals of [Mn(Cp*)2 ][Ni(α-tpdt)2 ] has so far
                                    1.3 Solid-state Structures and Magnetic Behavior       21

           1.0


           0.8

                                        PM
H C (kG)



           0.6


           0.4

                      AFM
           0.2
                                                      Fig. 1.12. Critical field dependence
                                                      for [Fe(Cp*)2 ][Ni(α-tpdt)2 ], where the
           0.0                                        closed and open symbols correspond to
              1.0    1.5    2.0   2.5   3.0    3.5    the data obtained with isothermal and
                       Temperature (K)                isofield measurements respectively.

prevented crystal structure determination, however a crystal structure similar to
that observed for the Cr analogue is expected for this compound, considering the
magnetic behavior observed in these compounds.


1.3.2            Type II Mixed Chain [M(Cp*)2 ][M (L)2 ] Salts

This type of chain arrangement was observed only in the case of α-
[Fe(Cp*)2 ][Pt(mnt)2 ]. In the crystal structure, layers of parallel DAADAA (type
II) chains, with a net charge (−) per repeat unit, [A2 ]2− D+ , alternate with lay-
ers presenting a D+ D+ A− repeating unit, with a net (+) per repeat unit [16]. A
view of the crystal structure along the type II chain direction, [100], is shown in
Figure 1.13(a). In the type II chain layers the acceptors are strongly dimerized
with a Pt–Pt distance of 3.575 Å (QW = 0.78) and the [A2 ]2− D+ [A2 ]2− D+ chains
present an out-of-registry arrangement, as shown in Figure 1.13(b). Apart from the
AA contacts no other short contacts were observed in these layers. The DDA layer
presents a unique arrangement, where the donors sit on top of the extremity of the
acceptors, these DDA units form edge to edge chains, as shown in Figure 1.13(c).
In these layers the closest interionic separations involve one C from the Cp and a
S atom from the acceptor, with a C–S distance of 3.952 Å (QW = 1.15).
    The magnetic susceptibility of α-[Fe(Cp*)2 ][Pt(mnt)2 ] follows Curie–Weiss be-
havior with θ = 6.6 K [16]. The dominant ferromagnetic interactions are assigned
to the magnetic DA interactions from the DDA layers, as the contribution from the
[A2 ]2− D+ chains is expected to be only from the isolated donors due to the strong
dimerization of the acceptors, S = 0 for [A2 ]2− .
                                                                                                                                                  22




Fig. 1.13. (a) View of the structure of α-[Fe(Cp*)2 ][Pt(mnt)2 ] along the DAADAA (type II) chains. (b) View of a type II chain layer. (c) View
of the DDA layer, d1 corresponds to the closest contact (3.952 Å, QW = 1.15). Hydrogen atoms were omitted for clarity.
                                                                                                                                                  1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates
                                  1.3 Solid-state Structures and Magnetic Behavior        23

1.3.3     Type III Mixed Chain [M(Cp*)2 ][M (L)2 ] Salts

The acceptor-acceptor magnetic interactions play a key role in the magnetic be-
havior of the [M(Cp*)2 ][M (L)2 ] salts based on type III chains, and in most cases
the AA interactions are AFM. Table 1.4 summarizes the key magnetic properties
of type III [M(Cp*)2 ][M (L)2 ] compounds.

Table 1.4. Magnetic characterization of type III [M(Cp*)2 ][M (L)2 ] salts.

Compound                        SD ; SA    θ, K       Comments                Ref.

[Fe(Cp*)2 ][Ni(dmit)2 ]         1/2; 1/2   −7.6 (a)   (b); Tm = 30 K (c)      45
[Mn(Cp*)2 ][Ni(dmit)2 ]           1; 1/2    2 (d)     FM (e); TC = 2.5 K      46
α-[Fe(Cp*)2 ][Pd(dmit)2 ]       1/2; 1/2   −22.3      (b)                     31
β-[Fe(Cp*)2 ][Pd(dmit)2 ] (f)   1/2; 1/2    2.6       (b)                     45
[Fe(Cp*)2 ][Pt(dmit)2 ]         1/2; 1/2   −14.4      (b)                     45
[Fe(Cp*)2 ][Ni(dmio)2 ] (f)     1/2; 1/2   −19.0      (b)                     45
[Fe(Cp*)2 ][Pd(dmio)2 ]         1/2; 1/2   −24.7      (b)                     45
[Fe(Cp*)2 ][Pt(dmio)2 ]         1/2; 1/2   −33.3      (b)                     45
[Fe(Cp*)2 ][Ni(dsit)2 ]         1/2; 1/2   −18.9      (b)                     31
(a) Non-Curie–Weiss behavior the given θ value relates to the high temperature region (T >
Tm ). (b) No magnetic ordering down to 1.8 K. (c) Minimum in χT vs. T . (d) Estimated value
from χ T vs. T plot in Ref. [46]. (e) Ferromagnetic transition. (f) Crystal structure not yet
determined.



1.3.3.1    [M(Cp*)2 ][M (dmit)2 ] (M = Fe; M = Ni, Pt and M = Mn; M = Ni)
The salts [Fe(Cp*)2 ][M(dmit)2 ], with M = Ni [17] and Pt [31], and
[Mn(Cp*)2 ][Ni(dmit)2 ] [30] are isostructural and the crystal structure consists
of 2D layers composed of parallel type III chains, ··A− A− D+ D+ A− A− D+ D+ ··,
where face-to-face pairs of acceptors alternate with side-by-side pairs of donors.
A view of the structure along the chain direction is shown in Figure 1.14(a) for
[Fe(Cp*)2 ][Ni(dmit)2 ]. The chains are regular and the Cp fragments of the donor
sit above dmit ligands of the acceptor, as shown for [Fe(Cp*)2 ][Ni(dmit)2 ] in Fig-
ure 1.14(b). Intrachain AA short contacts are observed in the [Ni(dmit)2 ]− dimers,
involving a Ni atom and one of the sulfur atoms from the five-membered C2 S2 C
ring from the ligand, with a Ni–S distance of 3.792 Å (QW = 0.96). The intrachain
DA separation is considerably larger and the shorter contacts between the acceptor
and the Cp rings correspond to a S–C contact (S from the C2 S2 C fragment) with
distances of 3.611 and 3.659 Å (QW = 1.05 and 1.06). Several short AA (S–S)
interchain contacts were observed in this compound and the crystal structure can
be better described as being based on layers of out-of-registry parallel chains, one
of these layers is shown in Figure 1.14(b). The intralayer interchain contacts are
                                                                                                                                                    24




Fig. 1.14. (a) Perspective view of the crystal structure of [Fe(Cp*)2 ][Ni(dmit)2 ] along the stacking direction (hydrogen atoms were omitted for
clarity). (b) View of one layer of the type II chains, d1 corresponds to the intradimer (AA) closest contact (3.792 Å, QW = 0.96), and d2 and d3
to short interchain contacts (3.422 and 3.547 Å, QW = 0.93 and 0.96) (Me groups were omitted for clarity). (c) View of two neighboring chains
from different layers, d4 is the closest interlayer contact (3.375 Å, QW = 0.91) (Me groups were omitted).
                                                                                                                                                    1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates
                                       1.3 Solid-state Structures and Magnetic Behavior       25

shorter than the intrachain and two types of contacts are observed. The longer con-
tact involves one of the S from the central MS4 fragment and one of the S from
the ligand C2 S2 C fragment, with a S–S distance of 3.547 Å (QW = 0.96), and the
shorter contact involves two S atoms from the central MS4 fragment, with a S–S
distance of 3.422 Å (QW = 0.93). There are also interchain interlayer AA short
contacts, involving S atoms from the C2 S2 C ligand fragments, with a S–S distance
of 3.375 Å (QW = 0.91), as shown in Figure 1.14(c).
   In spite of the similarities in the crystal structures of the compounds
[Fe(Cp*)2 ][M(dmit)2 ], with M = Ni and Pt, and [Mn(Cp*)2 ][Ni(dmit)2 ], they
present distinct magnetic behaviors. In the case of [Fe(Cp*)2 ][M(dmit)2 ], a min-
imum in the temperature dependence of χ T , is observed at 30 K [45], as shown
in Figure 1.15. This can be attributed to a change in the dominant magnetic inter-
actions, due to structural changes on cooling. At high temperatures the magnetic
susceptibility follows Curie-Weiss behavior, with a θ value of −7.6 K, which clearly
indicates that AFM interactions are dominant. However, below Tm = 30 K, χT
increases rapidly, indicating that FM become dominant in that region, this is further
confirmed by the magnetization field dependence at low temperatures, which for
low applied magnetic fields increases faster than predicted by the Brillouin func-
tion (solid line) and at high fields slowly approaches the saturation magnetization,
as shown in Figure 1.16. In the case of [Mn(Cp*)2 ][Ni(dmit)2 ] a FM transition
was reported to occur at 2.5 K [46], the field cooled (FCM), zero field cooled
(ZFCM) and remnant (REM) magnetization temperature dependences are shown
in Figure 1.17. This is the first and only case, to date, in this class of compounds to
present FM ordering and this behavior was analyzed in the light of the McConnell
I mechanism, namely for the intradimer magnetic interactions due to a spin polar-
ization effect in the acceptor molecules. According to the McConnell I model these
interactions are predicted to be FM as the atoms involved in the intradimer contacts


                  2.0
T (emu K mol-1)




                  1.5




                  1.0




                  0.5                                   Fig. 1.15. χT temperature dependence
                        0    100      200        300    for [Fe(Cp*)2 ][Ni(dmit)2 ] (squares) and
                            Temperature (K)             [Fe(Cp*)2 ][Pt(dmit)2 ] (circles).
26                       1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates


B)

                   2.0
Magnetization (N




                                                                 Fig. 1.16. Magnetization field de-
                   1.0                                           pendence for [Fe(Cp*)2 ][Ni(dmit)2 ]
                                                                 (squares) and [Fe(Cp*)2 ][Pt(dmit)2 ]
                                                                 (circles) at 1.8 K. The solid line cor-
                                                                 responds to the Brillouin function
                                                                 considering the donor and acceptor
                   0.0                                           spins, while the dashed line corresponds
                         0          20          40         60    only to the contribution from the donor
                                     Field (kG)                  molecules.




Fig. 1.17. Field-cooled (FCM), zero-field-cooled (ZFCM) and remnant (REM) magnetiza-
tion temperature dependences of [Mn(Cp*)2 ][Ni(dsit)2 ] (reproduceded with permission from
Ref. [46]).

present different signs in the atomic spin density, the Ni atom presents a positive
spin density while in the S atoms from the C2 S2 C ligands fragments, the spin den-
sity is negative [47]. In the case of [Fe(Cp*)2 ][Pt(dmit)2 ] the magnetic behavior
is dominated by AFM interactions as the magnetic susceptibility follows Curie–
Weiss behavior, with a θ value of −14.4 K [45], and the χT product decreases on
cooling, as shown in Figure 1.15. For this compound the magnetization isother-
mals (circles in Figure 1.16) at low temperature are consistent with total cancella-
                               1.3 Solid-state Structures and Magnetic Behavior   27

tion of the magnetic contribution from the acceptors, and the magnetization field
dependence follows the Brillouin function for the isolated donors, [Fe(Cp*)2 ]+ ,
(dashed line) as shown in Figure 1.16. In the case of [Fe(Cp*)2 ][M(dmit)2 ] (M
= Ni and Pt), the S–S intra and interlayer short contacts are expected to lead to
AFM interactions, as the spin density of the atoms involved in the shorter con-
tacts have the same sign. Considering that these contacts are even shorter than the
intradimer ones (FM coupling), dominant AFM interactions are expected, which
is consistent with the observed negative θ values for [Fe(Cp*)2 ][Pt(dmit)2 ], and
for [Fe(Cp*)2 ][Ni(dmit)2 ], at high temperatures. The change in behavior observed
in the case of [Fe(Cp*)2 ][Ni(dmit)2 ], can originate from a weakening of the intra
and interlayer AFM interactions. It is worth mentioning that, in the case of the
interchain intralayer interactions, the shorter contacts (involving two S atoms from
the central MS4 fragment) are expected to be AFM, while the weaker contacts
(involving a S from the central MS4 fragment and one of the S from the C2 S2 C
fragment) are predicted to give rise to FM interactions. In this case a slight change
in the interionic arrangement could change the nature of the intralayer magnetic
interactions. A similar situation was reported in the case of NH4 [Ni(mnt)2 ] · H2 O,
which shows dominant AFM interactions at high temperatures (T > 100 K), for
low temperatures FM interactions become dominant and ferromagnetic ordering
is exhibited at 4.5 K [7]. The magnetic behavior of [Fe(Cp*)2 ][Ni(dmit)2 ] is still
puzzling and requires further study.




1.3.3.2   [Fe(Cp*)2 ][M(dmio)2 ] (M = Pd and Pt), α-[Fe(Cp*)2 ][Pd(dmit)2 ]
          and [Fe(Cp*)2 ][Ni(dsit)2 ]
The compounds [Fe(Cp*)2 ][M(dmio)2 ], with M = Pd and Pt, are isostructural
and the crystal structure consists of a parallel arrangement of 1D type III chains.
The solid state structure is similar to that observed in [Fe(Cp*)2 ][Ni(dmit)2 ] and
presents a similar layered motif. However, for [Fe(Cp*)2 ][M(dmio)2 ] (M = Ni
and Pt) the dimers show a different configuration, in this case no slippage is
observed in the dimer and a short Pd–Pd contact was observed in the case of
[Fe(Cp*)2 ][Pd(dmio)2 ], with a Pd–Pd distance of 3.481 Å (QW = 0.76). In this
compound short intralayer AA contacts were also detected, involving a S from
the central MS4 fragment and one of the S from the C2 S2 C fragment, with a
S–S distance of 3.669 Å (QW = 0.99). No interlayer short contacts were ob-
served for [Fe(Cp*)2 ][Pd(dmio)2 ]. The compound α-[Fe(Cp*)2 ][Pd(dmit)2 ] is not
isostructural with [Fe(Cp*)2 ][M(dmio)2 ], with M = Pd and Pt, but presents a
similar molecular arrangement in the crystal structure. Again, in the case of α-
[Fe(Cp*)2 ][Pd(dmit)2 ], a strong dimerization was observed for the acceptors, pre-
senting also short Pd–Pd contacts, with a distance of 3.485 Å (QW = 0.76). Short
intralayer contacts, similar to those observed in the previous compound, were ob-
28      1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates

served, with a S–S distance of 3.558 Å (QW = 0.96). No interlayer short contacts
were observed for α-[Fe(Cp*)2 ][Pd(dmit)2 ].
    The magnetic susceptibility of [Fe(Cp*)2 ][M(dmio)2 ] (M = Pd and Pt) and
α-[Fe(Cp*)2 ][Pd(dmit)2 ] follows Curie–Weiss behavior, with θ values of −24.7,
−33.3 and −22.3 K, respectively. The magnetic behavior is clearly dominated
by the AFM intradimer interactions. At low temperatures, the magnetic field de-
pendence follows the predicted values for the isolated donors, as in the case of
[Fe(Cp*)2 ][Pt(dmit)2 ]. Unlike the [Ni(dmit)2 ] and [Pt(dmit)2 ] based compounds,
for [Fe(Cp*)2 ][M(dmio)2 ] (M = Pd and Pt) and [Fe(Cp*)2 ][Pd(dmit)2 ] the short
intradimer contacts are expected to lead to strong AFM interactions, which is ina-
greement with the experimental observations.
    The crystal structure of [Fe(Cp*)2 ][Ni(dsit)2 ] is similar to those described pre-
viously in this section. In this salt the acceptors are strongly dimerized through
Ni–Se bonds, the Ni(dsit)2 units are slipped (see Figure 1.18) and the metal adopts
a square pyramidal conformation, with an apical Ni–Se distance of 2.555 Å, which
is slightly larger than the average equatorial Ni–Se bond distance, 2.330 Å.
    The magnetic susceptibility of [Fe(Cp*)2 ][Ni(dsit)2 ] follows Curie–Weiss be-
havior, with a θ value of −19.8 K. The magnetic behavior is clearly dominated
by the AFM intradimer interactions. At low temperatures, the magnetic field de-
pendence follows the predicted values for the isolated donors, as in the case of
the analogous compounds presenting dominant AFM interactions, described pre-
viously.
    In the case of β-[Fe(Cp*)2 ][Pd(dmit)2 ] dominant FM interactions (θ = 2.6 K)
were observed and the crystal structure in this compound is expected to be sim-
ilar either to that described for [Fe(Cp*)2 ][Ni(dmit)2 ] or to that reported for
[Fe(Cp*)2 ][Ni(dmio)2 ]MeCN, which will be described in the next section (Sec-
tion 1.3.4.1.). For [Fe(Cp*)2 ][Ni(dmio)2 ] the observed large negative θ value
(−19 K) suggests that this compound must present a crystal structure similar to
those reported for the Pd and Pt analogues or for α-[Fe(Cp*)2 ][Pd(dmit)2 ].
    The supramolecular arrangement in the type III chain based salts, at high tem-
peratures, is consistent with the existence of dominant AFM interactions through
AA interactions. For the compounds with dominant FM interactions at low tem-
peratures, the magnetic behavior can be related to the distinct dimer arrangements.
The dimer arrangements along with the dimer overlap are illustrated in Figure 1.18,
for [Fe(Cp*)2 ][Ni(dmit)2 ] α-[Fe(Cp*)2 ][Pd(dmit)2 ] and [Fe(Cp*)2 ][Ni(dsit)2 ]. As
stated before the contacts in the case of [Fe(Cp*)2 ][Ni(dmit)2 ] are expected to give
rise to FM intradimer interactions, while in the case of the other two compounds
AFM intradimer interactions are anticipated.
Fig. 1.18. The dimer arrangements and dimer overlapping are illustrated for [Fe(Cp*)2 ][Ni(dmit)2 ] (top) and α-[Fe(Cp*)2 ][Pd(dmit)2 ] (center)
and [Fe(Cp*)2 ][Ni(dsit)2 ] (bottom).
                                                                                                                                                   1.3 Solid-state Structures and Magnetic Behavior
                                                                                                                                                   29
30        1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates

1.3.4     Type IV Mixed Chain [M(Cp*)2 ][M (L)2 ] Salts

The magnetic behavior of the [M(Cp*)2 ][M (L)2 ] salts based on type IV chains
shows a strong dependence on the intra and interchain arrangments. Table 1.5
summarizes the key magnetic properties of type IV [M(Cp*)2 ][M (L)2 ] compounds.


Table 1.5. Magnetic characterization of type IV [M(Cp*)2 ][M (L)2 ] salts.

Compound                         SD ; SA    θ, K       Comments                       Ref.

[Fe(Cp*)2 ][Ni(dmio)2 ]MeCN      1/2; 1/2    2.0       (a)                            32
[Fe(Cp*)2 ][Ni(bds)2 ]MeCN       1/2; 1/2    0 (b)     (a)                            17
[Fe(Cp*)2 ][Ni(bdt)2 ]            1; 1/2    −5.6 (c)   (a); Tm = 40 K (d)             33, 48
[Mn(Cp*)2 ][Ni(bdt)2 ]            1; 1/2    −22.6      Tm = 20 K (d); MM (e):         33, 48
                                                       TN = 2.3 K; HC = 200 G
                                                       (2 K)
[Cr(Cp*)2 ][Ni(bdt)2 ]           3/2; 1/2   +6.2       (a)                            33, 48
[Fe(Cp*)2 ][Co(bdt)2 ] (f)        3/2; 1    −23.0      (a)                            33
[Mn(Cp*)2 ][Co(bdt)2 ] (f)        3/2; 1    −4.9       (a)                            33
[Cr(Cp*)2 ][Co(bdt)2 ]            3/2; 1    −2.5       (a)                            33
[Fe(Cp*)2 ][Pt(bdt)2 ]           1/2; 1/2   −12.6      (a); Tm = 125 K (d)            33
[Mn(Cp*)2 ][Pt(bdt)2 ] (f)        1; 1/2    −20.5      Tm = 100 K (d); FIM (g):       33
                                                       TC = 2.7 K
[Cr(Cp*)2 ][Pt(bdt)2 ]           3/2; 1/2   +6.0       (a)                            33
[Fe(Cp*)2 ]2 [Cu(mnt)2 ]         1/2; 1/2   −8.0       (a)                            29
(a) No magnetic ordering observed down to 1.8 K. (b) θ value in the high temperature region,
at low temperatures θ > 0. (c) Non-Curie–Weiss behavior the given θ value relates to the high
temperature region (T > Tm ). (d) Minimum in χT vs. T . (e) Metamagnetic transition. (f)
Crystal structure not yet determined. (g) Ferrimagnetic transition.




1.3.4.1     [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN
The crystal structure of [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN consists of 2D layers com-
posed of parallel ··D+ D+ A− D+ D+ A− ·· chains (type IV), where side-by-side pairs
of donors alternate with an acceptor, with a net charge (+) per repeat unit
(D+ D+ A− ) [32]. These charged layers are separated by acceptor layers, as rep-
resented in the view along [010] in Figure 1.19, for [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN.
The chains are regular and the Cp fragments of the donor sit above the dmio ligands
of the acceptor, as shown in Figure 1.19(a). In this compound, unlike the previous
compounds, the C5 Me5 ligands from [Fe(Cp*)2 ]+ present an eclipsed conforma-
tion. No interionic short contacts are observed in [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN.
The closest interionic intrachain (DA) separation involves a S atom from the central
Fig. 1.19. (a) View of the crystal structure of [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN along the stacking direction (hydrogen atoms were omitted for
clarity). (b) View of the DDA layer, d1 corresponds to the intrachain (DA) closest contacts (3.945 Å, QW = 1.14) (Me groups were omitted for
clarity). (c) View of the anionic layer, d2 is the closest interlayer contact (3.777 Å, QW = 1.02).
                                                                                                                                               1.3 Solid-state Structures and Magnetic Behavior
                                                                                                                                               31
32        1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates

MS4 fragment of the acceptor and one of the C atoms from the C5 ring of the donor,
with a S–C distance of 3.945 Å (QW = 1.14). The chains in the layers are quite
isolated and the solvent molecules are located in cavities between the DDA chains
layers and the anionic layers, as shown in the view of the structure in Figure 1.19(b).
Short contacts were observed in the anionic layers involving S atoms from the
five-membered C2 S2 C ring of the dmio ligands, with a S–S distance of 3.777 Å
(QW = 1.02), as shown in Figure 1.19(c). Relatively close AA contacts between the
DDA chains and the anionic layers were also observed in [Fe(Cp*)2 ][Ni(dmio)2 ],
involving O atoms from the acceptor layers and S atoms from the C2 S2 C ring of
the dmio ligands, with a O–S distance of 3.398 Å (QW = 1.05).
   In the case of [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN, FM interactions dominate the mag-
netic behavior of the compounds [32], as seen from the positive θ value (2 K) ob-
tained from the Curie–Weiss fit. The observed magnetic behavior is attributed to
the intrachain interactions, as the contacts in the anionic layers are expected to
give rise to AFM interactions since the spin density of the atoms involved in these
contacts have the same sign.


1.3.4.2     [Fe(Cp*)2 ][Ni(bds)2 ]MeCN
The      crystal     structure    of     [Fe(Cp*)2 ][Ni(bds)2 ],      as   that    of
[Fe(Cp*)2 ][Ni(dmio)2 ]MeCN, consists of 2D layers composed of parallel
··D+ D+ A− D+ D+ A− ·· chains (type IV), which are separated by acceptor layers
[17], as represented in the view along [100] in Figure 1.20(a). In the case of
[Fe(Cp*)2 ][Ni(bds)2 ]MeCN, the chains are not regular and while one of the Cp
fragments of the donor sits above the C6 ring of the ligand, the second is displaced
towards the center of the acceptor. For the first Cp the closest DA interatomic
separation (C–C) has a distance of 3.451 Å (QW = 1.08), while for the second Cp
the closest DA contact (C–Se) corresponds to a distance of 3.752 Å (QW = 1.04),
as shown in Figure 1.20(b). The DDA chains are relatively isolated and the solvent
is located in cavities between the chains. In the case of [Fe(Cp*)2 ][Ni(bds)2 ]MeCN
no short interionic interlayer distances were observed involving molecules in the
DDA layers, not in acceptor layers or even in the anionic layers.
    The magnetic behavior of this compound is dominated by FM interactions [17],
which are attributed to the observed DA intrachain contacts.


1.3.4.3     [M(Cp*)2 ][M (bdt)2 ] (M = Fe, Mn and Cr; M = Co, Ni and Pt)
[Cr(Cp*)2 ][M (bdt)2 ] (M = Ni and Co) are isostructural, and, as in the case of
the [Fe(Cp*)2 ][Ni(dmio)2 ]MeCN and [Fe(Cp*)2 ][Ni(bds)2 ]MeCN salts, a crys-
tal structure, based on a DDA type IV chain supramolecular arrangement, is ob-
served [33]. However in [Cr(Cp*)2 ][M (bdt)2 ] the pairs of donors are perpendicu-
lar to each other, unlike the previous compounds, where the donor molecules are
                                  1.3 Solid-state Structures and Magnetic Behavior        33




Fig. 1.20. (a) Perspective view of the crystal structure of [Fe(Cp*)2 ][Ni(bds)2 ]MeCN normal
to the chain direction (hydrogen atoms were omitted for clarity). (b) View of the DDA layer,
d1 and d2 correspond to the intrachain (DA) closest contacts (3.451 and 3.752 Å, QW = 1.08
and 1.04) (Me groups were omitted for clarity).

parallel. A view along the chain direction, [101], is shown in Figure 1.21(a) for
[Cr(Cp*)2 ][Ni(bdt)2 ]. The shorter DA intrachain separations involve S atoms from
the acceptors and C atoms from the Cp rings of the donors (aligned with the chain
direction) presenting S–C distances of 3.702 and 3.857 Å (QW = 1.07 and 1.12), as
shown in the view of a DDA chain layer represented in Figure 1.21(b). The chains
in the same layer are relatively isolated, but short distances between the chains and
anions on the anionic layers were observed. As shown in Figure 1.21(c), besides the
intrachain contacts, relatively short interaionic separations were also observed be-
tween molecules in the chains and in the anionic layers. AA contacts were observed
involving C atoms from the terminal C6 ring of the ligands and Ni atoms from the
acceptors in the anionic layer, with a C–Ni distance of 4.206 Å (QW = 1.14). DA
contacts were also observed involving one of the C atoms from the Cp ring of the
donor perpendicular to the chain axis and one of the C atoms from the C6 ring of
the acceptor, with a C–C distance of 3.453 Å (QW = 1.08). Short contacts were
also observed in the anionic layers, as shown in Figure 1.21(d), with distances of
3.633 and 3.340 Å (QW = 1.05 and 1.04), for S–C and C–C contacts respectively.
In the case of [Fe(Cp*)2 ][M (bdt)2 ] (M = Ni and Pt), [Mn(Cp*)2 ][M(bdt)2 ] (M
= Ni and Co), and [Cr(Cp*)2 ][Pt(bdt)2 ], the crystal structures show a duplication
of the unit cell along b, but present similar supramolecular packing [33].
    In the case of the compounds [M(Cp*)2 ][Co(bdt)2 ] (M = Fe, Mn and Cr) and
[Cr(Cp*)2 ][M (bdt)2 ] (M = Ni and Pt), the magnetic susceptibility follows Curie–
Weiss behavior. The [M(Cp*)2 ][Co(bdt)2 ] salts present dominant AFM interactions
(θ = −23, −4.9 and −2.5 K for M = Fe, Mn and Cr respectively) [33], while the
[Cr(Cp*)2 ][M (bdt)2 ] present dominant FM interactions (θ = 6.2 and 6.0 K for M
= Ni and Pt respectively) [33]. In the case of the compounds [Fe(Cp*)2 ][M (bdt)2 ]
and [Mn(Cp*)2 ][M (bdt)2 ], with M = Ni and Pt, a minimum in the temperature
34       1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates




Fig. 1.21. (a) View of the crystal structure of [Fe(Cp*)2 ][Pt(bdt)2 ] along the chain direction
(hydrogen atoms were omitted for clarity). (b) View of the DDA layer, d1 and d2 correspond
to the intrachain (DA) closest contacts (3.702 and 3.857 Å, QW = 1.07 and 1.12) (Me groups
were omitted for clarity). (c) View of one of the DDA stacks and acceptors from neighboring
acceptor layers, d3 and d4 correspond to interlayer contacts (3.453 and 4.206 Å, QW = 1.08
and 1.14). (d) View of the anionic layer, d5 (S–C) and d6 (C–C) are the closest interlayer
contacts (3.633 and 3.340 Å, QW = 1.05 and 1.04).

dependence of χ T is observed at 40, 125, 20 and 130 K for M/M = Fe/Ni, Fe/Pt,
Mn/Ni and Mn/Pt respectively [33]. For these compounds the minima are attributed
to ferrimagnetic behavior, as in the case of [Mn(Cp*)2 ][Pt(bdt)2 ] FIM ordering was
observed at 2.7 K [33]. The magnetization field dependence, at 1.8 K, is shown in
Figure 1.22 (squares), after a fast increase at low fields the magnetization attains
an almost constant value that is in good agreement with that predicted for FIM
ordering, Msat = SD gD − SA gA ≈ 1.57 N µB , calculated for SA = 1/2, gA = 2.06
[49], SD = 1 and gD = 2.6 (due to the high g anisotropy of the donor the gD
value was obtained from susceptibility temperature dependence at high temper-
atures). The magnetization field dependence, at 2 K, of [Mn(Cp*)2 ][Ni(bdt)2 ] is
also shown in Figure 1.22 (circles). A metamagnetic transition was observed to
occur in this compound, with TN = 2.3 K and HC = 200 G at 2 K [33, 48], as
                                                           1.3 Solid-state Structures and Magnetic Behavior          35

                   2

                           Msat (FIM)
B)
Magnetization (N




                   1
                                    B)
                                          0.4
                                   M (N



                                          0.0                            Fig. 1.22. Magnetization field dependence
                                             0       500
                                                            H (G)        for [Mn(Cp*)2 ][Pt(bdt)2 ] (squares) and
                   0                                                     [Fe(Cp*)2 ][Ni(bdt)2 ] (circles) at 1.8 K. The
                       0            20           40                 60   inset shows the low field sigmoidal behavior
                                        Field (kG)                       observed in the case of [Fe(Cp*)2 ][Ni(bdt)2 ].


shown in the inset of Figure 1.22. The magnetization values above the critical
field, in the high field state, are of the same order as those observed in the case of
[Mn(Cp*)2 ][Pt(bdt)2 ] and are considerably inferior than the FM saturation mag-
netization value, Msat = SD gD + SA gA ≈ 3.53 N µB , calculated for SA = 1/2,
gA = 2.06 [49], SD = 1 and gD = 2.5 (the gD value was obtained from the
susceptibility temperature dependence at high temperature). Then the high field
state of [Mn(Cp*)2 ][Ni(bdt)2 ] is consistent with a FIM state. The complexity of
the crystal structure of the [M(Cp*)2 ][M (bdt)2 ] salts prevents clear interpretation
of the magnetic behavior and the discussion of the correlation between the crystal
structures and the magnetic properties.


1.3.4.4                    [Fe(Cp*)2 ]2 [Cu(mnt)2 ]
[Fe(Cp*)2 ]2 [Cu(mnt)2 ] presents a crystal structure based on an arrangement of
DDA type IV chains. Unlike the other compounds based on these types of chains
in [Fe(Cp*)2 ]2 [Cu(mnt)2 ] the chains are neutral, as the acceptor is a dianion,
[Cu(mnt)2 ]2− , and there are no anionic layers in this compound [29]. A view along
the chain direction, [101], is shown in Figure 1.23(a) for [Fe(Cp*)2 ]2 [Cu(mnt)2 ].
In this compound both donors, from the DD pair in the repeat unit, are perpendic-
ular to the chain direction, as shown in Figure 1.23(b). Short intrachain contacts
were observed and involve the Cu from the acceptor and a C from one of the Me
groups in the donor, with a Cu–C distance of 3.562 Å (QW = 0.96). The side-by
side donors are relatively close and C–C distances of 3.826 Å (QW = 1.20) were
observed, involving C atoms from the Cp fragments. No short interionic intrachain
contacts were observed and the chains are essentially isolated.
   For [Fe(Cp*)2 ]2 [Cu(mnt)2 ] the magnetic susceptibility follows Curie–Weiss be-
havior, with θ = −7.95 K [29]. The dominant antiferromagnetic interactions ob-
served for this compound are consistent with the type of contacts, C–S (DA) or
36       1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates




Fig. 1.23. (a) Perspective view of the crystal structure of [Fe(Cp*)2 ]2 [Cu(mnt)2 ] along the
chain direction. (b) View of one of the DDA chains, where d1 is the closest interionic contact
(3.562 Å, QW = 1.05), relatively short DD separations (d2 = 3.826 Å, QW = 1.20) were
detected. Hydrogen atoms were omitted for clarity.

C–C (DD), observed in the crystal structure, as the spin density is expected to be
of the same sign in the atoms involved in the contacts.


1.3.5    Salts with Segregated Stacks not 1D Structures

Most of the ET salts based on decamethylmetallocenium radical donors and
on planar metal dichalcogenide radical anions reported so far present crys-
tal structures with mixed linear chain basic motifs. The only known exception
is [Fe(Cp*)2 ][Ni(mnt)2 ], which exhibits a non-1D crystal structure based on a
D+ [A2 ]2− D+ repeat unit [16]. In the case of this compound the magnetic behavior
is dominated by intradimer antiferromagnetic interactions.
    As most of the work with this type of ET salts was essentially motivated
by the results obtained with the salts based on decamethylmetalocenium donors
and polynitrile planar acceptors, the use of different metallocenium deriva-
tives was limited to a small number of compounds. Among these only the
[Fe(C5 Me4 SCMe3 )2 ][M(mnt)2 ], M = Ni and Pt, which was described previously,
presented crystal structures based on mixed linear chain motifs. The work devel-
oped with salts of other metallocenium derivative donors, including also diamag-
netic donors, was also motivated by the observation of ferromagnetic ordering in
NH4 [Ni(mnt)2 ]H2 O [7], as the magnetic ordering in this compound is only due to
the acceptors. At room temperature, the crystal structure of this salt consists of reg-
ular stacks of eclipsed acceptors and the magnetic behavior of NH4 [Ni(mnt)2 ]H2 O
is dominated by AFM interactions down to ca. 100 K, where a structural transition
                                                1.4 Summary and Conclusions        37

occurs, below this temperature FM interactions become dominant, and magnetic
ordering occurs at 4.5 K.
   In the case of the salts with [M(mnt)2 )]− (M = Ni and Pt) acceptors, the an-
ionic stacks are isolated from each other by the cations and within the stacks the
[M(mnt)2 )]− units form dimers. The magnetic behavior of these compounds is
dominated by AFM interactions between the acceptor units in the dimers.



1.4 Summary and Conclusions

In this chapter we have reviewed the study of ET salts based on metallocenium
radical donors and on planar metal bis-dichalcogenate radical anions. The crystal
structures ( all molecular and crystal structure representations were performed using
SCHAKAL-97 [50]) of these salts were correlated with the magnetic properties,
and the magnetic coupling was analyzed in the perspective of the McConnell I
mechanism.
   The use of the planar metal bis-dichalcogenate acceptors in the preparation
of new molecule-based materials followed the report of bulk ferromagnetism in
decamethylmetallocenium-based ET salts with small polynitrile acceptors such
as TCNE and TCNQ. One of the goals related to the use of the metal bis-
dichalcogenate acceptors is to obtain an increase in the dimensionality in relation
to polynitrile-based ET salts and, as a consequence, to obtain new materials with
interesting cooperative magnetic properties. A large number of new ET salts have
been obtained, presenting a variety of molecular arrangements, which depend es-
sentially on the size of the anionic complexes, on the tendency of the acceptors to
associate as dimers and also on the extent of the π system in the ligands. These salts
exhibit a large variety of magnetic behavior. Different types of magnetic ordering
were observed at low temperatures.
   ET salts with small acceptors such as [M(edt)2 ]− , [M(tdt)2 ]− and [M(tds)2 ]− (M
= Ni, Pd, Pt), where the delocalized electrons are confined to the central M(S2 C2 )2
fragment, present crystal structures based on parallel arrangements of alternated
DADA chains, and in several of these compounds metamagnetic behavior was
observed, in good agreement with the predictions of the McConnell I mechanism.
   In ET salts based on anionic complexes with a large extent of the π system of the
ligands two types of structures were observed, depending on the tendency of the
complexes to form dimers. In the cases of [M(dmit)2 ]− and [M(dmio)2 ]− , which
show a strong tendency to dimerize, in most cases the crystal structure consists
of an arrangement of 2D layers composed of parallel chains, where face-to-face
pairs of acceptors alternate with side-by-side pairs of donors, DDAA. The magnetic
behavior of these ET salts is strongly dependent on the AA interactions, where a
competition between FM and AFM interactions is expected. AFM dominant inter-
38      1 Metallocenium Salts of Radical Anion Bis(Dichalcogenate) Metalates

actions were observed at high temperatures, in good agreement with the McConnell
I mechanism predictions. In the case of [M(Cp*)2 ][Ni(dmit)2 ] (M = Fe and Mn) at
low temperatures FM becomes dominant and in the case of [Mn(Cp*)2 ][Ni(dmit)2 ]
a FM transition occurs at 2.5 K, this is attributed to a change in the type of the dom-
inant magnetic interactions.
   In the case of the ET salts based on anionic complexes presenting a large extent
of the π system but no tendency to exist as dimers, such as [Ni(bds)2 ]− , [M(bdt)2 ]−
(M = Co, Ni and Pt), and [Cu(mnt)2 ]2− , in general the crystal structures are based
on 2D layers consisting of parallel chains where acceptors alternate with pairs of
donors, ADDADD, and these layers are separated by layers of acceptors. In these
compounds the relative orientation of the donor pairs depends on the acceptors.
In the case of [Fe(Cp*)2 ][Ni(bds)2 ] the donors are parallel and with their axes
roughly aligned along the stacking direction, for [Fe(Cp*)2 ]2 [Cu(mnt)2 ] the donors
are also parallel but their axes are perpendicular to the stacking direction, while
for the [M(Cp*)2 ][M (bdt)2 ] salts the donors from the pairs are perpendicular,
one is aligned with the stacking direction and the other is perpendicular to it.
While for [Fe(Cp*)2 ][Ni(bds)2 ] and [Fe(Cp*)2 ]2 [Cu(mnt)2 ] the magnetic behavior
is dominated by the intrachain DA magnetic interactions, which were observed to
be FM and AFM respectively. In the case of the [M(Cp*)2 ][M (bdt)2 ] compounds,
a large number of contacts were observed in the relatively complex structure, and
a variety of magnetic behaviors was observed.
   In spite of the simplicity of McConnell I model, it has shown to be quite ef-
fective in the interpretation of the magnetic behavior in the ET salts based on
metallocenium radical donors and on planar metal bis-dichalcogenate radical an-
ions. However in the compounds presenting complex structures with possible
competition between FM and AFM intermolecular contacts, e. g. the compounds
[M(Cp*)2 ][Ni(α-tpdt)2 ], [M(Cp*)2 ][M (dmit)2 ] and [M(Cp*)2 ][M (bdt)2 ], it was
not possible to achieve a clear understanding of the magnetic behavior with that
model.
   The study of these type of ET salts, which began in the late 80s, has gained
renewed interest in recent years and a large number of compounds are still under
study. Besides the significant number of compounds presenting metamagnetism,
the use of acceptors showing spin polarization, leads to salts presenting other types
of ordering, such as ferro and ferrimagnetism. The use of these types of acceptors
seems quite promising for the preparation of new molecule-based materials.



Acknowledgments

                                                                            ¸
The authors wish to thank their co-workers, in particular D. Belo, S. Rabaca,
R. Meira, I.C. Santos, J. Novoa and R.T. Henriques. The financial support from
Fundac˜ o para a Ciˆ ncia e Tecnologia is gratefully acknowledged.
     ¸a            e
                                                                            References        39

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2 Chiral Molecule-Based Magnets
     Katsuya Inoue, Shin-ichi Ohkoshi, and Hiroyuki Imai




2.1 Introduction

Construction of molecule-based magnetic materials, which possess additional
properties such as conductivity [1–4], photoreactivity [5, 6] or optical properties
is currently a challenging target. Specific goals for these molecule-based magnets
include the rational design of a magnet having (i) a desired geometrical structure
and/or dimensionality and (ii) an optical transparency [7, 8]. The physical charac-
teristics of current interest involve optical properties, particularly with respect to
natural optical activity. In the case of a magnet with non-centrosymmetric structure,
the space-inversion and time-reversal symmetry are simultaneously broken. More-
over, when a magnet is characterized by chiral structure, the magnetic structure of
the crystal is expected to be a chiral spin structure. These magnets display not only
asymmetric magnetic anisotropy but also various types of magneto-optical phe-
nomena such as the non-linear magneto-optical effect and magneto-chiral dichro-
ism [9–11]. Materials in this category are not only of scientific interest, but also
afford the possibility for use in new devices. To obtain non-centrosymmetric and
chiral molecule-based magnets, the geometric symmetry such as chirality must be
controlled in the molecular structure as well as in the entire crystal structure. In this
chapter we describe recent results regarding the construction, structure and mag-
netic and optical properties of molecule-based magnets with non-centrosymmetric
and chiral structures.



2.2 Physical and Optical Properties of Chiral or
    Noncentrosymmetric Magnetic Materials

Magnetic dipole moment and electric dipole moment are extremely important static
forces in solid state physics. The investigation of the properties and the search for
magnetic materials that contain ferroelectric order are subjects of increasing interest
[11, 12]. These multiferroic materials possess specific properties due to the com-
42      2 Chiral Molecule-Based Magnets

bined effect of ferromagnetic nature and ferroelectric nature in the same phase. The
generation of an electric dipole asymmetric field in the crystal is readily achieved
by introduction of chirality or non-centrosymmetric structure. These classes of ma-
terials are not identical to ferroelectric materials; however, they exhibit an electric
dipole asymmetric field in the crystal or material. They are expected to possess
unique magnetic anisotropy, field induced second harmonic generation and the
magneto-chiral optical effect due to the electric dipole asymmetric field.


2.2.1   Magnetic Structure and Anisotropy

In terms of the magnetic structure of chiral or non-centrosymmetric magnetic ma-
terials, the following aspects must be considered: (i) all spins are sited in asym-
metric physical and magnetic positions, and (ii) the materials exhibit an electronic
dipole moment. On the basis of (i), the spins experience an asymmetric magnetic
dipole field. The asymmetric magnetic dipole moments operate the spins aligned
asymmetrically through spin–orbital interaction. In order to facilitate matters, we
assume that the spins are sited on a helix and the ferro- or ferrimagnetic inter-
action occurs between nearest neighbor spins. In this case, the spins are aligned
in helical or conical spin alignment by an asymmetric magnetic dipole field and
ferromagnetic interaction. (Figure 2.1(a) and (b)) Moreover, chiral crystals display
an internal asymmetric electronic dipole field, thus, all magnetic spins are tilted by
Dzyaloshinsky–Moriya interaction. (Figure 2.1(c))


  (a)           (b)             (c)




                                        Fig. 2.1. Expected magnetic structure for chiral
                                        magnets.
              2.2 Properties of Chiral or Noncentrosymmetric Magnetic Materials     43

2.2.2     Nonlinear Magneto-optical Effects

Chiral magnets can exhibit nonlinear magneto-optical effects due to their noncen-
trosymmetric structure and spontaneous magnetization. Over the last 15 years, the
nonlinear magneto-optical phenomena have been intensively studied [14–22] and
magnetization-induced second harmonic generation (MSHG) has received spe-
cial attention due to its large magnetic effects, e. g., the second-order nonlinear
Kerr rotation on the Fe/Cr magnetic film surface is close to 90◦ [16]. In the elec-
tric dipole approximation, second harmonic generation (SHG) is allowed in me-
dia with broken inversion symmetry [23]. Most magnetic materials are, however,
centrosymmetric and, hence, the MSHG are mainly reported from the surface
of magnetic materials [15, 16]. MSHG observations from the bulk crystals are
limited. For antiferromagnetic materials, only chromium oxide Cr2 O3 [17] and
yttrium-manganese oxide YMnO3 [18] are reported to exhibit MSHG. The reports
of bulk MSHG for ferromagnetic materials are limited to Bi-substituted yttrium
iron garnet (Bi:YIG) magnetic film [19–21] and a ternary-metal Prussian blue
analog ((FeII CrII )1.5 [CrIII (CN)6 ]·7.5H2 O)-based magnetic film [22]. The MSHG
             x   1−x
effect is useful for the topography of magnetic domains [24]. Furthermore, apply-
ing a magnetic field can control the MSHG signal [20–22]. Hence, an attractive
method for studying nonlinear optics is to prepare ferromagnetic materials, which
display SH activity. Chiral magnets are advantageous when compared to conven-
tional metal or metal oxide magnetic materials because the space-inversion and
time-reversal symmetry are simultaneously broken. In the following sections, the
theoretical background of bulk MSHG is described and, as an example, the MSHG
effect on a Bi:YIG ferromagnetic film is explained.


2.2.2.1    Theoretical Background of MSHG
In the electric dipole approximation, the polarization, P, can be written as a function
of E [23]:
                                      .
   P = χ (1) · E + χ (2) : EE + χ (3) . EEE,
                                      .                                           (2.1)
where E is the electric field of the incident wave and χ (n) is the nth nonlinear
optical susceptibility tensor. When E is sufficiently weak, Eq. (2.1) is dominated
by the first term and P takes a simple linearized form. In contrast, as E increases,
the second optical response of the second term dominates Eq. (2.1) [23] and the
second optical response, Pi (2ω), can be rewritten as:
               (2)
   Pi (2ω) = χij k (−2ω; ω, ω)Ej (ω)Ek (ω),                                       (2.2)
where Ej (ω) and Ek (ω) are the fundamental optical fields. The second-harmonic
                                 (2)
optical susceptibility tensor (χij k ) is expressed as:
44        2 Chiral Molecule-Based Magnets
                                                                    2
                                                                         
                                                                   Ex
                   (2) (2) (2) (2) (2)                       Ey 
                                                                     2
       Px(2)          χxxx χxyy χxzz χxyz χxzx           χxxy 
                                                          (2)
                                                                    2
                                                                         
                                                                         
      Py(2)  = ε0  χyxx χyyy χyzz χyyz χyzx
                       (2)  (2)  (2)  (2)  (2)            (2)   Ez     
                                                         χyxy                         (2.3)
         (2)           (2)  (2)  (2)  (2)  (2)            (2)    2Ey Ez 
                                                                         
       Pz             χzxx χzyy χzzz χzyz χzzx           χzxy 
                                                                  2Ez Ex 
                                                                  2Ex Ey
where the x, y and z denote the optical field directions in the laboratory frame.
   Next the susceptibilities of magnetic substances will be examined. The linear
susceptibility χ (1) in Eq. (2.1) can be written as a function of its local magnetization
M:
       (1)       cr(0)     magn(1)             magn(2)
     χij (M) = χij + χij K           MK + χij KL MK ML + . . . ,                       (2.4)
                                                                                  cr(0)
where K and L denote the indices of the axial vector M. In Eq. (2.4), χij is
                                                        magn(1)        magn(2)
the nonmagnetic (crystallographic) portion and χij K            and χij KL are the linear
and bilinear magnetic parts that describe the Faraday (or Kerr) effect and magnetic
birefringence, respectively [25–27]. The non-vanishing elements in each tensor
                                                                   (1)
are determined by space-time symmetry operations. The χij is transferred to the
                                                 (1)
dielectric constant εij , i.e., εij = δij + 4π χij (δij : Kronecker’s delta). Usually, δij
describes the magneto-optical effects such as the Faraday effect.
   In ferromagnetic substances, which have noncentrosynmetric structures, the si-
multaneous breaking of space and time-reversal symmetry leads to the coexistence
of crystallographic and magnetization-induced electric-dipole contributions to the
nonlinear optical susceptibility. Under these circumstances, the second-order non-
                                   (2)
linear susceptibility tensor, χij k , can be written as:
       (2)         cr(0)   magn(1)            magn(2)
     χij k (M) = χij k + χij kL      ML + χij kLM ML MM + . . . ,                      (2.5)
         cr(0)                                                     magn(1)   magn(2)
where χij k is the crystallographic portion and the terms χij kL + χij kLM + . . .
describe the effect of the local magnetic order [28]. These magnetic terms lead to
magneto-optical effects in SHG. The total SH polarization of a magnetic medium
in the electric dipole approximation can be written as:
                                  magn(1)
     Pi (2ω) = Picr(0) (2ω) + Pi            (2ω)
                   cr(0)
             =   χij k (−2ω; ω, ω)Ej (ω)Ek (ω)
                      magn(1)
                 +χij kL (−2ω, ω, ω, 0)Ej (ω)Ek (ω)ML (ω)           + ...,             (2.6)
                          magn(1)
where Picr(0) (2ω) and Pi          (2ω) are the crystallographic and magnetic contribu-
                                                              magn(1)
tions, respectively. The properties of Picr(0) (2ω) and Pi            (2ω) are remarkably
             cr(0)                                          cr(0)
different. Pi (2ω) is represented by a polar tensor χij k of rank 3 as described in
                   magn(1)                                          magn(1)
Eq. (2.3), but Pi          (2ω) is described by an axial tensor χij kL of rank 4 [14].
                                       cr(0)              magn(1)
In nonabsorbing materials, the χij k is real, but χij kL          is an imaginary tensor
               2.2 Properties of Chiral or Noncentrosymmetric Magnetic Materials     45

[14]. The corresponding nonlinear waves have a 90◦ phase shift and thus cannot
interfere. However, if one or both of them are complex, then interference is al-
lowed and leads to effects, which are linear to the magnetization. In addition, the
                                                magn(1)
temperature dependence of Picr(0) (2ω) and Pi           (2ω) are different; Picr(0) (2ω)
                                                                   magn(1)
probes the degree of a crystal lattice noncentrosymmetry, but Pi           (2ω) reflects
a temperature variation in the magnetization.


2.2.2.2    Experimental Set-up
Figure 2.2 shows schematically the experimental set-up used for MSHG mea-
surements in the authors’ laboratory. Incident radiation is provided from an optical
parametric amplifier (Clark-MXR Vis-OPA; pulse width: 190 fs; repetition: 1 kHz)
pumped by a frequency-doubled Ti:Sapphire laser (Clark-MXR CPA-2001; photon
energy: 1.60 eV) or a Q-switched Nd:YAG laser (HOYA Continuum Minilite II;
pulse width: 6 ns; repetition: 15 Hz). Transmitted SH light is detected by a photo-
multiplier through color filters and a monochromator. Polarization combinations
between the incident and SH radiation are adjusted using a babinet-soleil compen-
sator and a pair of polarizers. A cryostat controls the temperature of the samples.
The magnetic field is applied along the direction of light propagation using the
electromagnet coil of a magneto-optical meter.


                                       Sample

                        Filter                    Filter    Monochromator
 S-polarized light

   Laser                                                                PMT

               Polarizer /
                Wave plate
Ti:Sapphire laser                Electromagnet             Analyzer


                             External magnetic field

Fig. 2.2. Schematic illustration of the SHG measurement system. The magnetic field was
applied along the light propagation direction using an electromagnetic coil.




2.2.2.3    Bulk MSHG of a Ferromagnetic Material
The magnetic terms of the second-order nonlinear susceptibility in Eq. (2.5) lead
to the magneto-optical effects in SHG. For example, Cr2 O3 has a centrosymmetric
                                                                              cr(0)
structure (point group 3m) and above the N´ el temperature all elements of χij k
                                            e
46        2 Chiral Molecule-Based Magnets

are zero. However, a noncentrosymmetric spin ordering (magnetic point group
                                                                       magn(1)
3m) below the N´ el temperature creates non-zero elements of χij kL , inducing
                  e
SH radiation [17]. In contrast, strain-induced Bi:YIG has a noncentrosymmetric
structure. Thus, below the magnetic ordering temperature (TC ) the tensor elements
          cr(0)     magn(1)
in both χij k and χij kL are non-zero [19–21]. As an example the MSHG effect on
the (111) film of Bi:YIG is described. In a Bi:YIG film, the distortion of the crystal
structure breaks the space-inversion symmetry, which is evident in the SHG [29]
and linear magnetoelectric effects. The crystal structure is in a non-centrosymmetric
point group, 3m (C3v ), and has a threefold axis along the normal of the film. In this
situation, the non-linear polarization is expressed by:
     Px(2) = xxxx (Ex − Ey ) + 2xxzx Ex Ex
              (2)   2    2       (2)


     Py(2) = −2xxxx Ex Ey + 2xxzx Ex Ey
                (2)           (2)


     Pz(2) = xzxx (Ex − Ey ) + xzzz Ez
              (2)   2    2      (2) 2
                                                                                 (2.7)

where the x and y axes are perpendicular to the mirror plane m (y//[110]). This
equation shows that SHG is allowed at normal and oblique incidences. Pisarev et
al. measured the SHG intensity (I ) angular dependence at the normal incidence
of the pump radiation as function of the rotation angle (ϕ) of the film around its
normal. I is described by:
     I = E 4 cos2 (3ϕ + α)                                                       (2.8)
where α is the angle between the axes of the polarizer and the analyser. This equation
can predict the angle dependence of I and is shown in Figure 2.3(a) and (b). In a
nonmagnetized (111) film, the SHG signal is observed with a 60◦ periodicity in
the rotational anisotropy. In fact, Pisarev et al. observed such a SHG pole-figure
pattern.
   In 1997, Pavlov et al. observed the magnetization-induced SHG effects of this
(111) film by applying a transversal magnetic field. In this film, the SHG rotational
anisotropy Iij (2ω, ϕ) is expressed as:
     IXX (2ω, ϕ) = E 4 (A cos2 3ϕ + BM 2 + 2CM cos 3ϕ)
     IY Y (2ω, ϕ) = E 4 A sin2 3ϕ ,                                              (2.9)
where XX and Y Y denote input-output polarizations of the light in the laboratory
environment. In addition, A, B, and C are combinations of real and imaginary
           cr(0)     magn(1)
parts of χij k and χij kL . For the XX polarization combination, a linear magnetic
response is expected to be observed as the calculated plots in Figure 2.3(a) and (b),
                          (2ω) is zero. The horizontal line passing through 0◦ and 180◦
                  magn(1)
but for Y Y the Pi
on each plot corresponds to the mirror plane, m. Figure 2.3(c) shows the observed
rotational anisotropy of the IXX at 295 K. The experimental data is consistent with
the tensor analysis prediction. The magnetized (111) film showed a 120◦ periodicity
for XX polarizations, with a 60◦ rotation +M and −M states. Thus, applying an
                      2.2 Properties of Chiral or Noncentrosymmetric Magnetic Materials      47

(a)       12

          10

          8

          6

          4

          2

          0

                0     50         100   150         200   250     300        350




                                          90
                                        15


(b)
                           120                             60




                150                                                    30




          180                                                             0
                                             0                          15




                210                                                    330




                           240                             300

                                             270




(c)


      180º                                                                        0º
Fig. 2.3. MSHG of (111) film Bi:YIG. Predicted angle dependence of SH intensity (a) and
rotational anisotropy (b) of the SHG intensity on (111) film, based on Eq. (2.8) and (2.9). Thin
solid, thick solid, and dotted lines are zero, positive, and negative external magnetic fields,
respectively. (c) Data of Pavlov et al. [20]: solid circles denote +M state and open circles
the −M state. XX denotes the input-output polarization combinations. Magnetic contrast
(difference between the +M and −M theoretical fits) is indicated by dark (positive) and light
(negative) shadowed areas.



external magnetic field can change the SHG response. A, B, and C are obtained
by fitting the data to Eq. (2.9). Figure 2.4 shows the temperature variations of the
crystallographic (A), interference (2CM), and pure magnetic (BM2 ) contributions
to the SHG intensity for the (111) film. The crystallographic contribution decreases
linearly with temperature, but the magnetization-related contributions vanish at Tc .
The interference term of 2CM shows a (1 − T /Tc ) dependence, but the pure
magnetic portion of BM2 vanishes at Tc .
48           2 Chiral Molecule-Based Magnets




                                                                      Fig. 2.4. The observed tempera-
                                                                      ture variations of crystallographic,
                                                                      magnetization-induced, and interfer-
                                                                      ence terms in the SHG intensity for
                                                                      the (111) film. Reproduced with per-
                                                                      mission from Ref. [20].


   Section 2.5 will show another example of the bulk MSHG effect
on ferromagnetic material composed of an electrochemically synthesized
(FeII CrII )1.5 [CrIII (CN)6 ] · 7.5H2 O magnetic film.
   x    1−x




2.2.3         Magneto-chiral Optical Effects

In 1982, Wagniere and Meier theoretically predicted the influence of a static mag-
netic field on the absorption coefficient of a chiral molecule [9]. In 1984, Barron
and Vbrancich referred to this effect as magneto-chiral dichroism (MChD). This
effect is a combined effect of the natural optical activity of chiral material and
the Faraday effect of the magnet (Figure 2.5) [10]. This MChD effect involves the
absorption coefficient of materials, which is dependent upon the direction of mag-
netization and light. In 1997, Rikken and Raupach observed the MChD effect of
tris(3-trifluoroacetyl-±-camphorato)europium (III) in the paramagnetic state [11].


(a)
 [VKXKVE# NCEKVR1 NCTWVC0 #10                                 (c)                    M
                                                              hν
                            Chiral Molecule                                  Chiral magnet crystal
                                                                     I0                              If
(b)            ν
             R J

                                                                                      M
VEGHH' [CFCTC(
 [VKXKVE# NCEKVR1 EKVGPIC/ #1/
                                                                                                               hν
                                                                             Chiral magnet crystal
                                 VGPIC/                              Ib                                   I0
               ν
              R J
                                                                              I            I
                                                                                  f            b
Magneto-Chiral Dichroism                          NOA + MOA



Fig. 2.5. Schematic illustration of (a) natural optical activity, (b) Faraday effect, and (c)
magneto-chiral dichroism.
                                         2.3 Nitroxide-manganese Based Chiral Magnets   49

The MChD effect depends on the magnitude of the magnetic moment. It is impor-
tant to generate fully chiral molecule-based magnets which are expected to exhibit
a strong MChD effect.



2.3 Nitroxide-manganese Based Chiral Magnets

From the conformation study of the Mn(hfac)2 complexes with oligo-nitroxide
radicals, (see Vol. II, Chapter 2), one-dimensional complexes exclusively form
isotactic polymeric chains. In these complexes, two tert-butylaminoxyl groups are
rotated out of the phenylene ring plane in a conrotatory manner; each molecule
in the crystal has no symmetry element and is, therefore, chiral, i. e., R or S.
Consequently, the 1-D polymeric chains are isotactic as all units are of the same
chirality. The crystal lattice as a whole is achiral due to the presence of enantiomeric
chains. When chiral organic radicals are employed in lieu of achiral biradicals, the
chiral substituent group will induce chirality in the main one-dimensional chain.


2.3.1    Crystal Structures

On the basis of requirements of molecular design, bismonodentate bisaminoxyl
radical 1 [30] or nitronylnitroxide radical 2 [31] with a chiral organic substituent
must be employed as bridging ligands of manganese(II) bishexafluoroacetylacet-
onate, MnII (hfac)2 . X-ray crystal structure analysis revealed that both complexes
[1·Mn(hfac)2 ]n and [2·Mn(hfac)2 ]n crystallize in the chiral space groups P 1 and
P 21 21 21 , respectively. The molecular structures of these complexes are depicted
in Figure 2.6. The MnII ion exists in an octahedral coordination environment with
four oxygen atoms of two hfac anions and two oxygen atoms of different radical
molecules in both crystals. As a result, the MnII ion and the chiral radical 1 or 2
form a one-dimensional structure. The shortest interchain contacts between the Mn
ion and the oxygen atom O of the radical’s NO group exceeds 9 Å, whereas the
shortest MnII –MnII interchain distance is greater than 10 Å in both crystals. In the

                                         S
             O                   O
                     S


 O                   O
     N           N       O               O
                             N       N


         1                       2               Scheme 2.1
50       2 Chiral Molecule-Based Magnets




Fig. 2.6. Crystal structures of (a) [1·Mn(hfac)2 ]n and (b) [2·Mn(hfac)2 ]n .


crystal of [1·Mn(hfac)2 ]n , the bisaminoxyl radicals are bound to the MnII ion in
trans-coordination to one another. In this complex, two tert-butylaminoxyl groups
are rotated out of the phenylene ring plane in a conrotatory manner; all molecules
in the crystal display S axis chirality. Since no inversion centers are present in this
space group, the chains are isotactic as all units and the crystal lattice as a whole,
are chiral.
   In the case of [2·Mn(hfac)2 ]n , The radicals are bound to the MnII ion in cis-
coordination to one another. A detailed description of the coordination sphere of
the MnII ion must take into account the possible configurations resulting from
the cis-coordination arrangement, which can lead to the or configuration. In
this complex, the metal center exhibits the all configuration. Due to the use of
the chiral ligand, the complex crystallized in a chiral space group, therefore, no
   chirality of the Mn(II) exists in this crystal. The absolute configuration of the
metal center is often affected by the chirality of organic ligands; additionally, our
result shows a similar effect of the chiral carbon atom of 1. No inversion centers
are present in this space group; consequently, the chains are isotactic as all units,
and the crystal lattice as a whole, are chiral.
                                  2.3 Nitroxide-manganese Based Chiral Magnets           51

2.3.2    Magnetic Properties

[1·Mn(hfac)2 ]n : The µeff value of 4.91 µB (χmol T = 3.01 emu K mol−1 ) at 300 K
is less than the theoretical value of 6.43 µB for paramagnetic spins of two 1/2 spins
of an organic radical and one 5/2 spin of d5 MnII , whereas it is larger than that of
3.87 µB for two 1/2 spins of organic radicals and 5/2 spins of d5 MnII in antifer-
romagnetic coupling. In concert with a lack of a minimum at lower temperature,
the room temperature µeff value suggests the occurrence of strong (more negative
than −300 K) antiferromagnetic coupling between the MnII ion and the aminoxyl
radical as a ligand (Figure 2.7). When the measurement was conducted in 5 Oe, the
magnetic susceptibility displayed a cusp at 5.4 K (Figure 2.7, inset). Magnetization
at 1.8 K revealed metamagnetic behavior (Figure 2.8). A saturation magnetization
value of ca. 2.7 µB was reached at 1.8 K at 3 T. When the interaction between the
MnII ion and 1 is antiferromagnetic, the value for [1·Mn(hfac)2 ]n is expected to be
3 µB (5/2 − 2/2 = 3/2), which is in close agreement with the observed value. This
magnetic behavior is similar to that found in a Mn(hfac)2 complex with non-chiral
biradicals. (See Vol. II, Chapter 2).
    [2·Mn(hfac)2 ]n : The µeff value of 6.48 µB (χmol T = 5.25 emu K mol−1 ) at 300 K
is equal to the theoretical value of 6.16 µB for isolated spins of one 1/2 spin of an
organic radical and one 5/2 spin of d5 MnII ion. The µeff value increased with de-
creasing temperature. In concert with the lack of a minimum at lower temperature,
the room temperature µeff value suggests the occurrence of strong (more negative




Fig. 2.7. Temperature dependence of effective magnetic moment for the polycrystalline sample
of [1·Mn(hfac)2 ]n . Inset: Temperature dependence of the magnetization in 5 Oe.
52       2 Chiral Molecule-Based Magnets




Fig. 2.8. Field dependence of the magnetization of [1·Mn(hfac)2 ]n .




Fig. 2.9. Temperature dependence of effective magnetic moment for the polycrystalline sample
of [2·Mn(hfac)2 ]n . Inset: Temperature dependence of the magnetization in 5 Oe.


than −300 K) antiferromagnetic coupling between the nitronyl nitroxide radical
and the MnII ion (Figure 2.9). Magnetization measurements have been performed
at 2 K (Figure 2.10). Magnetization increases very rapidly, reaching a plateau of ca.
3.6 µB at 1.5 T. When the interaction between the MnII ion and 2 is antiferromag-
netic, the value for [2·Mn(hfac)2 ]n is expected to be 4 µB (5/2−1/2 = 4/2), which
                2.4 Two- and Three-dimensional Cyanide Bridged Chiral Magnets     53




Fig. 2.10. Field dependence of the magnetization of [2·Mn(hfac)2 ]n .

is in close agreement with the observed value. When the field cooled magnetization
(FC) and zero field cooled magnetization measurements (ZFC) were carried out in
a much lower field of 5 Oe over the temperature range 1.8 K to 20 K, the magnetic
moment value increased sharply at ca. 5 K. Both the measurements exhibited a
plateau below 4.2 K (Figure 2.9, inset). AC susceptibility measurements revealed
that [2·Mn(hfac)2 ]n behaves as a ferrimagnet at 4.6 K.



2.4 Two- and Three-dimensional Cyanide Bridged Chiral
    Magnets

The major strategy relating to crystal design for magnetic materials exhibiting
higher ordering temperature and spontaneous magnetization involves generation
of an extended multidimensional array of paramagnetic metal ions with bridg-
ing ligands. The cyanide-bridged Prussian-blue systems are well known as the
most suitable for this purpose. These systems are generally obtained as bimetallic
assemblies with a three-dimensional cubic cyanide network by the reaction of hex-
acyanometalate [MIII (CN)6 ]3− with a simple metallic ion MII [32–35]. Extensive
research has led to the production of a material displaying magnetic ordering at Tc
as high as 372 K [36]. On the one hand, the attention of some chemists has been
                                                                    ¯
focused on specific coordination sites around MII in this system. Okawa and Ohba
have found that some organic molecules can be incorporated into this system as a
chelating or bidentate ligand L to MII [37, 38]. The incorporation of such a ligand
leads to the blockade of some coordinated linkages to MII of cyanide groups in
[MIII (CN)6 ]3− . It follows that various novel structures have been obtained in this
system, depending on the organic molecule. This method affords the possibility
54        2 Chiral Molecule-Based Magnets

of crystal design in cyanide-bridged systems. In this section, we will describe the
crystal design of a chiral magnet utilizing a cyanide-bridged system; additionally,
several examples are presented.


2.4.1     Crystal Design

When chiral molecule-based magnets exhibiting higher ordering temperature and
spontaneous magnetization are constructed, the chirality in the entire crystal struc-
ture as well as the high dimensionality of the extended arrays must be maintained. It
is more convenient for the cyanide-bridged systems to circumvent these difficulties
in order to construct higher-T c chiral magnets. Some chiral diamine ligands serve
as candidates for the chiral source in the entire crystal structure of this system. In
other words, a target magnetic compound can be generated by the reaction between
a hexacyanometalate [MIII (CN)6 ]3− and a mononuclear complex [MII (L)n ] based
on chiral diamines, as shown in Scheme 2.2. Note, however, that, in order to obtain
a ferromagnet, the combination of MII and MIII in the crystallization stage which
generates ferromagnetic interaction through MIII -CN-MII must be known. This
method holds many possibilities with respect to obtaining various chiral magnets
via alteration of the component substances.


                    O




  H 2N    NH2     H 2N    NH2      H 2N     NH2



(R) or (S)-1,2-   (R) or (S)-   (R, R) or (S, S)-
diaminopropane    alanamide     cycrohexanediamine   Scheme 2.2




2.4.2     Two-dimensional Chiral Magnet [39]

2.4.2.1     Crystal Structure
This compound crystallizes in the non-centrosymmetric P 21 21 21 space group. X-
ray crystal structure analysis reveals that it consists of two-dimensional bimetallic
sheets. Each [Cr(CN)6 ]3− ion involves four cyanide groups in order to bridge with
four adjacent MnII ions within the ab plane (Figure 2.11). The adjacent Cr–Mn dis-
tances through cyanide bridges within the ab plane are approximately 5.35 Å, which
is slightly longer than those in the 3D chiral magnet K0.4 [CrIII (CN)6 ][MnII (S)-
pn](S)-pnH0.6 (see next section). In addition to one MnII and one [Cr(CN)6 ]3− ion,
an asymmetric unit in this crystal also associates with one mono-protonated (S
or R)-diaminopropane ((S or R)-pnH) and two water molecules. An octahedron
around a MnII ion is completed with one (S or R)-pnH and one water molecule
                2.4 Two- and Three-dimensional Cyanide Bridged Chiral Magnets   55




Fig. 2.11. Crystal structure of [Cr(CN)6 ][Mn(S or R)-pnH(H2 O)](H2 O)].


which separate adjacent bimetallic sheets along the c-axis. The shortest and the
second shortest inter-sheet metal separation are observed between the Cr and Mn
atoms (the distances are 7.31 and 7.77 Å, respectively). In contrast, the shortest
inter-sheet homo-metal contacts are more than 8 Å. This observation suggests that
the ferromagnetic interaction operates preferentially between bimetallic sheets.



2.4.2.2   Magnetic Properties
The temperature dependence of magnetic susceptibility is shown in Figure 2.12,
using χmol T versus T plots. The χmol T value is 5.01 emu K mol−1 (6.33 µB ) at
300 K, and decreases with decreasing temperature down to a minimum value of
3.65 emu K mol−1 (5.41 µB ) at 85 K. The extrapolated effective magnetic moment
value is 7.07 µB , which is in close agreement with the non-coupled paramagnetic
high spin in the high temperature limit of 5/2+3/2 → 7.07 µB (Figure 2.12, inset).
Upon further cooling, the χmol T value increases and diverges. The 1/χmol versus
T plot in the range 300 to 140 K obeys the Curie–Weiss law with a Weiss temper-
ature θ = −77.0 K. This indicates that the antiferromagnetic interaction operates
between the adjacent CrIII and MnII ions through cyanide bridges at temperatures
above 140 K. The abrupt increase in the χmol T value around 40 K suggests the
onset of three-dimensional magnetic ordering.
   Both the field cooled (FC) and the zero field cooled magnetization measurements
(ZFC) with a low applied field (5 G) in the temperature range 5 K to 100 K display
a longrange magnetic ordering below 38 K (Figure 2.13). As shown in Figure 2.14,
the magnetization (M) increases sharply with an applied field and is saturated
rapidly. The saturation magnetization value of MS = 2 µB is in close agreement
with the theoretical value of antiferromagnetic coupling between CrIII and MnII
ions. The hysteresis loop (the remnant magnetization of 1800 emu G mol−1 and the
coercive field of 10 Oe) was observed at 5 K, suggesting a soft magnetic behavior.
56     2 Chiral Molecule-Based Magnets




Fig. 2.12. Temperature dependence of the χmol T value of [Cr(CN)6 ][Mn(S or R)-
pnH(H2 O)](H2 O)]. Inset: χeff − 1/T plot.




Fig. 2.13. Temperature dependence of the magnetization of [Cr(CN)6 ][Mn(S or R)-
pnH(H2 O)](H2 O)] in a low field (5 Oe).
                2.4 Two- and Three-dimensional Cyanide Bridged Chiral Magnets            57




Fig. 2.14. Field dependence of the magnetization of [Cr(CN)6 ][Mn(S or R)-pnH(H2 O)](H2 O)]
at 5 K.

2.4.3     Three-dimensional Chiral Magnet [40]

2.4.3.1    Crystal Structure
This compound crystallizes in the non-centrosymmetric P 61 space group. X-ray
crystallography reveals that it consists of a three-dimensional chiral polymer
(Figure 2.15). Each [Cr(CN)6 ]3− ion utilizes two cyanide groups to bridge two
MnII ions forming helical loops along the c-axis, whereas two of the remaining




                                                  Fig. 2.15. Crystal structure of
                                                  K0.4 [CrIII (CN)6 ][MnII (S)-pn](S)-
                                                  pnH0.6 .
58        2 Chiral Molecule-Based Magnets

four cyanide groups connect the adjacent loops. The shortest intra- and interloop
Mn–Cr distances are 5.21 and 5.31 Å, respectively. The MnII ion exists in an
octahedral environment with four cyanide groups of four distinct [Cr(CN)6 ]3− and
two nitrogen atoms of (S)-pn. In this crystal, two kinds of counter ion are included
so as to maintain overall neutrality. One is a potassium ion and the other is mono-
protonated diaminopropane (S)-pnH; the site occupancy of which is 0.4 : 0.6,
respectively. These counter ions are located within the cavity of helical loops.


2.4.3.2    Magnetic Properties
The magnetic behavior of the crystal under 5000 G is shown in Figure 2.16 as a
plot of χmol T versus T . The χmol T value is 4.88 emu K mol−1 (6.25 µB ) at room
temperature and decreases with decreasing temperature down to a minimum value
of 3.66 emu K mol−1 (5.41 µB ) at 110 K. Upon further cooling, the χmol T value
increases. The 1/χmol versus T plot in the range 300 to 110 K obeys the Curie–
Weiss law with a Weiss temperature θ = −30.9 K. This observation indicates that
the antiferromagnetic interaction operates between the adjacent CrIII and MnII ions
through cyanide bridges at temperatures above 110 K. The abrupt increase in the
χmol T value around 60 K suggests the onset of three-dimensional magnetic order-
ing. The extrapolated effective magnetic moment value of 7.2 µB is in close agree-
ment with the theoretical value in the high temperature limit (Figure 2.16, inset).
   Low-field magnetization measurements under an applied field of 5 G in the
temperature range 5 to 100 K were performed in order to confirm a longrange




Fig. 2.16. Temperature dependence of the χmol T value of K0.4 [CrIII (CN)6 ][MnII (S)-pn](S)-
pnH0.6 . Inset: χeff − 1/T plot.
                 2.4 Two- and Three-dimensional Cyanide Bridged Chiral Magnets             59




Fig. 2.17. Temperature dependence of the magnetization of K0.4 [CrIII (CN)6 ][MnII (S)-pn](S)-
pnH0.6 in a low field (5 Oe).




Fig. 2.18. Field dependence of the magnetization of K0.4 [CrIII (CN)6 ][MnII (S)-pn](S)-pnH0.6
at 5 K.

magnetic ordering around 60 K. Both field cooled magnetization (FCM) and the
zero field cooled magnetization (ZFCM) curves show an abrupt increase in M
below 53 K (Figure 2.17).
   The field dependence of magnetization at 5 K also reveals that the magnetiza-
tion (M) is saturated rapidly in the presence of an applied field. (Figure 2.18) The
saturation magnetization MS = 2 µB is close to the theoretical value of antifer-
60      2 Chiral Molecule-Based Magnets

romagnetic coupling between CrIII and MnII ions. A hysteresis loop (the remnant
magnetization of 30 emu G mol−1 and the coercive field of 12 G) was observed at
2 K, suggesting soft magnetic behavior.


2.4.4   Conclusion

The present compounds provide proof that the cyanide-bridged system affords
much potential for the design of molecule-based materials. The use of chiral lig-
ands in the synthesis of compounds based on the cyanide-bridged system leads to
two- and three-dimensional chiral magnetic networks. These systems are candi-
dates for asymmetric magnetic anisotropy, as well as for magneto-optical properties
including magneto-chiral dichroism (MChD). This phenomenon is attributable to
the ease with which these systems modulate optical activity, magnetization, order-
ing temperature and crystal color by changing paramagnetic metal ions and organic
chiral ligands.



2.5 SHG-active Prussian Blue Magnetic Films

Electrochemically synthesized ternary metal Prussian blue analog-based magnetic
films can display MSHG. (FeII CrII )1.5 [CrIII (CN)6 ]·7.5H2 O magnetic films show
                                x   1−x
a Faraday effect in the visible region and bulk SHG. Applying an external magnetic
field rotates the polarization plane of the SH light and the rotation angle is greater
than that from the Faraday effect. This SH rotation is caused by the magnetic
linear term in the second-order nonlinear optical susceptibility. In this section, the
magnetic properties, Faraday effect, SHG, and MSHG effects of these magnetic
films are described.


2.5.1   Magnetic Properties and the Magneto-optical Effect

Figure 2.19 illustrates schematically the crystal structure of Prussian blue analogs.
The thin films composed of (FeII CrII )1.5 [CrIII (CN)6 ]·7.5H2 O are prepared by
                                      x   1−x
reducing aqueous solutions, which contain K3 [Cr(CN)6 ], CrCl3 , and FeCl3 onto
SnO2 -coated glass electrodes under aerobic conditions [41]. Insoluble polynu-
clear metal cyanide thin films, which are ca. 2 µm thick, are deposited onto
an electrode surface when the reduction potential vs. SCE is −0.84 V and
the loaded electrical capacity is 600 mC. The color changes of the obtained
(FeII CrII )1.5 [CrIII (CN)6 ]·7.5H2 O transparent films, which are dependent on x,
   x    1−x
are due to the intervalence transfer (IT) band of FeII and CrIII in the visible region.
                                                                  2.5 SHG-active Prussian Blue Magnetic Films              61



                           O
                               H
                                H
                                     H
                                             H         O
                                                      HH
                                                                                   BIII
                               O             H           O
                                                     H

                                         H       H
                                                                                   C
                                                                   O
                                         O                                         N
                                                                  H H

                                                       O
                                                             H
                                                                    H
                                                                            O
                                                                                   AII
                                                            H H
                                                            O           H
                                                                  H
   O
                                                                  H H
H H
                                                                   O
       H         O
             H                                                                            Fig. 2.19. Schematic illustra-
                  H
                 H  O
                                                                                          tion of Prussian blue analogs:
                                                                                          AII [BIII (CN)6 ]·7.5H2 O.
                                                                                            1.5



For example, the films for x = 0, x = 0.20, x = 0.42, and x = 1 are colorless,
violet, red, and orange, respectively. As indicated in Figure 2.20, their IT bands
shift from a shorter wavelength to a longer wavelength in the visible region as x
decreases; e. g., λmax = 434 nm (x = 1); 496 nm (x = 0.42); 506 nm (x = 0.20);
510 and 610 nm (x = 0) [41].
   The magnetic susceptibility and magnetization of these thin films are depen-
dent on x. The saturation magnetizations (Ms ) for x = 0 and x = 1 at fields up
to 5 T were 1.0 µB and 6.7 µB , respectively, and intermediate compositions vary
systematically as a function of x. The minimum value of Ms is observed in a film
with an x value close to 0.11 because the parallel spins (CrIII and FeII ) and the
anti-parallel spins (CrII ) are partially or even completely canceled, depending on
x. In addition, the magnetization vs. temperature curves below Tc exhibit various


       1.5




       1.0
                                                     1
Abs.




                                                     0.42
                                                     0.20
       0.5                                           0



       0.0
                     400       600               800         1000           1200
                                                                                   Fig. 2.20. Vis-near-IR absorption spectra
                           Wavelength (nm)                                         for x = 0, 0.20, 0.42, and 1.
  62                                  2 Chiral Molecule-Based Magnets

                              2000

                                                                           1
                              1500
                                                                           0
Magnetization (G cm3 mol-1)



                                                                           0.08
                              1000
                                                                           0.11
                                500
                                                                           0.42
                                                                           0.13
                                  0


                               -500
                                                                                  Fig. 2.21. Magnetization vs.
                              -1000
                                                                                  temperature plots of elec-
                                                                                  trochemically synthesized
                                        0     50     100     150     200   250    (FeII CrII )1.5 [CrIII (CN)6 ]
                                                                                      x 1−x
                                                   Temperature (K)                ·7.5H2 O films in a field of 10 Oe.

  behaviors, which are dependent on x (field = 10 G) (Figure 2.21). Particularly, for
  compounds in which x is between 0.11 and 0.15, negative values of magnetization
  are exhibited below particular temperatures (compensation temperatures, Tcomp )
  [42–44]. Molecular field theory qualitatively reproduces these temperature depen-
  dent observations when two types of exchange couplings between nearest neighbor
  sites, FeII –CrIII (JFeCr = 0.9 cm−1 ) and CrII –CrIII (JCrCr = −9.0 cm−1 ), are consid-
  ered. Therefore, these phenomena are observed because the positive magnetization
  due to the CrII sublattice and the negative magnetizations due to the FeII and CrIII
  sublattices have different temperature dependences.
     Due to their transparency, the Faraday effect of Prussian blue analog-based
  magnetic films is in the visible region [45]. The Faraday ellipticity (FE) spectrum
  of the film for x = 1 shows a strong positive peak due to an IT band around 450 nm
  (Figure 2.22(a)). For this film, the Faraday effect increases below the Tc and the
  magnitude increases as the temperature decreases. In the Faraday rotation (FR)
  spectra, the dispersive line is observed at the same wavelength (Figure 2.22(b)).
  As x decreases, the FE peak shifts to a longer wavelength and their intensities
  gradually decrease. Figure 2.22(c) and (d) show the FE and FR spectra of a film
  where x = 0.33 at 50 K in an applied magnetic field of 10 kOe. The observed
  Faraday rotation angle is less than 0.22◦ for a given thickness at wavelengths
  between 350 and 900 nm and the rotation angles at wavelengths of 775 and 388 nm
  were 0.065◦ and 0.079◦ , respectively.
  a                                            0.12                                                                                                   0.12
                                                                                                            b
                                               0.10                                                                                                   0.10
                                                                                                                                                      0.08
                                               0.08
                                                                                                                                                      0.06
                                               0.06                                                                                                   0.04

                                               0.04                                                                                                   0.02
                                                                                                                                                      0.00
                                               0.02




               Faraday ellipticity (degree)
                                                                                                                                                      -0.02
                                               0.00




                                                                                                                Faraday rotation (Angle/degree)
                                                                                                                                                      -0.04
                                                      400   450   500   550   600   650   700   750   800
                                                                                                                                                              400   450   500   550   600   650    700   750   800
                                                                        Wavelength (nm)
                                                                                                                                                                                Wavelength (nm)

c                                             0.12                                                                                                     0.10
                                                                                                            d                                          0.08
                                              0.10
                                                                                                                                                       0.06
                                              0.08                                                                                                     0.04
                                                                                                                                                       0.02
                                              0.06
                                                                                                                                                       0.00
                                              0.04                                                                                                    -0.02

                                              0.02                                                                                                    -0.04
                                                                                                                                                      -0.06
                                              0.00                                                                  Faraday rotation (Angle/degree)
                                                                                                                                                      -0.08




    Faraday ellipticity (Angle/ degree)
                                              -0.02                                                                                                   -0.10
                                                      400   450   500   550 600 650       700   750   800                                                     400   450   500   550  600     650   700   750   800
                                                                                                                                                                                Wavelength (nm)
                                                                                                                                                                                                                     2.5 SHG-active Prussian Blue Magnetic Films




                                                                        Wavelength (nm)

Fig. 2.22. Faraday spectra of (FeII CrII )1.5 [CrIII (CN)6 ]·7.5H2 O films in an applied magnetic field of 10 kOe: Faraday ellipticity (a) and Faraday
                                 x 1−x
                                                                                                                                                                                                                     63




rotation (b) for x = 0 at 7 K. Faraday ellipticity (c) and Faraday rotation (d) for x = 0.33 at 50 K.
64      2 Chiral Molecule-Based Magnets

2.5.2    Nonlinear Magneto-optical Effect

The crystal structure of Prussian blue analogs is centrosymmetric face-centered
cubic (fcc) and hence the bulk SHG should be forbidden in the electric dipole ap-
proximation. In fact, powder samples of (FeII CrII )1.5 [CrIII (CN)6 ]·7.5H2 O do not
                                                x   1−x
exhibit SHG over the entire range of x. However, the electrochemically synthesized
films, which incorporate three metal ions, show SHG. Figure 2.23(a) shows the SH
intensity dependence on x at room temperature in films that are approximately 2 µm
thick. The SH signal for the electrochemically synthesized films is observed when
0 < x ≤ 0.42 [46] and its intensity increases drastically with x. Figure 2.23(b)
shows the SH intensity in the films when x = 0.33 as a function of the film thick-
ness. The observed oscillation of the SH intensity indicates a coherent correlation,
clearly demonstrating that the observed SHG is from the bulk crystal and not from
the surface. Figure 2.23(c) shows the Maker’s fringe patterns of the film when x =
0.25 for the polarization combinations of PIN –POUT and SIN –POUT . The SH intensity
is zero at 0◦ and increases monotonically as the angle changes up to 55◦ . This fringe
pattern is well known in poled ceramics, poled glasses, and poled polymers and
indicates that the electric polarization is perpendicular to the film plane (C∞v ). The
estimated magnitude of the nonlinear optical susceptibility χzyy of the film with x =
0.25 is approximately 1/7 of the susceptibility χxxx of quartz. The following mech-
anism is consistent with the origin of the observed SHG. The estimated bond length
of the FeII –NC–CrIII lattice is 5.31 Å from the lattice parameter of FeII [CrIII (CN)6 ]
                                                                           1.5
[47], which is greater than that of the CrII –NC–CrIII lattice (5.19 Å [48, 49]). There-
fore, the incorporation of FeII ions into the CrII –NC–CrIII lattice may strain the lat-
tice. [CrIII (CN)6 ] defects maintain the charge balance in the present compound and
these defects are preferentially generated next to the FeII sites rather than the CrII
sites in order to avoid generating lattice strain. The film is grown perpendicular to
the electrode and the distorted structure is accumulated in this direction, as shown
schematically in Figure 2.24. In addition, the AFM observation (not shown) indi-
cates that the microcrystals are also perpendicular to the film plane and thus the elec-
tric dipole moment could be perpendicular to the film plane. In fact, careful analysis
of the XRD pattern indicates that the structure of (FeII CrII )1.5 [CrIII (CN)6 ]·7.5H2 O
                                                        x   1−x
(0 < x < 1) is not symmetrical face-centered cubic, but a noncentrosymmetric
monoclinic structure of the space group C2 . This noncentrosymmetric orientation
of the crystal structure induces the SHG in this system.
    The magnetic effect on the polarization of SH radiation is measured using the
film with x = 0.33. Although the SH polarization does not exhibit rotation in
the presence of an external magnetic field at 300 K, the rotation of the SH output
is observed at 50 K, which is below TC (Figure 2.25). Moreover, reversing the
applied magnetic field inverts the rotational direction. The rotation angle of the
SH output is approximately 1.3◦ , which is much greater than the Faraday rotation
angle of 0.079◦ , at 50 K in an applied magnetic field of 10 kOe. Furthermore, the
SH optical rotation due to remnant magnetization is also observed and the angle
                                                                  2.5 SHG-active Prussian Blue Magnetic Films   65



                                                                                Film
SH intensity (a. u.)


                                                                                Powder




                                  0       0.2       0.4         0.6         0.8          1
                                                Compositional factor x
           SH intensity (a.u.)




                                 0        1         2            3          4            5
                                                  Film thickness ( m)

                                                        100
                                                        90
                                                        80
                                                                 Pin-Pout
     SH intensity (a. u.)




                                                        70
                                                        60
                                                        50
                                                        40
                                                        30
                                                        20
                                                        10               Sin-Pout
                                                            0
                                 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70
                                                   Angle (degree)

Fig. 2.23. (a) The SH intensity of PIN –POUT polarization combination versus x in the film and
powder forms of (FeII CrII )1.5 [CrIII (CN)6 ]·7.5H2 O (incident angle: 45◦ ). The thickness of
                     x 1−x
all the films was about 2 µm. (b) The SH intensity of PIN –POUT polarization combination
versus the film thickness ( ) for x = 0.33. (c) Maker’s fringe pattern of the film for x = 0.25
in the polarization combination of PIN –POUT and SIN –POUT at room temperature.
66       2 Chiral Molecule-Based Magnets


                                       Fe(II)
SnO2 coated glass                      Cr(II)
                                       Cr(III)CN6


                                                water




                                                                   III
                                                                  Cr
                                                        II   CN
                                                    Cr

Fig. 2.24. Schematic illustration of the crystal structure and electric polarization in electro-
chemically synthesized (FeII CrII )1.5 [CrIII (CN)6 ]·7.5H2 O films.
                           x 1−x

is 0.25◦ at 50 K The magnetic linear term of χij kL
                                                                  magn(1)
                                                               explains this SH rotation
because reversing the magnetic field inverts the rotational direction. The optical
symmetry of the present films in the paramagnetic region is confirmed to be C∞v
(the nonzero components are xzx = yzy, xxz = yyz, zxx = zyy, zzz in the
polar tensor of rank 3) due to the out-of-plane orientation of polycrystals with
                                         magn(1)                   cr
a C2 space group. Below TC , the χij kL          term and the χij k term are added to
the nonlinear susceptibility. This axial tensor of rank 4 has nonzero components
of xyzZ = −yxzZ, xxxY = −yyyX, xyyY = −yxxX, yxyY = −xyxX,
xzzY = −yzzX, and zxzY = −zyzX [50]. Here, the magnetic field was applied
along the direction of light propagation, i. e., the x and z axes at the film frame, and
the incident light was polarized to the s-direction (i. e., y axis). Applying a magnetic
field should radiate the p- and s-polarized SH outputs by the zyy tensor component
          cr                                                    magn(1)
in the χij k part and the yyyX tensor component in the χij kL part, respectively.
Moreover, if the applied magnetic field is inverted, then the phase of the s-polarized
SH output should be inverted because the sign of the yyy component is changed by
the yyyX component. This tensor behavior reproduces the experimental data very
well. Thus, the observed SH rotation is due to the magnetic linear term. The relative
value of the magnetic yyyX tensor component can be evaluated from the observed
SH rotation angle. To estimate this tensor component, the laboratory frame x y z
is used. The source terms of the p- and s-polarized SH outputs can be rewritten as
                           magn(1)        magn(1)
χx y y = χzyy sin θ and χy y y Z = −χyyyX sin θ, respectively. Then, the tangent
  cr         cr
                                           magn(1)                   magn(1)
of the rotation angle is described as |χy y y Z |/|χx y y | = |χyyyX |/|χzyy |. The
                                                       cr                      cr(0)
   magn(1)
|χyyyX |/|χzyy | and from the rotation angle in Figure 2.25 the estimated ratio
                cr(0)

is 0.023 at 50 K under 10 kOe. Moreover, the above relationship suggests that the
rotation angle is independent of the incident angle. In fact, the observed rotation
                                               2.5 SHG-active Prussian Blue Magnetic Films   67


                                                          M(+)    M(-)
SH intensity (a.u.)




                                                 ±1.3°




                      -30                  0                             30
                            Analyzer rotation angle (degree)

Fig. 2.25. The SH intensity vs. the analyzer angle in the film for x = 0.33 in an applied
magnetic field of 10 kOe at 50 K. The analyzer angle of 0◦ corresponds to the direction of
s-polarized SH radiation.


angles of the SH polarization are similar to the incident angles, in the range 5 <
θ < 35◦ . The microscopic origin of MSHG is mainly considered to be due to
the interaction of the spin-orbit coupling through the electric-dipole nonlinearity,
which is allowed by the broken inversion symmetry.
   Figure 2.26 shows the temperature dependence of the SH intensity without an ap-
plied magnetic field for films where x = 0.25 and 0.13. The observed SH intensity
dependence on temperature in films when x = 0.25 resembles the magnetization
vs. temperature plots. When x = 0.13, the shape of the SH dependence on tem-
perature nearly corresponds to the absolute value of magnetization vs. temperature
plots in Figure 2.21. Hence, the magnetic domains are randomly oriented under
                                                             magn(1)
the zero field cooling conditions and the contribution of χij kL is compensated
by integrating the magnetic domains. Therefore, the possibility of a contribution
           magn
from theχij k term can be excluded. It is known that the magnetic strain relates
to the magnetization value, but reversing the magnetization does not change its
sign. Thus the main origin of the SH intensity dependence on temperature is the
magnetic crystal strain.
   The numerous different structures of molecule-based magnets are an advantage
for bulk SHG and MSHG since some molecule-based magnets are noncentrosym-
metric, and simultaneously have a second-order optical nonlinearity and sponta-
neous magnetization. In fact, Gatteschi et al. and Nakatani et al., respectively,
reported SHG in a methoxyphenyl nitronyl-nitroxide radical crystal [51] and in
hybrid layered materials such as [(dmaph)PPh3 ][MnII CrIII (ox)3 ] [52]. In these sys-
tems, some interference effects are observed and from this point of view, chiral
magnets are useful in studying non-linear magneto-optics of magnetic materials.
68                              2 Chiral Molecule-Based Magnets

                      2.0
                                                                                    0.13
                      1.8
                                                                                    0.25
                      1.6                   6
SH intensity (a.u.)




                                                                          6
                                                R OQE
                                                                              %
                      1.4

                      1.2

                      1.0

                      0.8

                       0
                      0.6
                            0        50     100         150         200           250      300
                                                  Temperature (K)

Fig. 2.26. Temperature dependence of the SH intensities generated from the films for x = 0.13
and 0.25 in a zero applied magnetic field (PIN –POUT polarization).



2.6 Conclusion

Notable features of molecule-based magnets include designability and trans-
parency. A novel category of materials suitable for chiral or noncentrosymmetric
magnets has been successfully fabricated for application in the field of molecule-
based magnetic materials. These materials display new optical phenomena such as
the magnetization-induced nonlinear optical effect and the magneto-chiral optical
effect due to their noncentrosymmetric or chiral magnetic structure. This category
of materials is of keen scientific interest, and, moreover, these materials afford the
possibility of use in new types of devices. In this chapter, we have described the
design, structure, and some of the physical properties for several new chiral and
noncentrosymmetric molecule-based magnets. These systems afford the possibility
of opening new fields in magnetism.




Acknowledgments
                                                        ¯
K.I. and H.I. acknowledge their co-workers Professor H. Okawa and Dr. M. Ohba
(University of Kyushu) and Professor K. Kikuchi (Tokyo Metropolitan University).
S.O. acknowledges his co-workers Professor K. Hashimoto and Dr. K. Ikeda (The
University of Tokyo).
                                                                          References       69

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3 Cooperative Magnetic Behavior
  in Metal-Dicyanamide Complexes
     Jamie L. Manson




Abstract

Several magnetic solids comprised of dicyanamide (dca), [N(CN)2 ]− , bridging
ligands have been shown to possess interesting magnetic behavior. Among these
are the binary solids M(dca)2 {M = V, Cr, Mn, Fe, Co, Ni and Cu} which have
rutile-like structures and order either canted anti- or ferromagnetically with critical
temperatures ranging between 1.7 and 47 K. It has also been possible to construct
architectures that incorporate organic co-ligands (e. g. pyrazine, pyrimidine) into
the framework which contribute to the bulk cooperative magnetic behavior. In this
chapter, these structures and their subsequent magnetic behavior are described and
some comparisons drawn between the related M(tcm)2 (tcm = tricyanomethanide)
compounds. Future prospects for new materials are also discussed.



3.1 Introduction

The dicyanamide (dca) anion, [N(CN)2 ]− , is an extremely versatile ligand for
assembling transition metal cations into various lattice and spin arrays. First utilized
by Köhler [1] nearly three decades ago, this anion has been resurrected by many
research groups worldwide, exploiting its coordinative properties in an attempt to
“engineer” polymeric structures that exhibit bulk magnetic behavior [2]. Although
many interesting structure types have been synthesized and characterized, only a
handful display cooperative magnetic properties which is the scope of this review.
   As shown in Scheme 3.1, the dicyanamide anion can coordinate to a metal ion
in several ways: (i) monodentate through one of the nitrile nitrogen atoms, (ii)
bidentate through both nitrile N atoms, (iii) bidentate through one nitrile and the
amide N-atom, (iv) tridentate through both nitriles and the central amide N-atom
and, (v) tetradentate where the central amide and one of the nitrile nitrogen atoms
are µ-coordinated while the remaining nitrile moiety is bis-bidentate to two dif-
ferent metal ions. These bonding modes arise from the various canonical forms of
the [N(CN)2 ]− ion. All of these coordination schemes have been observed experi-
72               3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes

mentally except for (iii). For instance, scheme (i) is observed in several molecular
species such as the spin crossover complex Fe(abpt)2 (dca)2 {abpt = 4-amino-3,5-
bis(pyridin-2-yl)-1,2,4-triazole} that contains no covalent bonding interactions be-
tween metal centers [3]. The second mode, scheme (ii), occurs most frequently
and has been observed exclusively in various polymeric 1-, 2- and 3D network
structures. So far, the “binary” M(dca)2 {M = V, Cr, Mn, Fe, Co, Ni, Cu and Cd}
compounds are the only known examples that portray bonding scheme (iv) [4–14].
Scheme (v) occurs only in diamagnetic Na(dca) [15] and Tl(CH3 )2 (dca) [16].

         N                                             N
     C           C                                 C          C
N                    N                         N                  N
         (i)             M                 M           (ii)           M

         M                                             M

          N                                            N
     C           C                                 C          C
N                    N                         N                  N
                         M                 M                          M
         (iii)                                         (iv)

                                 M

                                 N
                             C         C
                     M   N                 N
                                               M
                                                                          Scheme 3.1. Possible dicyanamide coordi-
                         M
                                 (v)                                      nation modes.

    A related polycyano species is the tricyanomethanide (tcm) anion, [C(CN)3 ]−
which affords bonding characteristics similar to dca [1a, 17]. The most significant
difference between them is the symmetry of these planar anions; dca has nominal
C2v symmetry while tcm is D3h . When all three nitrile nitrogen atoms of either
species coordinate to a metal ion, spin frustration is a plausible exchange scenario
[18]. Owing to symmetry considerations, tcm is more susceptible because an equi-
lateral geometry is produced that leads to a greater number of degenerate ground
state spin configurations. This is not to say that frustration does not occur in the
case of µ3 -bonded dca but the lack of the third nitrile substituent imposes shorter
3-atom exchange paths relative to tcm which offers only 5-atom bridges that greatly
alter the magnetic exchange.
    Three-coordinate tcm, as found in divalent M(tcm)2 {M = V, Cr, Mn, Fe, Co,
Ni, Cu, Zn, Cd, and Hg}, leads to 3D rutile-like network structures that possess
large “zeolitic-like” channels that are filled by a second identical interpenetrating
lattice, Figure 3.1 [18, 19]. The relationship to the rutile phase of TiO2 is readily
apparent with the M2+ cations and the large tcm− anions replacing Ti4+ and O2− ,
respectively. The obvious difference between these systems is the lack of interpen-
etration observed in the more compact TiO2 lattice. Moreover, the 3-fold symmetry
of tcm− could afford geometrical spin frustration since it can be regarded as a 3D
                       e
analog of the Kagom´ lattice [20]. From a magnetism point-of-view, the V-, Cr-,
                                               3.2 “Binary” α-M(dca)2 Magnets         73

and Mn(tcm)2 compounds are the most interesting. The V- and Cr-analogs afford
Weiss constants of −69 and −45 K, respectively, indicating sizeable antiferromag-
netic interactions between M2+ ions via M–N≡C–C–C≡N–M linkages [18a]. A
significantly reduced θ -value of −5.1 K was found for S = 5/2 Mn(tcm)2 [18b].
The MnN6 coordination sphere is a nearly perfect octahedron with Mn–N distances
ranging between 2.22 and 2.27 Å. In contrast, the Cr2+ ion in Cr(tcm)2 has an S =
2 ground state that is susceptible to Jahn–Teller distortion (Cr–N distances of 2.08
and 2.45 Å) and, as a result, the effect of spin frustration is diminished, which sta-
bilizes long-range antiferromagnetic ordering below 6.12 K, as shown by specific
heat and neutron diffraction data [18a]. Above 6.12 K, the magnetic susceptibil-
ity data show a broad maximum centered near 10 K which has been attributed
to 2D Ising behavior. The V2+ ion in V(tcm)2 is S = 3/2 and does not have an
orbital contribution to the magnetic moment similar to the half-integer spin Mn
compound. In the light of the amorphous nature of V(tcm)2 samples, it is likely
to have an analogous undistorted crystal structure akin to Mn(tcm)2 and exhibit
marked spin frustration, as observed, although no maximum in χ(T ) was detected
above 2 K [18a]. The remaining paramagnetic transition metal ions in the first row
display magnetic properties associated with single ion anisotropy and no long range
magnetic ordering [18c, 19]. It has also been possible to build a variety of other
crystalline lattices by introducing potentially bridging organic ligands into the de-
sign strategy [21]. Such efforts have not yet yielded magnetically ordered systems.



3.2 “Binary” α-M(dca)2 Magnets

Independently and simultaneously, several research groups worldwide have studied
the M(dca)2 compounds [4–14]. Combining paramagnetic M2+ and dca− ions in
a 1:2 stoichiometry in concentrated aqueous media leads to rapid precipitation
of polycrystalline powders of various colors, depending on M. Slow diffusion or
solvent evaporation of dilute aqueous solutions over a long period of time affords
well-formed crystals for M = Mn, Co and Cu. Unlike other well-known polycyano
species, it is very difficult to produce and stabilize a radical anion form of dca. Hence
the dca anion (as well as tcm) is diamagnetic, in contrast to electron acceptors such
as TCNE, TCNQ, and DCNQI [22]. Like many other polycyano species, dca− is a
weak-field ligand.

3.2.1    Structural Aspects

The crystal structures of the M(dca)2 salts are similar to M(tcm)2 (see Figure 3.1)
except for the lack of double-interpenetrating lattices in the former. For M = Mn,
Cr, Mn, Fe, Co, Ni and Cu, the compounds crystallize in the orthorhombic space
74      3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes




Fig. 3.1. Rutile-like crystal structure of double-interpenetrating M(tcm)2 depicting the two
individual lattices.



group Pnnm with four molecules per unit cell and M = V, Cr are believed to be
isostructural, based on powder X-ray diffraction data [4–14]. A summary of useful
crystallographic parameters is provided in Table 3.1. The divalent metal ions in
this class of solids possess octahedral coordination environments (also referred to
as α-phase) consisting of four nitrile nitrogen atoms in the equatorial plane and
two axially-bonded amide-N atoms from six different dca− ligands, Figure 3.2.
One-dimensional “chains” propagate along the c-axis which are further connected




Fig. 3.2. Octahedral coordination sphere of the M2+ ion as found in α-M(dca)2 .
Table 3.1. Crystallographic and magnetic data for the α-M(dca)2 {M = V, Cr, Mn, Fe, Co, Ni and Cu} compounds. The space group symmetry
for all compounds is Pnnm.

M(dca)2            a (Å)         b (Å)         c (Å)       V (Å3 )   θ (K)    Tc (K)    M (emu Oe mol−1 )a   Hc (Oe)b   γ (deg.)   Ref.

V             amorphous               –             –            –    −69        12.4          6800            20        0.017      5b
Cr (XPD)        5.922(2)      7.478(3)      7.564(3)      334.9(3)   −154          47          1000            250        0.74       5
Mn (SC)        6.1126(3)     7.2723(3)     7.5563(4)     335.90(3)    −25          16          4919            406        0.13      12
Mn (SXPD)     6.14998(6)    7.31503(6)    7.53668(6)    339.054(6)    −16          16          7000            750        0.05      5b
Mn (NPD)       6.1486(4)     7.3155(3)     7.5371(2)     339.02(3)     NR    16.55(3)          5400            800        <5         8
Fe                    NR            NR            NR           NR        3       18.5          8000           17800        7.2     13,23
Co (SC)          5.970(1)      7.060(1)      7.406(1)    312.15(8)     9.7          9         11000            710          0       13
Co (SXPD)      6.0109(3)     7.0724(4)     7.3936(4)     314.32(3)       9        8.7           NR             NR           0      5a,13
Co (NPD)       5.9853(2)     7.1030(2)    7.39384(7)     314.34(1)       9    9.22(4)         14000            800          0       5a
Ni (NPD)c      5.9735(2)     7.0320(2)    7.29425(7)     306.40(3)      21    21.3(2)         11,900          7000          0       5a
Cu (SC)         6.120(1)      7.339(1)       7.173(1)    322.17(8)     0.7        1.7           NR             NR         NR        13
Abbreviations: XPD = X-ray powder diffraction, SC = single crystal X-ray diffraction, SXPD = synchrotron X-ray powder diffraction, NPD =
neutron powder diffraction, NR = not reported.
a 2 K and 50 kOe. b 2 K. c 198 K.
                                                                                                                                           3.2 “Binary” α-M(dca)2 Magnets
                                                                                                                                               75
76      3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes




                                          Fig. 3.3. Crystal structure of non-interpene-
                                          trating rutile-like α-M(dca)2 . M, C and N atoms
                                          are depicted as shaded, filled and open spheres,
                                          respectively.


to neighboring chains by M–Namide coordinative bonds to build up the 3D network,
Figure 3.3. Each dca anion is µ3 -bonded to three different M2+ ions, as illustrated
in scheme (iii). It will be shown in Sections 3.2.2 and 3.2.3 that the µ3 -bonding
mode plays a significant role in the cooperative magnetic properties of this series
of materials and earmarks the difference with-respect-to the M(tcm)2 compounds
described previously.
    Close inspection of the metal coordination environments in each of these struc-
tures reveals some interesting points. Typically the high-spin octahedral Mn2+ ion
will be the least distorted in comparison to the other first row transition metals due
to its half-filled d-orbitals meaning that there are no complications arising from or-
bital angular momentum. Interestingly, the crystal structure of Mn(dca)2 features a
significant tetragonal distortion with regard to the structurally known systems with
four Mn–Neq distances of 2.181 (2) Å and two Mn–Nax distances of 2.302 (2) Å at
room temperature [8, 12]. The difference between Mn–Neq and Mn–Nax is larger
than observed in the isostructural Fe [2.126 (1) and 2.219 (2) Å] [8, 23], Co [2.095
(1) and 2.162 (2) Å] [6, 9], Ni [2.053 (1) and 2.140 (2) Å] [6, 9] but less than Jahn–
Teller distorted Cu [1.979 (3) and 2.473 (4) Å] [13] compounds. By comparison,
the Mn–N distances in Mn(tcm)2 range from 2.222 (1) to 2.272 (2) Å [18b].


3.2.2   Ferromagnetism

From detailed magnetic susceptibility, magnetization and specific heat measure-
ments, it was shown that M = α-Co-, Ni- and Cu(dca)2 exhibit ferromagnetic
ordering below 9, 21 and 1.7 K, respectively [5, 7, 10, 11, 13, 14, 23]. Because of
the low critical temperature of the Cu-analog, further studies were hampered. Plots
of χ T (T ) and 1/χ between 2 and 300 K for α-Co and Ni(dca)2 , Figure 3.4, gave
preliminary indications for ferromagnetic behavior based on fits to the Curie–Weiss
                                                                          3.2 “Binary” α-M(dca)2 Magnets   77

                    70                                                           250
                    60
                                                                                 200
χT (emuK/mol)




                                                                                       1/χ (mol/emu)
                    50
                    40                                                           150

                    30
                                                                                 100
                    20
                                                                                 50
                    10

                     0                                                        0
                         0           50       100    150      200   250     300
                                                     T (K)

  Fig. 3.4. T -dependence of χ T and 1/χ between 2 and 300 K for α-Co (•, ◦) and Ni(dca)2
  ( , ). [5a]

  law, giving g-factors and θ -values of 2.60 and 9 K for α-Co(dca)2 and 2.20 and
  21 K for Ni(dca)2 , respectively [5]. Zero-field and field-cooled M(T ) acquired
  for various field strengths revealed dramatic irreversibilities below Tc in both the
  α-Co and Ni compounds, Figure 3.5. At the bifurcation temperature, Tb , which for
  a ferromagnet is identical to Tc , the ac susceptibility shows a single sharp peak at
  the ordering temperature. This is strong evidence for the presence of single domain
  particles contained within the sample. The M(T ) data could be fitted to a power law
  to extract the β-exponents for α-Co and Ni(dca)2 which are 0.52 (3) and 0.47 (4),
  respectively, in good agreement with mean-field theory that predicts a value of 0.5
  [13]. Additionally, a significant χ (T ) component in the complex ac susceptibility
  signifies hysteresis in the materials. This is further supported by M(H ) measure-

                    2000
                                                                     ZFC/FC 5 Oe
                                                                     ZFC/FC 10 Oe
                                                                     ZFC/FC 20 Oe
    M (emuOe/mol)




                    1500                                             ZFC/FC 50 Oe


                    1000


                     500


                             0
                                 0        5         10       15     20      25         30
                                                           T (K)
  Fig. 3.5. Zero-field and field-cooled M(T ) acquired for Ni(dca)2 at H = 5, 10, 20 and 50 Oe.
  [5a]
78                 3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes

                15000

                10000
M (emuOe/mol)


                 5000

                     0

                 -5000

                -10000

                -15000
                     -20   -15   -10   -5     0       5   10   15   20

                                            H (kOe)
Fig. 3.6. M(H ) at 2 K for α-Co (•) and Ni(dca)2 (◦).

ments well below Tc which show coercive fields of 800 and 7000 Oe, respectively,
Figure 3.6 [5, 12]. For Ni(dca)2 saturation magnetization occurs at 8 T (2 K), while
for a pure ferromagnet Ms should occur instantaneously [24]. Generally, because
of the larger single ion anisotropies associated with Co2+ -containing compounds,
it is rather unusual that a larger Hcr was observed for the Ni2+ system. Presently the
origin of this behavior is unknown. Specific heat data for α-Co and Ni(dca)2 show
large λ-type anomalies at the Curie temperature, as expected, consistent with the
magnetization results. Also note that divalent Co and Ni are typically associated
with Ising behavior while Cu2+ is generally a Heisenberg ion [25]. The magnetic
data for these materials are summarized in Table 3.1.
    Neutron diffraction has been utilized to determine the zero-field magnetic struc-
tures of α-Co and Ni(dca)2 [9]. The diffraction data below Tc did not display any
superlattice reflections indicative of antiferromagnetic ordering but did show addi-
tional magnetic scattering at the nuclear peaks, consistent with a ferromagnetic spin
orientation. At 1.6 K it was found that the magnetic moments align ferromagneti-
cally along the crystallographic c-axis, Figure 3.7. The magnetic order parameter
vanished at Tc while no ordered magnetic moment is observed above Tc . Magnetic
moments of 2.67 (5) and 2.21 (10) µB have been reported for α-Co and Ni(dca)2 , re-
spectively, corresponding to g-values of 5.34 and 2.21, which is consistent with dc
magnetization and ac susceptibility data. Bordallo and co-workers have also stud-
ied the magnetic excitation spectra of α-Co and Ni(dca)2 using inelastic neutron
scattering methods [24].
    Kurmoo and co-workers have recently studied the critical spin fluctuations just
above Tc using muon spin relaxation (µSR) techniques [26]. Because implanted
muons are sensitive to the onset of long range magnetic ordering they can be used
as a “microscopic magnetometer” [27]. In the paramagnetic region above Tc strong
muon-spin relaxation was observed, which arises from low-frequency fluctuations
                                              3.2 “Binary” α-M(dca)2 Magnets           79




                                        Fig. 3.7. Zero-field ferromagnetic structure of α-
                                        Co and Ni(dca)2 at 1.6 K. M, C and N atoms are
                                        depicted as shaded, filled and open spheres, re-
                                        spectively.


of the magnetic moments in the 109 –1010 Hz range. Strongly damped oscillations
were observed in α-Co(dca)2 below Tc .


3.2.3   Canted Antiferromagnetism

The divalent metal ions with d3 , d4 , d5 and d6 electronic configurations, namely
V, Cr, Mn and Fe, display markedly different magnetic behavior relative to α-Co-,
Ni. According to magnetic susceptibility, low-H M(T ), and M(H ) studies the
                                              e
magnetic moments are noncollinear with N´ el temperatures of 12.4 K (V), 47 K
(Cr), 16 K (Mn) and 18.5 K (Fe) [4, 5b, 6, 8, 12, 13, 23]. Fits of the 1/χ data to the
Curie–Weiss law yielded θ -values of −69, −154, −16, and −3 K for V-, Cr-, Mn-,
and Fe(dca)2 , respectively. Upon cooling from room temperature, χT (T ) decreases
gradually due to antiferromagnetic correlations between metal spin carriers. At low
temperatures, maxima in χ T (T ) are reached signifying magnetic saturation and/or
bulk antiferromagnetic ordering, Figure 3.8. The increase in χT (T ) arises from
an uncompensated magnetic moment due to canting of the spins. Spin canting can
occur provided a center of symmetry does not exist, which is the case for these
compounds. Single ion anisotropy and/or exchange anisotropy may be responsible
for the observed behavior [28].
   Zero-field cooled and field-cooled M(T ) measurements obtained in low external
fields show behavior reminiscent of a simple ferromagnet although with much
smaller magnetization values. Further support for spin canting comes from high-
field M(T ) data which show a gradual change in the shape of the magnetization
curve, meaning that the spontaneous moment is being quenched. The degree of
canting can be gleaned from the H -dependence of the M(T ) data. For example, for
Cr(dca)2 the canted magnetic moment persists up to relatively high magnetic fields
(at least 5 kOe) while much smaller fields saturate the canted moment in Mn(dca)2 ,
   80                       3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes

                    7                                                    200
                    6
χ T (emuK/mol)

                                                                         150




                                                                               1/χ (mol/emu)
                    5
                    4
                                                                         100
                    3
                    2
                                                                         50
                    1

                    0                                                 0
                        0         50    100   150     200    250    300

                                              T (K)
   Fig. 3.8. χ T and 1/χ for Cr- (•, ◦) and V(dca)2 ( , ) obtained at H = 1 kOe. The solid
   lines serve as a guide to the eye only.

                   300
                             FC
                   250
   M (emuOe/mol)




                   200

                   150       ZFC

                   100

                    50

                     0
                         0         10    20    30     40     50     60
                                              T (K)
   Fig. 3.9. Representative zero-field and field-cooled M(T ) data for Cr- (•) and Mn(dca)2 (◦)
   collected for H = 100 Oe.

   Figure 3.9. This general observation likely stems from the marked difference in
   single-ion anisotropies, the Cr2+ ion being much more affected than Mn2+ . A
   summary of the various magnetic properties can be found in Table 3.1.
      Field-dependent M(H ) at 2 K for M = V, Cr, Mn and Fe show hysteresis with
   coercive fields, Hcr , as large as 17.8 kOe (Fe) [5b, 6, 8, 12, 13, 23]. Saturation
   magnetization is not achieved in any of these systems for magnetic fields less
   than 5 kOe. M(H ) for Mn(dca)2 is essentially linear between zero and 50 kOe
   although a sizeable hysteresis loop was observed with Mr = 63 emu Oe mol−1
   and Hcr = 750 Oe (5 K), Figure 3.10 [6, 8]. A field-driven spin flop transition
   was revealed for Mn(dca)2 at 5.2 kOe (2 K) while the spin flop to paramagnetic
   transition occurs at a much higher field value. From the remnant magnetization it
                                                        3.2 “Binary” α-M(dca)2 Magnets   81

                300

                200
M (emuOe/mol)


                100

                   0

                -100

                -200

                -300
                    -3     -2    -1      0      1   2        3

                                      H (kOe)
Fig. 3.10. M(H ) for Mn(dca)2 taken at 5 K. [8]

was possible to elucidate a spin canting angle of 0.05◦ and show that the data could
be well described by a power law which yielded β = 0.380 (5) [6, 8].
   At 2 K, Cr(dca)2 shows an initial rapid rise in M(H ) for low fields but then
decreases slope near 3.5 kOe and becomes linear with increasing field to 50 kOe
which is an artifact of its spin canted ground state [5b]. At 50 kOe a very small
magnetization value of 1000 emu Oe mol−1 is obtained which is well below the
expected value of 25,700 emu Oe mol−1 . This obviously indicates that very high
magnetic fields are necessary to fully ferromagnetically align the magnetic mo-
ments in Cr(dca)2 . A Hcr of 250 Oe was observed.
   The low temperature magnetic structure of Mn(dca)2 has been determined by
neutron diffraction measurements [8]. Below the magnetic ordering temperature,
the spin orientation lies primarily along the a-axis with a small uncompensated
moment along the b-direction. From these measurements it was determined that
the spin canting angle is less than 5◦ . Each Mn2+ ion has a magnetic moment of
4.61 (1) µB that is reduced from the expected value of 5 µB as a result of partial
spin delocalization onto the dca anions.


3.2.4                  Mechanism for Magnetic Ordering

The question that remains is that while M = V, Cr, Mn, Fe, Co, Ni and Cu form
an isostructural series, what is the origin of the differing magnetic behavior? This
has been addressed by Kmety et al. [8] who invoked Anderson and Goodenough
rules to describe the magnetic interactions in these complex solids. Based on the
Anderson superexchange model that considers symmetry relationships between
cations and anions, it predicts a decrease of ferromagnetic interactions with a
decreasing number of 3d electrons. Accordingly, the orbital overlaps are on average
non-orthogonal (M = V, Cr, Mn, Fe) and orthogonal (M = Co, Ni, Cu). Similarly,
82      3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes

Goodenough proposed that the exchange coupling between identical ions must
change from ferro- to antiferromagnetic at some crossover value associated with
the superexchange angle. The superexchange angles were determined to range
from 141.1 (1) to 143.5 (1)◦ for Mn- and Ni(dca)2 , respectively, dependent upon
ionic radii, bond lengths, and bond angles. Subsequently, the crossover from canted
antiferromagnetism to collinear ferromagnetism occurs at a superexchange angle
of 142.0 (5)◦ for the M(dca)2 family.


3.2.5    Pressure-dependent Susceptibility

Kurmoo and co-workers measured the ac susceptibility of M = Fe, Co and Ni as a
function of pressure [29]. Initially, the magnetic ordering temperature increases for
all three systems. Up to ∼17 kbar, the Tc for Ni(dca)2 increases by 6% while that
of α-Co actually decreases by 16%, suggesting a transformation from ferro- to an-
tiferromagnetic exchange interactions in the latter. Fe(dca)2 displays a continuous
increase in TN upon applying pressure (26%). These results indicate that there is a
competition between antiferromagnetic and ferromagnetic interactions within the
three-atom M–N≡C–N–M component, which is the most dominant superexchange
pathway. In other words, increasing the number of holes in the t2g orbitals promotes
an increase in antiferromagnetic character. The authors also predict an increase in
Tc with increasing spin quantum number and that TN for Fe(dca)2 should be higher
than α-Co(dca)2 , as observed.



3.3     β-M(dca)2 Magnets

3.3.1    Structural Evidence

In early work by Köhler and co-workers [1b] it was proposed that a second β-
polymorph existed for Mn and Co(dca)2 . It has subsequently been shown that only
α-Mn(dca)2 exists, which is not surprising considering that Mn2+ ions generally
prefer six-coordination [5b]. The structure of this phase is believed to consist of
tetrahedral metal centers that are µ-bonded (scheme ii) by bridging dca anions so
as to form corrugated 2D layers analogous to diamagnetic Zn(dca)2 , Figure 3.11
[30, 31]. The layers pack in a staggered fashion and are slipped by a/2 with-
respect-to adjacent layers so as to maximize packing efficiency, Figure 3.12. Köhler
indicated that dissociation of pyridine (py) ligands from pink colored Co(dca)2 (py)2
led to the formation of blue α-Co(dca)2 [1b]. This finding was recently reproduced
by Miller and Murray and their co-workers [5, 31]. Unfortunately this preparative
procedure affords a poorly crystalline material unsuitable for structural evaluation
                                                      3.3 β-M(dca)2 Magnets          83




                                             Fig. 3.11. Crystal structure of Zn(dca)2
                                             showing the 2D buckled-layers. Zn, C and
                                             N atoms are depicted as shaded, filled and
                                             open spheres, respectively.




                                                      Fig. 3.12. Packing diagram for
                                                      Zn(dca)2 . The layers are slipped
                                                      a/2 with-respect-to neighboring
                                                      sheets. Zn, C and N atoms are
                                                      depicted as shaded, filled and
                                                      open spheres, respectively.


although several attempts have been made to characterize the deep blue residue by
synchrotron X-ray and neutron diffraction [5b]. According to UV-Vis spectroscopy
on β-Co(dca)2 , the blue color originates from an absorption at 16,800 cm−1 that
is assigned to the spin-allowed 4 A2 (F) → 4 T1 (F) transition, typically exhibited by
tetrahedral Co2+ species [32]. It was later shown that light doping of Co2+ into the
Zn(dca)2 lattice did in fact afford blue crystals isostructural to pristine Zn(dca)2
[31].
    Mn(dca)2 (py)2 , which is analogous to the β-Co(dca)2 precursor, has a 1D lin-
ear chain structure consisting of octahedral Mn2+ linked to one another by four
equatorially-bonded dca substituents while the two remaining axial-positions are
84      3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes




                                                            Fig. 3.13. Crystal structure
                                                            of the 1D chain compound
                                                            Mn(dca)2 (py)2 .


occupied by non-bridging pyridine molecules, Figure 3.13 [33]. In contrast to the
Co-analog, removal of the two py ligands does not lead to the β-form but instead
to octahedral α-Mn(dca)2 [5b].


3.3.2   Magnetic Behavior of β-Co(dca)2

The reported magnetic response of 0.12% doped Co/Zn(dca)2 was that of a magnet-
ically dilute material where no long range magnetic ordering was detected down
to 15 K [31]. The room temperature magnetic moment of 4.6 µB was in good
agreement with that expected for tetrahedral Co2+ with a 4 A2 ground state. Neat
β-Co(dca)2 exhibits canted antiferromagnetic behavior below TN = 8.9 K, as indi-
cated by detailed ac susceptibility, dc magnetization and heat capacity studies [5].
A Curie–Weiss fit of the reciprocal magnetic susceptibility yielded g = 2.27 and
θ = −7 K for T > 60 K. The zero-field and field-cooled M(T ) data are some-
what field-dependent, where the bifurcation temperature decreases with increasing
field from 9.2 (50 Oe) to 8.5 (100 Oe) and then to 8.0 K (500 Oe). Measurements
obtained using ac susceptibility (Hdc = 0 Oe, Hac = 1 Oe) show a frequency depen-
dence that typically arises from a spin-disordered ground state such as that found in
spin glasses and superparamagnets [34]. This finding attests to the synthetic route
utilized to prepare bulk β-Co(dca)2 which is largely amorphous. Similar to the
α-phase, hysteresis was observed with Hcr = 680 Oe (2 K). Furthermore, cooling
well below TN reveals a second phase transition at 2.7 K that has been ascribed to
a spin reorientation.
                                                 3.4 Mixed-anion M(dca)(tcm)       85

3.3.3   Comparison of Lattice and Spin Dimensionality in α- and
        β-Co(dca)2

Recall that the Tc reported for α-Co(dca)2 is nearly identical to that of β-Co(dca)2 .
This is very surprising in that the two polymorphs possess completely different
topologies (2D versus 3 D) and bond connectivities that directly effect the su-
perexchange properties. It was shown previously that the dominant exchange path
in the α-form consists of Co–N≡C–N–Co (3-atom pathway) while it must be Co–
N≡C–N–C≡N–Co (5-atom pathway) in the β-phase. In low-dimensional magnetic
systems, long range magnetic ordering can only occur if intermolecular interac-
tions are of sufficient magnitude. This is undoubtedly the case for β-Co(dca)2
which exists as 2D closely packed layers. The shortest metal-metal separations
for α- and β-Co(dca)2 , respectively, are 5.933 and 4.480 Å [based on the Zn(dca)2
compound]. The smaller distance found in the β-phase arises because of interdig-
itation of neighboring layers. Clearly, the number of magnetic nearest-neighbors
(and most likely next-nearest neighbors) plays an important role in any magnetic
system and is no different here. There are eight magnetic nearest-neighbors in
α-Co(dca)2 while there are only four (within a layer) in β-Co(dca)2 . This indi-
cates that a dipolar exchange mechanism must be operative, which promotes a
relatively large interaction energy that offsets the weaker interaction afforded by
the longer Co–N≡C–N–C≡N–Co pathway. It is worth noting that, based on a
mean-field argument, the exchange coupling constant, J /kB , is a factor of ∼1.6
larger for β-Co (−0.7 K) compared to that computed for the rutile-like phase
(0.45 K).



3.4 Mixed-anion M(dca)(tcm)

3.4.1   Crystal Structure

Combining stoichiometric amounts of M, dca and tcm in aqueous solution leads
to a new series of compounds of M(dca)(tcm) {M = Co, Ni, Cu} composition
[35]. It was noted that trace amounts of M(tcm)2 impurities were present in
all samples, as shown by powder X-ray diffraction. The structure of this mixed
anion polymer is regarded as a hybrid between the interpenetrating M(tcm)2
and non-interpenetrating α-M(dca)2 solids, Figure 3.14. As a result, a new self-
penetrating network is formed that has an analogous rutile-like motif. The struc-
ture consists of three long tcm bridges and one short/two long links of dca.
Multiple lattice interpenetration is thwarted owing to the significantly smaller
M3 (dca)3 six-membered rings present in the structure. Simplistically, 1D ML2
“chains” are tethered together by the shorter M–Namide dca links to afford the
86      3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes




                                              Fig. 3.14. Structural diagram of the mixed-
                                              anion compound M(dca)(tcm) {M = Co,
                                              Ni, Cu}. Shaded, filled and open spheres
                                              represent M, C and N, respectively.


3D network. Four chains in TiO2 form a square channel while the intercon-
nected chains in the M(dca)(tcm) network do not, which promotes the novel
self-penetrating feature. Further details of the structure can be found in Ref.
[35].



3.4.2   Magnetic Properties

Dc magnetization and ac susceptibility measurements suggest that the M = Co and
Ni systems are ferromagnetic or weakly ferromagnetic while M = Cu is a simple
paramagnet between 2 and 300 K. Long range magnetic ordering occurs below 3.5
(Co) and 8.0 K (Ni), values ∼1/3 those of the corresponding M(dca)2 compounds
[35]. χ T (T ) for both materials gradually increases upon cooling, reaching maximal
values close to TN . Small dc fields show a fairly large magnetization that gradually
diminishes with increasing H , similar to α-Co and Ni(dca)2 . This suppression is
attributed to spin canting. The complex ac susceptibilities show peaks at TN in
addition to significant χ (T ) components. Hysteretic behavior was observed with
Hcr less than 100 Oe. The field-dependent M(H ) response rises very rapidly, typical
of a ferromagnet, but then begins to increase slowly with no sign of saturation
up to 50 kOe. This also suggests the presence of competing antiferromagnetic
interactions. Effects due to single-ion anisotropy likely play a role, rendering it
difficult to quantify the exchange interactions for these materials.
                           3.5 Polymeric 2D (cat)M(dca)3 cat = Ph4 As, Fe(bipy)3          87

3.5 Polymeric 2D (cat)M(dca)3 cat = Ph4 As, Fe(bipy)3

3.5.1    (Ph4 As)[Ni(dca)3 ]

The 2D anionic network consists of a (4, 4) connectivity [36] identical to that found
in (Ph4 P)M(dca)3 {M = Mn, Co} [37, 38]. One-D M–(N≡C–N–C≡N)2 –M ribbons
are cross-linked by singly-bridged M–N≡C–N–C≡N–M chains, Figure 3.15, and
the bulky cations reside between the layers. The singly-bridged Ni· · ·Ni distance is
8.67 Å while the doubly-bridged chains have an average separation of 7.37 Å [36].
    The magnetic properties were found to be strikingly similar to those of parent
Ni(dca)2 . Ferromagnetic ordering occurs below 20.1 K [compared to 21 K for
Ni(dca)2 ], as denoted by a sharp peak in χ (T ). Use of Ph4 P in place of Ph4 As
yielded an identical result. The magnetic data appear to be inconsistent with that of
neat Ni(dca)2 , as shown by physical mixtures of (Ph4 As)[Ni(dca)3 ] containing 1%
Ni(dca)2 . The magnetization isotherms display markedly different behavior, more
characteristic of a soft magnet. At present the origin of the magnetic ordering in this
system is unclear, although these findings have been reproduced by other research
groups [39]. Similar studies on the Mn- and Co-analogs revealed no evidence for
3D magnetic ordering, only very weak exchange interactions and/or single ion
anisotropy.




Fig. 3.15. 2D layered structure of (Ph4 P)M(dca)3 {M = Mn, Co} that is analogous to
(Ph4 As)Ni(dca)3 . The cations have been omitted for clarity. Shaded, filled and open spheres
represent M, C and N, respectively.
88      3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes

3.5.2   [Fe(bipy)3 ][M(dca)3 ]2 {M = Mn, Fe}

Replacement of the tetrahedral cations in the previous example with D3 -symmetric
ones leads to a novel 2D anionic hexagonal array, Figure 3.16 [40a]. Each M2+ ion
in the layers is bridged by three pairs of dca anions via the nitrile nitrogen atoms
to three other M ions. The cations reside within the large hexagonal windows
as opposed to between the layers and successive layers are offset relative to one
another. It is worth noting the similarity of this system to that of the well-known
metal-oxalate networks [40b]. In the M-oxalates, the cations sit between the layers.
   Although no long range magnetic ordering was observed in this series, this is
yet another example that demonstrates the utility and coordination chemistry of the
dca anion. As with other µ-bonded M–N≡C–N–C≡N–M materials, the exchange
interactions are just too weak to allow 3D magnetic ordering. The [Fe(bipy)3 ]2+
cation is low-spin S = 0 and thus magnetically inert. Murray and co-workers are
currently engaged in replacing this cation with magnetically active ones, such as
those that show spin crossover behavior [40a].




                                                           Fig. 3.16. Anionic 2D hexag-
                                                           onal array displayed by
                                                           [Fe(bipy)3 ][Fe(dca)3 ]2 . The
                                                           cations have been omitted
                                                           for clarity. Shaded, filled and
                                                           open spheres depict Fe, C
                                                           and N, respectively.




3.6 Heteroleptic M(dca)2 L Magnets

Of great interest and importance to the scientific community is the ability to system-
atically manipulate crystal structures in an effort to design and control cooperative
magnetic properties. One strategy involves the use of ancillary organic ligands that
can simultaneously organize metal centers into specific patterns or arrays. In this
regard, several research groups have explored various combinations of dca− and
organic Lewis bases such as pyrazine (pyz), pyrimidine (pym), pyridine (py), 4,4 -
bipyridine (4,4 -bipy), 2,2 -bipyridine (2,2 -bipy), and 4-amino-3,5-bis(pyridin-2-
                                          3.6 Heteroleptic M(dca)2 L Magnets      89

yl)-1,2,4-triazole (abpt). Table 3.2 provides an extensive list of the structurally
known metal-dca compounds, including diamagnetic systems.



3.6.1   Mn(dca)2 (pyz)

The crystal structure consists of two interpenetrating ReO3 -like frameworks that
are assembled from 2D Mn(dca)2 square-like grids which are cross-linked by pyz
ligands along the a-axis, Figure 3.17 [41, 42]. Similar layered motifs have been
observed in some other systems such as Mn(dca)2 (H2 O)2 ·H2 O [12], Mn(dca)2 (2,5-
Me2 pyz)2 (H2 O)2 [43] (see Section 3.6.2) and Mn(dca)2 (EtOH)2 ·Me2 CO [12]. At
198 K, the material crystallizes in the monoclinic space group P 21 /n with a =
7.3514 (11), b = 16.865 (2), c = 8.8033 (12) Å, β = 90.057 (2)◦ and V = 1091.4
(3) Å3 , according to X-rays for a twinned crystal [41b]. In another report, Murray
and co-workers indicated that the compound is orthorhombic, Pnma, between 223
K and room temperature and attribute the structural change to dynamic disorder of
the dca anions [42]. The nuclear structure was also determined at 1.35 K (which
is in the magnetically ordered phase) using neutron diffraction [a = 7.3248 (2),
b = 16.7369 (4), c = 8.7905 (2) Å, β = 89.596 (2)◦ and V = 1077.65 (7) Å3 ].
At 1.35 K, the high-spin Mn2+ center is quite distorted with four Mn–Neq bond
distances ranging from 2.14 (1) to 2.24 (1) Å and two slightly longer Mn–Nax
distances of 2.27 (1) and 2.29 (1) Å while the N-Mn–N bond angles reflect a slight
deformation from the ideal geometries. The significance of this distortion will
be shown to have a profound effect on the magnetism. The shortest metal-metal
distance is that between interpenetrating lattices, which is 6.42 Å. Furthermore,
the other first-row transition metal ions form isostructural networks and a second
β-phase has also been identified for M = Co, Ni, Cu, and Zn [42, 44].




                                                    Fig. 3.17. Interpenetrating
                                                    ReO3 -like network structure of
                                                    Mn(dca)2 (pyz) emphasizing the
                                                    two individual lattices. [2]
                                                                                                                                                  90

Table 3.2. X-ray structural data for numerous dia- and paramagnetic M-dca complexes arranged according to lattice dimensionality. Unless
otherwise noted, all structures were determined at or near room temperature. The corresponding M-dca bonding mode (see Scheme 3.1) is given
in parentheses following the compound name.

Compound                              Space       a (Å)        b (Å)        c (Å)     α (◦ )       β (◦ )       γ (◦ )      V (Å3 )       Ref.
                                      Group
                                                                                     Molecular
Cu(dca)(tcm)(phen)2 (i)               P 21 /n     10.080(7)    12.972(7)    19.874(13) 90          100.22(6)    90          2557.4(28)    57
Cu(dca)2 (phen)2 (i)                  P 21 /c     8.756(4)     14.611(6)    18.979(8) 90           101.21(4)    90          2381.7(18)    58
Mn(dca)2 (phen)2 (i)                  P 21 /c     9.7989(2)    15.0160(5)   17.7189(5) 90          104.595(2)   90          2523.04(12)   59
Zn(dca)2 (phen)2 (i)                  P 21 /c     9.6800(3)    15.0697(7)   17.7166(8) 90          104.628(2)   90          2500.64(18)   59
Ni(dca)2 (4-Meiz)4 (i)                P1          9.448(3)     9.918(3)     15.173(5) 107.85(2)    93.67(2)     104.74(2)   1293.1(7)     60
Cu(dca)(BF4 )(2,2 -bipy) (i)          P bca       8.6469(5)    17.8651(8)   28.7434(15) 90         90           90          4440.2(4)     61
Fe(dca)2 (abpt)2 (i)                  P1          8.4618(5)    9.6086(3)    9.6381(7) 83.661(4)    86.642(5)    65.821(4)   710.44(7)     3
                                                                                     1D chains
Mn(dca)2 (py)2 (ii)                   P 21 /n     7.5401(7)    13.2643(4)   8.6973(9) 90           114.954(2)   90          788.65(11)    33
Mn(dca)2 (DMF)2 (ii)                  P1          6.4242(3)    7.4907(4)    8.4034(4) 103.021(3)   106.485(4)   99.390(4)   366.46(3)     12
Mn(dca)2 (2,2 -bipy) (ii)             C2/c        6.6769(3)    17.2008(2)   13.0142(4) 90          90.110(2)    90          1494.65(8)    33,63
Mn(dca)2 (4,4 -bipy)·H2 O (ii)        I ba2       22.378(6)    22.517(5)    13.519(5) 90           90           90          6812(3)       33
Mn(dca)2 (bpym) (ii)                  C2/c        6.684(3)     17.213(7)    13.042(5) 90           90.27(2)     90          NR            62
Mn(dca)2 (4-bzpy)2 (ii)               P 21 /n     6.374(2)     7.584(2)     26.766(5) 90           91.87(2)     90          1293.3(6)     63
Mn(dca)2 (bpym)·H2 O (i,ii)           P nma       17.5112(4)   11.9955(4)   7.4684(2) 90           90           90          1568.77(9)    64
Fe(dca)2 (bpym)·H2 O (i,ii)           P nma       17.5814(7)   11.9453(5)   7.3292(3) 90           90           90          1539.24(11)   64
Co(dca)2 (bpym)·H2 O (i,ii)           P nma       17.8642(2)   11.9216(2)   7.2860(2) 90           90           90          1551.71(4)    64
                                                  17.768(7)    7.368(4)     21.404(8) 90           92.78(2)     90          2799(2)       65
                                                                                                                                                  3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes




Mn(dca)2 (NITpPy)4 (ii)               P 21 /n
Mn(dca)2 (NH2 -pyz)1.5 H2 O (ii)      C2/c        16.8243(8)   7.5106(3)    24.8192(12) 90         107.287(2)   90          2994.5(2)     43
Co(dca)2 (2-NH2 -pym) (ii)            P 42 /mbc   17.1243(2)   17.1243(2)   7.3816(1) 90           90           90          2164.59(5)    66
Ni(dca)2 (2-NH2 -pym) (ii)            P 42 /mbc   17.0863(6)   17.0863(6)   7.3099(2) 90           90           90          2134.1(1)     66
Cu(dca)2 (2-NH2 -pym)2 (ii)           C2/c        13.579(6)    15.453(5)    7.570(7)    90         92.03(5)     90          1596.7(17)    67
Mn(dca)(NO3 )(terpy) (ii)             P 21 /n     8.825(3)     13.928(4)    14.650(4) 90           96.05(3)     90          1790.7(9)     68
Table 3.2. (Continued.)

Compound                            Space a (Å)             b (Å)        c (Å)     α (◦ )     β (◦ )       γ (◦ )     V (Å3 )       Ref.
                                    Group

Mn(dca)2 (terpy)(H2 O) (ii)         P1        7.574(2)      8.795(3)     14.948(6) 78.16(3)   79.73(3)     81.80(2)   953.1(6)      68
Cu(dca)2 (3-OHpy)2 (i,ii)           P bca     7.266(2)      13.925(3)    30.327(6) 90         90           90         3068.5(12)    56
(PPh4 )2 Co(dca)4 (ii)              C2/c      23.3789(10)   7.5684(3)    28.3778(12) 90       105.621(1)   90         4835.7(3)     37
Cu2 (dca)2 (bipy)1.5 (MeCN)2 (ii)   C2/m      29.5142(7)    7.5761(3)    11.3905(4) 90        106.141(2)   90         2446.5(1)     69
Ru2 (O2 CMe)4 (dca)·MeCN (ii)       C2/m      10.174(2)     13.016(3)    7.0750(14) 90        101.83(3)    90         917.0(3)      70
Zn3 (O2 CMe)4 (dca)2 (bipy)3 (ii)   C2/c      21.603(1)     11.457(1)    17.798(1) 90         104.245(4)   90         4269.6(5)     71
(Me)3 Sn(dca) (ii)                  P nam     17.644(9)     6.565(4)     7.684(3)    90       90           90         NR            72
Ag(dca) (ii)                        P 31 21   3.601(2)      3.601(2)     22.868(22) 90        120          90         NR            73
Ag(dca) (ii)                        P nma     16.133(8)     3.612(2)     5.983(4)    90       90           90         348.8(1)      74
κ-(BEDT-TTF)2 [Cu(dca)Cl]           P nma     12.977(3)     29.979(4)    8.480(2)    90       90           90         3299(1)       75
                                                                                  2D layers
Mn(dca)2 (MeOH)2 (ii)               C2/m      12.409(1)     7.481(1)     6.528(1)    90       119.979(3)   90         524.93(11)    12
Fe(dca)2 (MeOH)2 (ii)               C2/m      12.2247(7)    7.3921(5)    6.4610(4) 90         120.119(1)   90         505.03(5)     12,76
Mn(dca)2 (EtOH)2 ·(CH3 )2 CO (ii)   C2/c      11.316(1)     11.358(1)    12.488(1) 90         96.918(3)    90         1593.4(2)     12
[Mn(dca)2 (H2 O)2 ]·H2 O (ii)       P 21 /n   7.3165(2)     11.6229(5)   11.3590(5) 90        103.241(5)   90         940.28(6)     12
[Ni2 (dca)4 (bpym)]·H2 O (ii)       P nma     16.111(3)     12.755(2)    10.455(2) 90         90           90         2148.4        77
[Co2 (dca)4 (bpym)]·H2 O (ii)       P nma     16.1684(5)    12.9860(3)   10.4207(3) 90        90           90         2187.96(11)   64
[Fe2 (dca)4 (bpym)]·H2 O (ii)       P nma     16.203(3)     13.122(3)    10.438(2) 90         90           90         2219(1)       78
[Fe2 (dca)4 (bpym)(H2 O)2 (ii)      P 21 /n   8.384(2)      9.223(2)     13.983(3) 90         90.95(3)     90         1081.1(7)     78
Cu(dca)2 (phen) (ii)                P 21 /c   9.8389(3)     11.2975(5)   14.2340(5) 90        100.988(2)   90         1553.17(10)   79
β-Cu(dca)2 (pyz) (ii)               C2/m      9.7659(8)     6.8787(7)    7.3870(5) 90         95.254(7)    90         494.15(6)     44
β-Zn(dca)2 (pyz) (123 K) (ii)       Cmmm      7.1189(2)     9.6994(4)    7.3988(3) 90         90           90         510.88(3)     42
Zn(dca)2 (ii)                       P nma     7.6209(4)     7.5958(4)    12.0477(7) 90        90           90         697.65(7)     30
                                                                                                                                            3.6 Heteroleptic M(dca)2 L Magnets




(Me)2 Sn(dca)2 (ii)                 P 21 /c   6.178(3)      11.265(10)   6.860(6)    90       99.56(5)     90         NR            72
(PPh4 )Mn(dca)3 (ii)                P 2/n     13.4354(10)   7.4426(5)    14.1556(10) 90       101.087(1)   90         1389.06(17)   37,38
                                    P 2/n     13.3903(6)    7.5745(3)    14.3935(6) 90        99.663(2)    90         1439.15(10)   37
                                                                                                                                                 91




(PPh4 )Co(dca)3 (ii)
                                                                                                                                                      92

Table 3.2. (Continued.)

Compound                                  Space a (Å)             b (Å)         c (Å)      α (◦ )      β (◦ )       γ (◦ )       V (Å3 )       Ref.
                                          Group
(AsPh4 )Mn(dca)3 (ii)                     P 2/n     13.3943(4)    7.5841(1)     14.3076(4) 90          99.893(1)    90           1431.81(6)    38
(AsPh4 )Ni(dca)3 (ii)                     P 2/n     13.6963(5)    14.7418(3)    14.1266(5) 90          103.315(1)   90           2775.6(2)     36
(AsPh4 )Co(dca)3 (ii)                     P 2/n     13.5777(4)    14.8711(2)    14.1776(4) 90          102.196(1)   90           2798.1(1)     36
(AsPh4 )2 [Ni2 (dca)6 (H2 O)]·H2 O (ii)   P 21 /c   14.2441(8)    7.3046(3)     29.057(2) 90           102.404(2)   90           2952.7(3)     36
(AsPh4 )2 [Co2 (dca)6 (H2 O)]·H2 O (ii)   P 21 /c   14.2905(4)    7.3703(2)     28.9937(8) 90          102.207(1)   90           2984.7(1)     36
[Fe(bipy)3 ][Mn(dca)3 ]2 (ii)             F dd2     28.7821(7)    12.5280(3)    23.7374(4) 90          90           90           8559.3(3)     40
[Fe(bipy)3 ][Fe(dca)3 ]2 (ii)             F dd2     28.8799(6)    12.4011(3)    23.5140(3) 90          90           90           8421.4(3)     40
[Ni(bipy)3 ][Mn(dca)3 ]2 (ii)             F dd2     28.8625(5)    12.5231(2)    23.9239(3) 90          90           90           8647.2(2)     40
Cu(dca)(MeCN) (ii)                        P nma     13.0351(4)    7.7296(2)     6.1895(2) 90           90           90           623.63(3)     69
α-Cu(dca)(bpe) (ii)                       P na21    7.3835(1)     15.2140(5)    12.1963(4) 90          90           90           1370.04(7)    69
Cu(dca)(Me4 pyz)0.5 (ii)                  P 21 /c   3.8969(1)     18.5279(9)    9.9978(5) 90           92.039(3)    90           721.40(5)     69
Cu4 (dca)4 (4,4 -bipy)3 (MeCN)2 (ii)      P1        8.2104(3)     10.0447(3)    13.9494(4) 98.995(2)   93.178(2)    101.633(2)   1108.43(6)    69
                                                                                       3D networks
Mn(dca)2 (pyz) (198 K) (ii)               P 21 /n   7.3514(11)    16.865(2)     8.8033(12) 90          90.057(2)    90           1091.4(3)     41b
α-Fe(dca)2 (pyz) (173 K) (ii)             P 21 /n   7.1848(4)     16.6920(13)   8.6952(6) 90           90.041(5)    90           1042.80(12)   42
α-Co(dca)2 (pyz) (123 K) (ii)             P 21 /n   7.0965(4)     16.6139(9)    8.6342(5) 90           90.047(3)    90           1017.98(10)   42
α-Cu(dca)2 (pyz) (ii)                     Pn        24.2549(7)    6.8571(2)     24.6445(7) 90          91.023(2)    90           4098.2(2)     44
Mn(dca)2 (2,5-Me2 pyz)2 (H2 O)2 (ii)      C2/c      18.5410(10)   11.9929(7)    11.7793(5) 90          126.195(2)   90           2113.8(2)     43
Mn2 (dca)4 (bpym) (ii)                    P 21 /c   7.396(3)      11.498(7)     12.349(9) 90           106.61(5)    90           1006.3(1)     62
Cu2 (dca)4 (bpym) (ii)                    P 21 /c   7.5609(9)     11.477(42)    11.792(2) 90           106.565(6)   90           971.6(1)      62
Zn2 (dca)4 (bpym) (ii)                    P 21 /c   7.446(4)      11.478(4)     12.064(4) 90           107.75(2)    90           982.0(7)      77
                                                                                                                                                      3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes




Mn(dca)2 (H2 O) (iv)                      Ama2      7.5743(2)     17.4533(7)    5.6353(2) 90           90           90           744.97(4)     35
Co(dca)(tcm) (173 K) (iv)                 Ama2      7.4129(3)     17.0895(6)    5.5991(2) 90           90           90           709.31(5)     35
Cu(dca)(tcm) (iv)                         Ama2      7.1884(3)     17.6983(7)    5.7395(3) 90           90           90           730.19(6)     35
Fe(dca)2 (pym)·EtOH (ii)                  P nma     12.917(1)     12.0440(6)    9.2575(8) 90           90           90           1440.2(2)     47
Table 3.2. (Continued.)

Compound                                 Space        a (Å)        b (Å)        c (Å)        α (◦ )   β (◦ )      γ (◦ )   V (Å3 )       Ref.
                                         Group

Co(dca)2 (pym)·EtOH (ii)                 P nma        12.8586(4)   11.9268(4)   9.2126(2)    90       90          90       1412.86(7)    47
Cu(dca)2 (pym)·MeCN (ii)                 P nma        12.5520(5)   11.6557(3)   9.4003(4)    90       90          90       1375.29(9)    49
Co(dca)2 (4,4 -bipy) (ii)                P nma        16.9221(7)   11.4251(4)   8.6147(3)    90       90          90       1665.4(6)     80
Mn(dca)2 (apo) (ii)                      P 21 /n      9.8655(3)    12.1640(4)   10.5046(3)   90       94.795(2)   90       1256.18(7)    81
Co(dca)2 (apo) (ii)                      P 21 /n      9.8222(3)    11.8553(4)   10.4718(4)   90       94.866(2)   90       1214.99(7)    81
Ni(dca)2 (apo) (ii)                      P 21 /n      9.7889(5)    11.7071(6)   10.5283(4)   90       94.610(3)   90       1202.64(10)   81
(PPh3 Me)Mn(dca)3 (123 K) (ii)           P 21 21 21   13.9593(3)   17.2000(2)   20.8587(3)   90       90          90       5008.2(2)     38
β-Cu(dca)(bpe) (ii)                      Cc           12.2904(3)   44.675(1)    14.6413(3)   90       93.004(2)   90       8028.1(3)     69
β-Na(dca) (v)                            Pbnm         6.5015(5)    14.951(2)    3.6050(3)    90       90          90       350.42(5)     15
(Me)2 Tl(dca) (v)                        P 21 /c      6.739(3)     11.830(7)    9.891(7)     90       117.81(3)   90       NR            16
Abbreviations: NR = not reported, phen = 1,10-phenanthroline, Meiz = methylimidazole, abpt = 4-amino-3,5-bis(pyridin-2-yl)-1,2,4-triazole,
bipy = bipyridine, DMF = N,N -dimethylformamide, bpym = bipyrimidine, bzpy = 4-benzoylpyridine, NITpPy = 2-(4-pyridyl)-4,4,5,5,-
tetramethylimidazoline-1-oxyl-3-oxide, pyz = pyrazine, pym = pyrimidine, terpy = 2,2 :6 ,2 -terpyridine, Me = methyl, Et = ethyl, apo =
2-aminopyridine-N-oxide, bpe = 1,4-bis(4-pyridyl)ethene.
                                                                                                                                                3.6 Heteroleptic M(dca)2 L Magnets
                                                                                                                                                     93
  94                    3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes

      A comprehensive dc magnetization, ac susceptibility, specific heat, neutron
  diffraction, and electronic structure study has been reported [41a]. Susceptibil-
  ity data show a sharp maximum at 2.7 K while Cp (T ) shows a λ-anomaly at 2.5
  K that is indicative of 3D magnetic ordering, Figure 3.18. The 2–300 K mag-
  netic data can be very well described by an S = 5/2 1D Heisenberg hamiltonian
  which afforded g = 2.01 (1) and J /kB = −0.27 (1) K. This exchange coupling
  is attributed to the Mn–pyz–Mn intrachain interaction and is consistent with theo-
  retical calculations. The zero-field magnetic structure consists of Mn2+ moments
  [ M = 4.45 (10) µB ] that are aligned parallel to the ac-diagonal owing to a com-
  petition between the single-ion anisotropy and the dipolar field manifested by the
  second interpenetrating lattice [45]. From the magnetic order parameter, it was
  possible to deduce TN = 2.53 (2) K and β = 0.38, which is expected for a 3D
  Heisenberg antiferromagnet. Field-dependent M(T ), M(H ) and Cp (H ) display
  features characteristic of spin flop, Hsf , and paramagnetic, Hc , phase transitions at
  4.3 and 28.3 kOe, respectively, Figure 3.19. These results have been recently con-
  firmed by neutron diffraction which shows no superlattice reflections above Hc ,

                   0.70
                                                                     12
                                                       C (J/mol-K)




                   0.65                                              10
                                                                      8
                   0.60                                               6
χ ' (emu/mol)




                                                                      4
                   0.55                                               2
                                                               p




                                                                      0
                   0.50                                                   1 1.5 2 2.5 3 3.5
                                                                               T (K)
                   0.45                                                                        Fig. 3.18. Low-T ac susceptibil-
          ac




                   0.40                                                                        ity acquired for Mn(dca)2 (pyz)
                                  TN = 2.53 K
                                                                                               showing the cusp associated
                   0.35
                                                                                               with long range magnetic or-
                   0.30
                       0            2           4                     6          8        10   dering. The inset shows Cp (T )
                                                                                               taken in zero-field on a small
                                                    T (K)                                      pellet.

                  0.7

                  0.6
χ' ac (emu/mol)




                  0.5
                  0.4

                  0.3
                  0.2
                        4.3 kOe                     28.3 kOe
                  0.1
                                                                                               Fig. 3.19. H -dependence of χac
                   0
                        0         10       20                        30         40        50   for Mn(dca)2 (pyz) obtained at
                                                                                               2 K (Hac = 1 Oe, ω = 10 Hz)
                                                H (kOe)                                        [41a].
                                               3.6 Heteroleptic M(dca)2 L Magnets         95

indicating a ferromagnetic-like spin configuration [46]. Complete saturation occurs
at 100 kOe (2 K) reaching a value of 4.87 NµB . Mn(dca)2 (pyz) is the only com-
pound in the series shown to undergo long range magnetic ordering, presumably
due to its large effective spin value of 5/2. By comparison, a considerably stronger
1D exchange coupling strength of −3.90 K was found for α-Cu(dca)2 (pyz) [44b].



3.6.2    Mn(dca)2 (2,5-Me2 pyz)2 (H2 O)2

The extended structure of this compound is polymeric and consists of slightly
puckered 2D Mn(dca)2 (H2 O)2 layers that reside in the bc-plane, Figure 3.20 [43].
The layers are held together by hydrogen bonding interactions between the coordi-
nated H2 O and the nitrogen atoms of the 2,5-Me2 pyz molecules, Figure 3.21. Every
other MnN4 O2 chromophore is rotated 5.3◦ with respect to its nearest neighbor and
the Mn–Neq and Mn–O bond distances are all very similar [2.198 (2), 2.212 (2)
and 2.218 (2) Å]. The intralayer Mn· · ·Mn separation is 8.405 Å while the inter-
layer Mn–OH2 · · ·2,5–Me2 pyz· · ·OH2 –Mn interaction affords a longer distance of
11.475 Å.
   Ac susceptibility shows a maximum in χac (T ) near 1.8 K which suggests a long
range magnetic ordering of the spins [43]. At the maximum, a very sharp spike
was observed that is often attributed to a spontaneous magnetization induced by
spin canting, Figure 3.22. Similar behavior was observed in the parent Mn(dca)2
compound [6, 8, 12]. The T -dependent magnetic susceptibility could be modeled




Fig. 3.20. Portion of the crystal structure of Mn(dca)2 (2,5-Me2 pyz)2 (H2 O)2 depicting only
the 2D Mn(dca)2 (H2 O)2 layers. Hydrogen atoms have been omitted for clarity purposes.
 96                  3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes




                                                       Fig. 3.21. Hydrogen-bonded 3D network
                                                       of Mn(dca)2 (2,5-Me2 pyz)2 (H2 O)2 . Hydro-
                                                       gen bonding interactions are shown as dashed
                                                       lines.


                  0.78

                  0.76
χ' ac (emu/mol)




                  0.74

                  0.72

                  0.70
                            T = 1.78 K
                  0.68       N


                  0.66
                      1.5    1.75    2   2.25    2.5   2.75    3

                                         T (K)

 Fig. 3.22. χac (T) for Mn(dca)2 (2,5-Me2 pyz)2 (H2 O)2 showing the sharp spike that arises from
 noncollinear antiferromagnetic ordering of the Mn2+ moments.


 by a 3D spin hamiltonian which gave g = 2.00 (1) and J /kB = −0.175 (1) K. The
 weak exchange interaction is typical of a large number of µ-bonded metal-dca solids
 that contain Mn2+ ions. M(H ) at 1.9 K indicates that saturation magnetization is
 not quite obtained although a large value of 4.93 NµB is reached, which is very
 close to the expected value of 5 µB .



 3.6.3               Mn(dca)2 (H2 O)

 The crystal structure is isomorphous to M(dca)(tcm) as described in Section 3.4
 which has a self-penetrating 3D architecture [35]. Because a symmetry-imposed
 mirror plane lies perpendicular to the chain axis, the dca·H2 O moiety is disordered
 over two positions, Figure 3.23. At first glance, this disordered group appears
 geometrically equivalent to tcm, hence tcm can also be readily substituted into this
 system. The Mn–Namide distance is unusually long at 2.417 (4) Å, suggesting a
 very weak coordination.
                                                3.6 Heteroleptic M(dca)2 L Magnets          97




Fig. 3.23. Segment of the crystal structure of Mn(dca)2 (H2 O) illustrating the disorder of the
dca and H2 O moities. Dashed lines represent hydrogen bonds.

   Mn(dca)2 (H2 O) is a canted antiferromagnet (weak ferromagnet) below TN = 6.3
K, as indicated by a sharp peak in χ (T ) [35]. At 300 K, the magnetic moment
is consistent with high-spin Mn2+ and gradually decreases upon cooling, as a
result of antiferromagnetic correlations between spin centers. At TN , an abrupt
increase occurs due to the formation of a spontaneous magnetization, reaching
moments as large as 10.9 µB (Hdc = 20 Oe). External fields in excess of ∼200 Oe
essentially saturate the canted moment yielding magnetic behavior more typical
of a collinear antiferromagnet. Hysteresis experiments at 2 K showed a coercive
field of 250 Oe and a remnant magnetization, Mr , of 112 emu Oe mol−1 . Complete
saturation magnetization was not observed up to fields of 5 T (2 K) which display a
linear M(H ) response consistent with a spin canted system. A considerably reduced
magnetization value of 1.7 µB was obtained at 5 T, well below the anticipated value
of 5 µB for Mn2+ .


3.6.4    Fe(dca)2 (pym)·EtOH

Three-dimensional scaffolds similar to Mn(dca)2 (pyz) can also be prepared using
pyrimidine (pym) which is 1,3-diazine. This scheme, however, only seems to work
for M = Fe, Co, and Cu [47] but not Mn or Ni [48, 49]. Ishida and co-workers
recently described a preliminary account of the synthesis and characterization of
Fe(dca)2 (pym)·EtOH [47]. The crystals were found to contain 0.5–1.0 ethanol per
formula unit. The polymeric structure consists of puckered 2D Fe(dca)2 sheets in
the ac-plane that are connected together by bridging pym ligands along the b-axis,
Figure 3.24. Structural disorder occurs for each of the bridging dca ligands [47a].
The Fe2+ center is slightly elongated with four Fe–Neq distances ranging between
2.138 (4) and 2.142 (4) Å and two Fe–Nax distances of 2.202 (4) Å. The intralayer
Fe· · ·Fe separation is 7.9458 (5) Å while the intrachain distance is 6.0220 (3) Å.
   The magnetic behavior was measured between 2 and 300 K and fitted to the
Curie–Weiss expression, giving C = 4.40 emu K mol−1 (θ = −7.0 K) and
C = 1.73 emu K mol−1 (θ = −4.4 K) for the Fe and Co-analogs, respectively
[47a]. In an external field of 5 kOe, χ T (T ) decreases continuously down to ∼8 K
98      3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes




Fig. 3.24. Three-dimensional framework structure of Fe(dca)2 (pym)·EtOH viewed parallel to
the (010) direction. The ethanol molecules have been omitted for clarity purposes. Fe, C and
N atoms are represented by shaded, filled and open spheres, respectively.


and then increases abruptly to reach a peak at 3.6 K. Below this the data decrease
again as a result of likely saturation effects. χac (T ) showed a sharp peak at 3.2 K
due to long range magnetic ordering. Similar behavior was found for the Co-analog
but a lower Tc was observed near 1.8 K. Low-field M(T ) in the region near TN
give strong indications for canted antiferromagnetism. According to M(H ) at low
temperatures, both compounds exhibit an initial rapid increase in the magnetiza-
tion due to the spontaneous moment. At higher fields, the magnetization becomes
approximately linear up to the highest field measured of 90 kOe. Such behavior
is generally associated with spin-canted systems. It is worth noting that Co- and
Fe(dca)2 (pym)·EtOH join an ever increasing library of canted/weak ferromagnets.



3.6.5    Fe(dca)2 (abpt)2

Materials comprised of Fe2+ ions have received much interest over the years be-
cause of their ability to show spin-crossover behavior which can be provoked by
light, temperature or pressure [50]. Systems such as these usually involve FeN6
coordination spheres although some exceptions occur. In contrast to the aforemen-
tioned polymeric materials, Fe(dca)2 (abpt)2 exists as discrete mononuclear entities,
Figure 3.25 [3]. Two abpt ligands chelate to the Fe2+ center to occupy all four equa-
torial sites. The remaining axial positions are occupied by monodentate dca anions.
This structural arrangement contrasts with that of Fe(o-phenanthroline)2 (NCS)2
which adopts a cis-conformation [51]. The crystal packing of Fe(dca)2 (abpt)2 con-
        3.7 Dicyanophosphide: A Phosphorus-containing Analog of Dicyanamide            99




                                            Fig. 3.25. Room temperature molecular struc-
                                            ture of Fe(dca)2 (abpt)2 . Scheme 3.1 Possible
                                            dicyanamide coordination modes.


sists of chains that lie along the [001] direction. Relatively strong intermolecular
contacts exist so as to define two-dimensional sheets in the [101] plane.
   While this material does not exhibit long range magnetic order, it is included here
because the spin-crossover phenomenon is a cooperative effect. Fe(dca)2 (abpt)2 is
the first example of a spin-crossover complex that contains dca− . Magnetic sus-
ceptibility data show an incomplete two-step spin transition. Tsc , the temperature at
which 50% of the spin conversion occurs, is ∼86 K, one of the lowest temperatures
observed for a Fe2+ spin-crossover material. Further details of this study can be
found in Ref. [3].




3.7 Dicyanophosphide: A Phosphorus-containing Analog
    of Dicyanamide

As noted in this chapter, the chemistry of dicyanamide, especially with regard
to metal complexes, has been extensively investigated. However, little is known
about its phosphorus-containing analog. Dicyanophosphide (dcp), [P(CN)2 ]− , was
first reported in the literature in 1977 [52]. Shortly thereafter, it was structurally
characterized and shown to have a molecular structure similar to dca [53]. The
same authors published a limited report on the reactivity of dcp [54]. Because
phosphorus has d orbitals available for bonding, the metal ion complexes with
dicyanophosphide would be of great interest with respect to their differences in
magnetic coupling. Magnetically ordered M(dca)2 complexes are readily prepared
in aqueous media using the water soluble Na(dca), but unfortunately the analo-
gous synthesis with dcp is not possible as it is hydrolytically unstable [55]. Re-
100     3 Cooperative Magnetic Behavior in Metal-Dicyanamide Complexes

actions of dicyanamide with divalent metal ions in non-aqueous media produce
1D and 2D network structures with no magnetic ordering [37]. Hence, M(dcp)2
complexes have eluded their rational preparation [55]. Ultimately, a comparison
of the magnetic properties of M(dca)2 and M(dcp)2 materials is desired, provided
a non-aqueous route to these materials can be achieved.




3.8 Conclusions and Future Prospects

It has been demonstrated that the coordinative versatility of the dicyanamide ligand
leads to a large variety of structural and magnetic properties. In the examples
shown, it is clear that the µ3 -bonded dca configuration (scheme (iv)) stabilizes the
strongest exchange coupling between spin-bearing metal sites. This is in marked
contrast to µ-bonding via the nitrile N-atoms that affords a five-atom superexchange
pathway and thus very weak magnetic interactions. Conceivably, it may be possible
to achieve µ-bonding via the amide nitrogen and one of the nitrile substituents that
would provide a shorter three-atom pathway and significant exchange interactions.
With all of the now known metal-dca compounds, bonding scheme (iii) remains
elusive. Individually, the structures described in this chapter contain only one type
of dca bonding mode and new topologies may arise if multiple bonding modes
can coexist in a single material. Recently reported Cu(dca)2 (3-OHpy)2 {OHpy
= hydroxypyridine} does in fact feature two coordination modes, mono- and µ-
bonded dca− [56].
    Mixed-anion species such as the tcm/dca combination discussed in Section 3.4
afford interesting hybrid structures with somewhat reduced TN s relative to neat
M(dca)2 . Other possible alternatives that can be envisioned include N3 − /dca− ,
NCS− /dca− , NCO− /dca− , other pseudohalides, and perhaps carboxylate deriva-
tives. Additional complexity stemming from the use of organic co-ligands is also
anticipated. Such efforts will require clever synthetic strategies to ensure phase-
pure materials that contain the desired ingredients. Furthermore, the vast majority
of metal-dca materials contain divalent (or diamagnetic) transition metal ions while
trivalent ions such as rare earth, Fe3+ , Cr3+ , Mn3+ , etc. have yet to be explored.
    Ferrimagnetic materials consisting of dca- anions have not been realized owing
to the difficulty in preparing appropriate building blocks. Alternatively, it should be
possible to create solid solutions that will allow tunability of the desired magnetic
properties such as Tc , remnant magnetization, and coercivity. Likewise, attention
must be paid to prevent multi-phase materials.
                                                                           References       101

Acknowledgments

It is a great pleasure to acknowledge the following people for their significant
contributions to this work: D.N. Argyriou, A.M. Arif, G.M. Bendele, H.N. Bordallo,
L. Chapon, J.E. Crow, A.J. Epstein, R. Feyerherm, U. Geiser, E. Goremychkin, J.
Gu, Q.-Z. Huang, C.D. Incarvito, C.R. Kmety, D.W. Lee, L. Liable-Sands, A.
Loose, J.W. Lynn, S.R. Marshall, J.S. Miller, S. Pagola, F. Palacio, J.W. Raebiger,
D.H. Reich, A.L. Rheingold, J.A. Schlueter, P.W. Stephens, and M.B. Stone.



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4 Molecular Materials Combining Magnetic and
  Conducting Properties
     Peter Day and Eugenio Coronado




4.1 Introduction

Planar organic donors or acceptors such as TTF derivatives and TCNQ derivatives,
(Scheme 4.1) have been extensively used in the synthesis of molecular conductors
and superconductors. For example, when TTF reacts with TCNQ a partial electron
transfer occurs from the donor to the acceptor giving rise to the charge transfer
salt [TTF]δ+ [TCNQ]δ− which shows metallic properties. Its structure consists of
uniform segregated chains of the donor and the acceptor which stack in the solid
state giving rise to delocalised electron energy bands due to overlapping between
the π-orbitals of adjacent molecules. Electron delocalisation is also obtained in the
solids formed by the ion-radicals resulting from oxidation (or reduction) of one of
these two kinds of molecules and a charge-compensating counterion. In this context,
cation-radical salts of organic donors formulated as [Donor]m Xn have provided
the best examples of molecular conductors and superconductors. Typically, the
counterion X is a simple inorganic monoanion of the type Cl− , Br− , I− , PF− , AsF− ,
                                                                        3    6      6
BF− , ClO− , NO− , . . . The structures of these salts consist of segregated stacks of
    4      4      3
the planar radical cations interleaved by the inorganic anions (Figure 4.1). A way
to incorporate localised magnetic moments in these materials is to use magnetic
anions as charge-compensating counterions.
   Inorganic chemistry provides a wide choice of metal complexes of various nucle-
arities and dimensionalities that can be used with this aim. They range from simple
mononuclear complexes of the type [MX4 ]n− (M = Fe(III), Cu(II); X = Cl, Br);
[M(C2 O4 )3 ]3− (M = Fe(III), Cr(III)), [M(CN)6 ]3− (M = Fe(III)), to cluster-type
complexes (polyoxometallates), to chain complexes as the substituted dithiolates
[M(mnt)2 ]− (mnt = maleonitriledithiolate, M = Ni, Pt and Pd), to layered struc-
tures as the bimetallic oxalate complexes [M(II)M(III)(ox)3 ]− (M(II) = Mn, Co,
Ni, Fe, Cu; M(III) = Fe, Cr). Most of the examples so far reported of hybrid molec-
ular materials combining a conducting component with a magnetic component are
based on the above organic/inorganic combination [1, 2]. In this chapter we will
focus especially on the achievements so far reported in these materials. Before
doing so, however, we will introduce the main reasons that justify the intense effort
devoted to this kind of molecular material.
106         4 Molecular Materials Combining Magnetic and Conducting Properties

        S          S            NC                     CN

        S          S
                                NC                     CN
             TTF
                                             TCNQ
       S           S             S                     S
                                         S      S

       S           S                     S      S      S
                                 S
        TM-TTF                        BEDT-TTF or ET
       Se          Se
                                 Se      S      S      Se

       Se          Se
                                 Se      S      S      Se
        TM-TSF                   BEDSe-TTF or BEST
                                 S       Se     Se     S


                                 S       Se     Se     S
                                 BEDT-TSeF or BETS
                                 S       S      S

                                         S      S       S
      perylene (per)
                                      BET-TTF or BET        Scheme 4.1




                                                            Fig. 4.1. Schematic arrange-
                                                            ment of an organic–inorganic
                                                            composite compound.




4.2 Interest of Conducting Molecular-based Magnets

From a physical point of view hybrid materials formed by two molecular net-
works are interesting because they can exhibit a coexistence of the two distinct
physical properties furnished by the two networks, or novel and improved proper-
ties with respect to those of the two networks due to the interactions established
between them. In the particular case of the materials combining magnetic and con-
ducting properties a quite interesting case of coexistence we can look for is that
                            4.2 Interest of Conducting Molecular-based Magnets     107

of ferromagnetism with superconductivity. These two cooperative properties are
considered as mutually exclusive. Their coexistence has been the subject of long
debate in solid state physics and has been investigated from both theoretical and
experimental points of view in extended inorganic lattices [3]. A second reason for
examining the interplay of the localised moments normally found in molecular-
based magnetic materials with conduction electrons lies in the possibility that it
will provide a further mechanism for exchange interaction through the so-called
RKKY interaction.


4.2.1   Superconductivity and Magnetism

The fundamental difference between superconductivity and normal metallic con-
duction lies in the fact that in the former the current carriers are pairs of electrons
(Cooper pairs), while in the latter, to a first approximation, the electrons move inde-
pendently. Interaction between electrons and lattice vibrations is the most common
means of overcoming the Coulomb repulsion, creating a modest attractive poten-
tial. However, the presence of a magnetic field can overcome the pairing energy and
return the superconductor to the normal state. Thus superconductors are charac-
terised by critical field as well as critical temperature. However, not only externally
applied fields are effective; in a ferromagnet there is the internal field due to the
ordered moments, while even in antiferromagnets or paramagnets there are local
fields. It has therefore been pointed out, with justice, that magnetism and supercon-
ductivity are inimical to each other. Ginzburg [4] first pointed out that co-existence
between superconductivity and ferromagnetism was impossible.
    In conventional superconductors, even a few percent of paramagnetic impurity
atoms in the lattice are sufficient to suppress superconductivity [5]. The first com-
pounds in which long range magnetic order and superconductivity both figured
were discovered in the 1970s, with the ternary lanthanide Rh borides and Chevrel
phases LnMo6 S8 [6, 7] On lowering the temperature the former first become super-
conducting (e. g. Tc2 is 8.9 K for the Er compound), but then return to the normal
state (Tc2 ∼ 0.9 K in ErRh4 B4 ) when they become ferromagnetic. There is even
a narrow temperature range just above Tc2 over which the two states co-exist, al-
though the magnetic order is not collinear ferromagnetic, but sinusoidal [8, 9]. It
is certainly significant that in both series of compounds the source of the magnetic
moments is the 4f lattice of lanthanide ions, while the superconductivity comes
from conduction bands formed mainly from the 4d orbitals of the transition metal.
Any exchange interaction is undoubtedly very weak, because of the large distance
between the two kinds of ion and small f–d orbital overlap. Similar considerations
are likely to apply in the magnetic molecular charge transfer salts, where cations and
anions are widely separated. One recent example of an oxide superconductor is even
more spectacular: RuSr2 GdCu2 O8 has a layer structure reminiscent of the high tem-
perature cuprate superconductors, with double CuO4 layers alternating with layers
108     4 Molecular Materials Combining Magnetic and Conducting Properties

of corner-sharing RuO6 octahedra interspersed with Gd and Ba. It becomes ferro-
magnetic at 132 K and superconducting at 40 K, without loss of ferromagnetism
[10]. The astonishing lack of impact of the magnetic order on the superconductivity
has been ascribed to a fortuitous effect of crystal symmetry, ensuring that nodes in
the conduction electron density occur exactly at the magnetic centers.
    Several of the LnMo6 S8 phases become antiferromagnetic rather than ferromag-
netic at low temperature, and in these cases the superconductivity is not suppressed
[11, 12]. For example, Tc and TN are, respectively, 1.4 and 0.8 K for GdMo6 S8 . This
is because the localised magnetic moments vanish when averaged over the scale of
the superconductivity coherence length of around 100 Å. However, the critical field
is influenced by the onset of long range antiferromagnetic order, being decreased
below TN in LnMo6 S8 (Ln = Gd, Tb, Dy) but enhanced in SmRh4 B4 .
    The advantage of molecular materials compared to the extended inorganic solids
is that the interactions between the two molecular networks can be made very weak,
since the intermolecular contacts are of the Van der Waals type or hydrogen bonds.
The drawback is the high difficulty in designing and crystallising such hybrid
materials. The usual combination of a discrete magnetic anion with an oxidised
organic donor may be appropriate to obtain a material exhibiting conductivity or
even superconductivity, but the magnetic network will most probably behave as a
paramagnet. A rational strategy to introduce ferromagnetism in the material is to
use, as inorganic anion, an extended magnetic layer, as for example the bimetallic
oxalato-complexes. However, this novel approach requires the formation of the
layered network at the same time that the organic donor is oxidised. As we can
imagine, the crystallisation of such a hybrid is not an easy task. Furthermore, even if
one succeeds in getting crystals from such a combination, that does not guarantee
the superconductivity in the organic network as no control on the packing and
oxidation state of the donor is possible. Thus, the design of such materials remains
a chemical challenge.


4.2.2   Exchange Interaction between Localised Moments
        and Conduction Electrons

The second point of interest arises from the interaction between the two networks
as it may result in an exchange coupling between the localised magnetic mo-
ments through a mechanism that resembles the so-called RKKY-type of exchange
proposed in the solid state to explain the magnetic interactions in transition and
rare-earth metals and alloys [13]. This kind of indirect interaction is of long range,
in contrast to the superexchange one, and presents an oscillatory behavior which
can give rise to ferro- or antiferromagnetic coupling, depending on the distance
between the moments. In the lanthanide metals for example, the partially filled 4f
shells give rise to strongly localised magnetic moments which do not have over-
lapping orbitals. Therefore, the spin coupling between these f-electrons occurs via
                            4.2 Interest of Conducting Molecular-based Magnets      109

the conducting electrons (mainly of s-type) which are strongly coupled with the
f-electrons. Thanks to this intra-atomic f–s coupling, the f-electrons of a given site
are able to strongly polarise the spins of the conduction electrons which are in the
vicinity. This local polarisation leads to a modulation of the electron densities in the
band which is different for the up and down spins. A second magnetic ion situated
at a certain distance from this ion will be informed by the conduction electrons of its
spin direction. As a result, these two localised magnetic moments will be coupled
by an effective coupling Jind . The sign and magnitude of this indirect coupling is
given by the following expression:
                2
           9π Jdir n 2
   Jind =                 F (2kF R)                                            (4.1)
            2 EF N
                                                                            n
where Jdir is the direct interaction between localised and itinerant spins, N is the
                                                                 √
number of conduction electrons per magnetic site and kF = 2me EF / is the
momentum of the electron at the Fermi level, EF (Fig. 4.2).
   Therefore, this indirect interaction is expected to be proportional to the direct
interaction between localised and itinerant spins. Its strength decreases as 1/R 3 ,
where R is the distance between the magnetic sites, in the same way as a dipolar




                                                      Fig. 4.2. Oscillating exchange
                                                      interaction with distance between
                                                      two localised moments in the
                                                      RKKY model.
110     4 Molecular Materials Combining Magnetic and Conducting Properties

interaction. Its sign is determined by the oscillating function F (x) which can
give either ferromagnetic or antiferromagnetic coupling between the magnetic
sites, depending on their separation R. The period for these oscillations depends
on the concentration of conduction electrons, n, since in the free electron model
kF = (3/8πn)1/3 .
   In molecular conductors containing discrete magnetic anions, an indirect ex-
change interaction between the magnetic moments via the conduction electrons is,
in principle, possible. However, its strength is expected to be quite small as the
direct interaction between the two networks via a coupling between the itinerant
π-electrons and the d-electrons of the magnetic center, is also very weak. Still, the
physics associated with this exchange interaction may differ in several aspects from
that predicted by the RKKY model. Thus, the model assumes that the conduction
electrons can be described by the free electron model. In molecular conductors
this model is too crude as the electrons are strongly correlated; furthermore, these
systems have low dimensional electronic structures. On the other hand, while in
classical metals the direct interaction involves an intra-atomic coupling between
the unpaired electrons of the metal (d or f) and the s-electron carriers, in the mag-
netic synthetic metals this interaction involves an intermolecular π–d coupling.
These important differences justify the effort currently being devoted to preparing
and physically characterising this novel type of molecular material.
   To conclude this section, it is worth mentioning that the association between
cation-radicals and magnetic anions is not the only way to obtain molecular ma-
terials having conducting electrons and localised magnetic moments. Materials
formed by a single network can also provide examples of this kind. An illustra-
tive example is the compound [Cu(pc)]+0.33 [I− ]0.33 (pc = phthalocyanine) [14, 15].
                                               3




             J s-d




J d-d




  LOCAL                           Fig. 4.3. Coupling between    Cu2+    moments    in
            s-electron carriers
 MOMENTS                          [Cu(Pc)]+0.33 (I− )−0.33 .
                                                  3
                            4.3 Magnetic Ions in Molecular Charge Transfer Salts     111

The compound is a one-dimensional metal formed by columnar stacks of partially
oxidised Cu(pc) units separated by a distance of 3.2 Å. The electron delocalisation
occurs through the overlap between the π -molecular orbitals of aromatic rings of
adjacent phthalocyanine molecules. The paramagnetic Cu(II) ions are embedded
in this “Fermi sea” of itinerant electrons. Owing to the large Cu–Cu distance, the
Cu2+ ions are expected to be magnetically uncoupled. However, coupling between
the Cu2+ local moments (represented as Jd–d in Figure 4.3) of ca. 4 cm−1 has been
detected by EPR, NMR and magnetic susceptibility studies. It has been proposed
that such coupling occurs through the conduction electrons which are strongly
coupled to the local magnetic moments (Jπ –d coupling).




4.3 Magnetic Ions in Molecular Charge Transfer Salts

Over the last 15 years there have been many attempts to introduce magnetic cen-
ters into conducting molecular lattices by synthesising charge transfer salts with
transition metal complexes as anions. Because of the great diversity of metals,
ligands, connectivity and structure types it is difficult to present a unified picture
of what has been accomplished, but since the primary interest in the present chap-
ter concerns the magnetic species, the following sections are organised from the
point of view of the metal-containing complexes. These may be monomeric with
monoatomic or polyatomic ligands, discrete clusters or polymeric structures infi-
nite in one or two dimensions. The different organic molecules used to form such
hybrid organic/inorganic materials are summarised in Scheme 4.1.


4.3.1     Isolated Magnetic Anions

4.3.1.1    Tetrahalo-metallates
Following the discovery of the first molecular charge transfer salts that behaved
as superconductors, many attempts have been made to synthesise analogous com-
pounds containing paramagnetic moments inside the lattice. The so-called Bech-
gaard salts [16] of TTF, TMTTF and TMTSF contain diamagnetic tetrahedral and
octahedral anions such as [ClO4 ]− and [PF6 ]− so it was natural to seek examples
with tetra- and hexa-halometallates. These examples are summarized in Table 4.1.
The first such compound whose structure was determined, (TMTTF)[FeCl4 ], how-
ever, not only has a different stoichiometry from the 2:1 Bechgaard salts but a
completely different packing of the donor molecules, which form stacks but with al-
ternate long axes orthogonal and no significant interaction between them, although
there are several S· · ·Cl contacts of less than the sum of the van der Waals radii [17].
Table 4.1. Structures and physical properties of charge transfer salts containing tetra- and hexa-halogeno-metallate anions.
                                                                                                                                           112



Compound                      Packing                         Electrical Properties                   Magnetic Properties          Ref.

(TMTTF)[FeCl4 ]               Orthogonal linear stacks;      insulator (σRT > 10−5 S cm−1 )           PM; θ = −5 K                 17
                              isolated anions
(TMTSF)[FeCl4 ]               Two independent linear stacks, –                                        AFM below 4 K;               19
                              isolated anions                                                         C = 4.2 emu K mol−1
                                                                                                      θ = −7.5 K
(Perylene)3 [FeCl4 ]          Stacks of donor tetramers;      semiconductor (σRT = 0.17 S cm−1 ;      Dimers of FeCl− ;
                                                                                                                    4              27
                              anions in pairs                 Ea = 0.12 eV)                           J = −1.26 K
(Perylene)3 [FeBr4 ]          Stacks of donor tetramers;      semiconductor                           Dimers of FeBr− ;
                                                                                                                    4              27
                              anions in pairs                                                         J = −3.72 K
(TTF)14 [MnCl4 ]4             TTF trimers and monomers;       semiconductor (σRT = 0.15 S cm−1 ;      PM; C = 1.14 emu K mol−1 ;   36,37
                              isolated anions                 Ea = 0.2 eV)                            θ = −4 K
(TTF)14 [CoCl4 ]4             Same as Mn salt                 semiconductor (σRT = 0.15 S cm−1 ;      PM;                          36,37
                                                              Ea = 0.2 eV)                            C = 0.657 emu K mol−1 ;
                                                                                                      θ = −4 K
(TTF)[MnCl3 ]∼0.75            No structure                    semiconductor (σRT = 15 S cm−1 ;        AFM Mn2+ chain               36
                                                              Ea = 0.1 eV)                            C = 3.50 emu K mol−1 ;
                                                                                                      θ = −14 K
(BEDT-TTF)[MnCl4 ]0.3–0.4 No structure                        semiconductor (σRT = 0.5 S cm−1 )       PM; C = 1.30 emu K mol−1 ;   38
                                                                                                      θ = −1 K
(BEDT-TTF)[CoCl4 ]0.3–0.4 No structure                        semiconductor (σRT = 0.5 S cm−1 )       PM; C = 0.87 emu K mol−1 ;   38
                                                                                                      θ = −1.3 K
(BEDT-TTF)3 [MnCl4 ]2         β donor layers; MnCl4 layers semiconductor (σRT = 25 S cm−1 ;           –                            39
                                                                                                                                           4 Molecular Materials Combining Magnetic and Conducting Properties




                                                           Ea = 0.04 eV)
PM = Paramagnetic; AFM = antiferromagnetic
Table 4.1. (Continued.)

Compound                       Packing                         Electrical Properties              Magnetic Properties          Ref.

(BEDT-TTF)3 [CuBr4 ]           α-stacked layers;               semiconductor (σRT = 0.25 Scm−1 ; AFM;                          49,55
                               planar CuBr2−
                                           4
                                                               Ea = 0.07 eV)                     C = 2.77 emu K mol−1
                                                                                                 θ = −140 K;
                                                                                                 1st order transition 59 K
(TTMTTF) [CuBr4 ]              non-planar TTMTTF2+             insulator (σRT = 10 −10 S cm−1 )  PM; θ = −0.5 K                55
(BETS)2 [FeCl4 ]               λ donor stacks; anions layers   metal–insulator transition 8.5 K; AFM; TN = 8.5 K               28
                                                               superconducting > 3.2 kbar
(BETS)2 [FeCl4 ]               κ donor stacks; anions layers   superconducting: Tc = 0.1 K       AFM; TN = 0.45 K              35
(BETS)2 [FeBr4 ]               κ donor stacks; anion layers    superconducting: Tc = 1.1 K       AFM; TN = 2.5 K               34
(BET-TTF)2 [FeCl4 ]            2 types of donor layers;        metal–insulator transition ∼20 K  PM;                           42
                               isolated anions                                                   Fe· · ·Fe AFM dimers at low
                                                                                                 temperature (J = −0.22 K)
(BEDT-TTF)2 [FeCl4 ]          Layers of dimerised stacks;      semiconductor: Ea = 0.21 eV       PM; θ = −4 K                  20
                              layers of anions
(BEDT-TTF)[FeBr4 ]            Donors dimerised; no stacks      insulator                          PM                           20
(BEDT-TTF)3 [CuCl4 ]·H2 O     Layers of stacked trimerised     metal                              PM                           40
                              donors; layers of anions
(BEDT-TTF)3 [NiCl4 ]·H2 O     Layers of stacked trimerised     metal–insulator transition 100 K   –                            54
                              donors; layers of anions
(BEDT-TTF)2 [ReCl6 ]·C6 H5 CN Layers of a-stacked donors;      semiconductor (σRT = 3 S cm−1 ;    PM; C = 1.10 emu K mol−1 ; 57
                              layers of ReCl6 and C6 H5 CN     Ea ∼ 0.07–0.15 eV)                 θ = −0.14 K
(BEDT-TTF)2 [IrCl6 ]          3D lattice of donor dimers and   semiconductor                      PM;                        57
                              anions                           (σRT = 10−2 S cm−1 ;               C = 0.234 emu K mol−1 ;
                                                                                                                                       4.3 Magnetic Ions in Molecular Charge Transfer Salts




                                                               Ea = 0.23 eV)                      θ = −0.37 K
PM = Paramagnetic; AFM = antiferromagnetic
                                                                                                                                       113
114     4 Molecular Materials Combining Magnetic and Conducting Properties

Both this salt, and one containing [MnCl4 ]2− , are semiconductors and paramagnets
with small negative Weiss constants. The corresponding Se salt (TMTSF)[FeCl4 ]
was shown to contain two kinds of columnar stacks, one with the long molecular
axes parallel, and the other orthogonal, as in the TMTTF salt [18]. Curiously, this
structure was reported again, quite independently and without reference to the ear-
lier work [19]. The magnetic properties are dominated by the Fe, with χT at room
temperature reaching 4.2 emu K mol−1 (cf. 4.375 for S = 5/2). The [FeCl4 ]− are
well isolated, though like the TMTTF salt, there are Se· · ·Cl close contacts. There
is a small negative Weiss constant (−7.5 K) but significantly, the susceptibility
becomes anisotropic below 4 K, suggesting the onset of antiferromagnetism [19].
   The tetrahaloferrate(III) salts of the extended electron donor BEDT-TTF present
a fascinating contrast [20]. Electrochemical synthesis under the same conditions
yielded different chemical stoichiometries for the salts containing [FeCl4 ]− and
[FeBr4 ]− . The structure of (BEDT-TTF)2 [FeCl4 ] consists of dimerised stacks of
BEDT-TTF molecules by the sheets of tetrahedral [FeCl4 ]− anions. The anions
are situated in an ‘anion cavity’ formed by the ethylene groups of the BEDT-TTF
molecules, which are arranged in the sequence · · ·XYYXXYYX· · · (Figure 4.4).
Adjacent molecules of the same type (XX and YY ) stack uniformly on top of each
other but with a slight displacement between neighbors along the long in-plane
molecular axis. On the other hand, the long in-plane molecular axes of adjacent
molecules of different type (XY and YX ) are rotated relative to one another.
Furthermore, X and X (or Y and Y ) are closer to each other (≈ 3.60 Å) than X and
Y (3.81 Å). The shortest distances between BEDT-TTF molecules are shorter than
the sum of the van der Waals radii of two sulfur atoms (3.60 Å), thus suggesting
the possibility of a quasi-one-dimensional interaction along the a direction.
   On the other hand, in (BEDT-TTF)[FeBr4 ], there are no stacks but planes of
closely spaced BEDT-TTF, in marked contrast to most of the compounds contain-
ing this donor molecule. The only short S· · ·S distances (<3.50 Å) are between
two BEDT-TTF molecules in different pairs but there is no continuous network of




                                           Fig. 4.4. The crystal structure of (BEDT-
                                           TTF)2 [FeCl4 ], showing the XXYYXX stack-
                                           ing sequence of donor cations.
                           4.3 Magnetic Ions in Molecular Charge Transfer Salts   115

short S· · ·S contacts through the lattice. The [FeBr4 ]− form a three-dimensional
lattice separated by the pairs of BEDT-TTF molecules. One [FeBr4 ]− has short
intermolecular distances to two donor molecules but no extended interaction be-
tween BEDT-TTF molecules through the [FeBr4 ]− is possible, which correlates
with the insulating behavior of this compound.
    The structure of the [FeCl4 ]− salt is closely related to those of (BEDT-
TTF)2 [InBr4 ] [21], α-(BEDT-TTF)2 [PF6 ] [22], β-(BEDT-TTF)2 [PF6 ] [23] and
(BEDT-TTF)2 [AsF6 ] [24], with the salts containing octahedral anions exhibiting
interstack side-by-side contact distances nearly identical to those found in (BEDT-
TTF)2 [FeCl4 ]. There are no short contact distances between sulfur atoms along the
molecular stacking direction in any of these compounds and so their conduction
properties are highly one-dimensional. For example, in β-(BEDT-TTF)2 [PF6 ] the
ratio of the conductivities along the direction of side-by-side contacts to that along
the molecular stacking direction is 200:1 [22, 23] (BEDT-TTF)2 [FeCl4 ] is also
semiconducting, like the PF6 and AsF6 salts, with an activation energy of 0.21 eV.
    Given that the formal charge per donor molecule is +1/2 in the [FeCl4 ]− salt, the
unpaired spins on the organic cations contribute to the susceptibility. For example,
the molar susceptibility of (BEDT-TTF)2 [GaCl4 ], which has a similar structure but
a diamagnetic anion, has a broad maximum near 90 K, which can be fitted from
70–300 K either by a one-dimensional (Bonner–Fisher) or quadratic layer antifer-
romagnetic model to yield exchange parameters J /k of respectively 66.5(5) and
89.6(1) K, similar to those found in the semiconducting α -(BEDT-TTF)2 X with X
= AuBr2 , Ag(CN)2 , or CuCl2 [25], where the absolute values of the susceptibility
agree with expectations for localised moments corresponding to S = 1/2 per pair
of donor molecules. In the [FeCl4 ]− salt, on the other hand, the susceptibility is
dominated by the anion. From the low temperature data, a value of the Weiss con-
stant can be extracted and the parameters of the fit (S = 5/2, g = 2, θ = −4 K)
used to calculate the difference between observed and calculated susceptibility
at all temperatures to obtain the contribution from the BEDT-TTF. The resulting
difference gives a good fit to a singlet–triplet model (Figure 4.5) [26].
    Apart from the organo-chalcogen donors, conducting charge transfer salts are
known with various condensed ring aromatic molecules, of which the most ex-
tensively studied is perylene (Per) (Scheme 4.1). Thus it was pertinent to make
salts of this donor with transition-metal-containing anions. The crystal structures
of compounds with the stoichiometry (Per)3 [FeX4 ] (X = Cl, Br) consist of stacks
of tetramerised Per4 and [FeX4 ]− [27]. The [FeX4 ]− are located in pairs, but with
quite a large separation between the Fe (∼7.9 Å). The Cl compound is a semicon-
ductor with a high room temperature conductivity (0.175 S cm−1 ) and an activation
energy of 0.12 eV. Magnetically, the properties are dominated by the Fe, and no
long range order is reported, though the reported Weiss constants (FeCl4 −12.1 K;
FeBr4 −39.9 K) are quite high. On the other hand the susceptibility at low tem-
perature was fitted to a dimer model with J /k = −1.26 K (FeCl4 ) and −3.72 K
(FeBr4 ), in spite of the long distance between the Fe.
116    4 Molecular Materials Combining Magnetic and Conducting Properties




                                                Fig. 4.5. Total susceptibility of (BEDT-
                                                TTF)2 [FeCl4 ] (circles) and the BEDT-
                                                TTF contribution (squares).

   Among the large variety of conducting charge transfer salts containing
monomeric transition metal anions, very few show clear experimental evidence
of interaction between the pπ and d-electron sublattices. In particular, changes
in conduction that can be associated with ordering of d-moments are quite diffi-
cult to identify. Consequently there has been a lot of interest in the contrasting
behavior in two isomorphous salts λ-(BETS)2 MCl4 depending on whether M is
the closed-shell GaIII or S = 5/2 FeIII (Figure 4.6). Both are metals but, whereas
the former becomes superconducting at 8.5 K, the latter undergoes antiferromag-
netic order accompanied by a sharp metal–insulator transition at almost the same
temperature [28]. A clear correlation between magnetic ordering and the conduc-




                                              Fig. 4.6. The crystal structure of λ-
                                              (BETS)2 [FeX4 ] (X = Cl, Br).
                           4.3 Magnetic Ions in Molecular Charge Transfer Salts      117

tion is identified by the observation that the metallic state can be re-established at
low temperature on applying fields in excess of 110 kOe, under which conditions
the Fe moments became saturated ferromagnetically [29, 30]. On the other hand,
more recent studies of the variation of the conductivity of both salts with pressure
throw some doubt on the significance of the magnetic transition in bringing about
the metal–insulator transition. This temperature falls with increasing hydrostatic
pressure until it transforms sharply into a transition to a superconducting state at
3.2 kbar. The latter transition takes place at 1.8 K, and decreases with increasing
pressure, like most molecular superconductors. At the same pressure, Tc of the Ga
salt is 3.0 K, with nearly identical pressure dependence [31], suggesting that the
properties of the conduction electrons are very similar in the non-magnetic and
magnetic salts. The phase diagram of the [FeCl4 ]− salt is shown in Figure 4.7(a)
in the P , T plane. This different low temperature conduction at ambient pressure




                                                        Fig. 4.7. The electronic phase
                                                        diagram of λ-(BETS)2 [FeCl4 ]
                                                        in (a) the P , T plane [31]; (b)
                                                        the H , T plane.
118     4 Molecular Materials Combining Magnetic and Conducting Properties

is therefore most likely to be due to the small difference in their unit cell volumes.
Above 3.5 kbar λ-(BETS)2 FeCl4 is an antiferromagnetic metal above Tc , with a
peak in the susceptibility at 4 K and typical spin flip behavior at high field [32].
However, very recently it was reported that in fields above 17 T this salt becomes
superconducting [33] and Figure 4.7(b) shows the phase diagram in the H, T plane.
    In the BEDT-TTF salts, many superconductors have the κ-phase stacking ar-
rangement, in which face-to-face dimers are organised with the planes of near
neighbors orthogonal. It is therefore of great interest to observe the properties of
κ-phase BETS-TTF salts, bearing in mind that the latter have more stable metal-
lic states because of replacement of S by Se in the central part of the molecule.
Both [FeCl4 ]− and [FeBr4 ]− salts with this structure have been reported; both are
antiferromagnetic superconductors [34, 35], TN and Tc being much lower in the
chloride than the bromide. In the chloride salt, the resistivity changes at TN , which
could be taken as evidence in this case that the π- and d-electrons interact. On
the other hand, it may be the result of a small movement in the lattice, possibly
as a result of magnetostriction. Further, whilst the magnetic phase transition in
the [FeBr4 ]− salt is fully three-dimensional, the temperature dependence of the
heat capacity in the [FeCl4 ]− case reveals considerable two-dimensional character,
since the magnetic entropy only reaches 86% of its saturation value as high as 3TN .
Most likely, the more polarisable Br furnishes a more effective exchange pathway
than Cl, including overlap between the organic and inorganic layers.
    Turning to other tetrahalo-metallate anions, the first reports of TTF salts with
Mn and Co-tetrahalo-anions did not identify either their precise stoichiometry or
crystal structure [36] but later work from the same group [37] defined the unusual
composition (TTF)14 [MCl4 ]4 for M = Mn, Co, Zn and Cd. The donor molecules in
the monoclinic structure are of two types: each unit cell contains two (TTF)2+ and
                                                                                3
a TTF0 orthogonal to one another, with the anions isolated between the trimers. All
three compounds, whether magnetic or not, are semiconducting with high room
temperature conductivities in the region of 0.1 S cm−1 . The magnetic behavior
of the Mn and Co compounds is simple Curie–Weiss in type, with small negative
Weiss constants that may well be related to zero-field splitting rather than magnetic
exchange.
    Stoichiometries of the corresponding BEDT-TTF salts were first deduced by
elementary analysis alone as (BEDT-TTF)[MCl4 ]0.3–0.4 for M = Mn, Co, Zn [38]
but a crystal structure determination for one example indicates that it is (BEDT-
TTF)3 [MnCl4 ]2 [39]. In the latter structure, there are alternating layers contain-
ing respectively BEDT-TTF+ in the β stacking mode and MnCl2− together with
                                                                     4
isolated BEDT-TTF2+ . This unusual alternation has also been found in the non-
magnetic salt (BEDT-TTF)5 [Hg9 Br11 ] [40]. Both the structurally characterised salt
and the earlier ones are reported as semiconducting with relatively high room
temperature conductivities, (BEDT-TTF)3 [MnCl4 ]2 in particular being much more
conducting than is usual for β -salts. Again, the magnetic behavior appears to be
that of a Curie–Weiss paramagnet. In fact, the EPR of a BEDT-TTF-CoCl4 salt
                          4.3 Magnetic Ions in Molecular Charge Transfer Salts   119

(of unspecified formula) is said to contain signals from both conduction electrons
and localised 3d moments at low temperature [41], with the resonance field H
of the conduction electrons showing a shift below 100 K. A plot of H −1 versus
temperature is linear, suggesting that an internal field is produced by the localised
3d moments, whose static susceptibility follows the Curie–Weiss law. In contrast,
(TTF)2 [MnCl4 ] shows no EPR signal due to TTF+ . Observation of two EPR sig-
nals in the CoCl4 salt indicates that the two spin systems are behaving essentially
independently of each other as in the BEDT-TTF-CuCl4 salt described below, but
in contrast to (BEDT-TTF)3 [CuBr4 ].
   Another interesting example is the radical salt prepared with the BET-TTF
donor (Scheme 4.1) and the paramagnetic [FeCl4 ]− anion: β-(BET-TTF)2 [FeCl4 ]
[42]. This salt shows a metallic behavior with a room temperature conductivity of
60 S cm−1 and a M–I transition around 20 K. The EPR spectrum of this salt shows
a single signal centered at g = 2.017 with a linewidth of 400 G. No signal from
the BET-TTF is detected, in contrast with the isostructural salt of the diamagnetic
[GaCl4 ]− anion that exhibits a signal at g = 2.0065 with a linewidth of 13 G [42].
Such a feature has been attributed to the presence of a weak exchange interaction
between Fe(III) spins through the conducting electrons.
   The anions [CuX4 ]2− (X = Cl, Br) adopt a wide variety of geometries, from
square-planar to flattened tetrahedral, and the crystal structures (and hence proper-
ties) of the BEDT-TTF salts with these anions are much more varied and interesting
than those of the other 3d ions. Amongst them is the first example of a metallic
molecular charge transfer salt, (BEDT-TTF)3 [CuCl4 ].H2 O [43] in which magnetic
resonance has been observed simultaneously from conduction and localised elec-
trons. Other examples, containing [CuBr4 ]2− and [CuCl2 Br2 ]2− have the largest
change of conductivity with pressure ever seen in conducting organic solids, and
more substantial interaction between the conduction electrons and 3d moments.
   The crystal structure of (BEDT-TTF)3 [CuCl4 ]·H2 O consists of stacks of BEDT-
TTF parallel to the c-axis, with short interstack S–S contacts leading to the for-
mation of layers (Figure 4.8) [43]. The latter are interleaved by the [CuCl4 ]2−
and H2 O in the same general arrangement as in (BEDT-TTF)2 FeCl4 . However, in
(BEDT-TTF)3 CuCl4 ·H2 O there are three crystallographically independent BEDT-
TTF molecules (I, II, III) and two different stacks (A and B). Stack A contains only
BEDT-TTF of type I, and stack B has an alternate arrangement of II and III. Within
the ac-plane, the stacks form an XYYXYYX array. The anions lie in planes parallel
to the layers of the donor, within which pairs of [CuCl4 ]2− anions are connected
by hydrogen bonds through the two water molecules to form discrete units. The
Cu–Cl bond lengths (average 2.25 Å) and angles (150◦ ) are both quite normal for
Cu(II) halides with a Jahn–Teller distortion. The bond lengths and angles of the
three independent BEDT-TTF molecules are almost identical while the two differ-
ent overlap modes are the same in each stack. (BEDT-TTF)3 [CuCl4 ]·H2 O is the
only BEDT-TTF salt with 3:2 charge stoichiometry that remains metallic down to
very low temperatures at ambient pressure. Normally such salts undergo metal (or
120     4 Molecular Materials Combining Magnetic and Conducting Properties




                                     Fig. 4.8. The BEDT-TTF layers in (BEDT-
                                     TTF)3 [CuCl4 ]·H2 O.


semi-metal) to insulator (or semiconductor) transitions, some of which are sharp
(e. g. (BEDT-TTF)3 (ClO4 )2 ) [44] and others broad (e. g. (BEDT-TTF)3 Cl2 ·2H2 O)
[45].
    Being metallic down to at least 400 mK (BEDT-TTF)3 [CuCl4 ]H2 O is a good
prototype system to study the interaction between localised moments and conduc-
tion electrons, as shown by two observations [46]. First, there is a shift in g value
and broadening of the EPR line, the former being distinctly larger than those found
in β- or α - phase BEDT-TTF salts (2.003–2.010) [47]. Second, at low tempera-
ture the spin susceptibility of the conduction electrons falls below its Pauli limit
while that of the localised electrons increases. Most striking, however, the prod-
uct of the spin susceptibility of the Cu resonance and the temperature rises at low
temperature, indicating a short range ferromagnetic interaction. Fitting the data
to the Bleaney–Bowers [48] model indicates a ferromagnetic exchange constant
of 4(1) K. Since the shortest Cu–Cu distance is 8.5 Å, direct exchange interaction
between the Cu moments should be very small. On the other hand, the [CuCl4 ]2−
are arranged as dimers bridged by H2 O, which may provide an exchange pathway.
Nor can we rule out the possibility that exchange between Cu moments is also
mediated by the free carriers of the BEDT-TTF layers (the RKKY mechanism).
    Whilst the interaction between the BEDT-TTF and the metal ion spins is
weak though observable in (BEDT-TTF)3 [CuCl4 ]·H2 O, in semiconducting (BEDT-
TTF)2 [FeCl4 ] and insulating (BEDT-TTF)[FeBr4 ], it is negligible [20]. By contrast,
in (BEDT-TTF)3 [CuBr2 Cl2 ] the interaction between the two sublattices is strong,
and structural phase transitions transform the electrical and magnetic properties
[49]. The crystal structures of the [CuBr4 ]2− and [CuCl2 Br2 ]2− salts are very differ-
ent from the [CuCl4 ]2− salt, and their electronic properties are unrelated. Whereas
the CuCl2− form a flattened tetrahedron, as expected for Jahn–Teller d9 ion, the
          4
anions in the bromo-salts are square planar. In fact, this is the first compound in
which planar CuBr2− has been found [50]. Nevertheless, the stoichiometry of all
                     4
three salts is 3:1. Two crystallographically independent BEDT-TTF molecules (X
                           4.3 Magnetic Ions in Molecular Charge Transfer Salts   121




                                        Fig. 4.9. Layers of BEDT-TTF and [CuBr4 ]2− in
                                        (BEDT-TTF)3 [CuBr4 ].



and Y) are found in the bromo-compounds; from their bond lengths, the charges
are defined as 0 and +1 [51]. Both crystal structures consist of layers of BEDT-
TTF, stacked in XYYXYY sequence in the α-phase mode of packing, separated
by square planar tetrahalogenocuprate(II) (Figure 4.9).
   The room-temperature conductivities of the [CuBr4 ]2− and [CuCl2 Br2 ]2− salts
are very similar, being low for metallic organic conductors and high for semicon-
ductors but they are affected dramatically by pressure [49, 52], showing the largest
increase in conductivities with pressure of any known organic conducting solids:
25 S cm−1 kbar−1 up to 8 kbar, finally attaining a plateau at 22 kbar with 500 times
the ambient pressure value. At low temperatures (59 K) there are phase transi-
tions that take both salts from semi-metallic to semiconducting at pressures above
3 kbar. Their magnetic properties are also unusual in that the susceptibility of the
conduction electrons on the BEDT-TTF stacks is very high. The abrupt drop in
susceptibility (Figure 4.10) at low temperature is due to the loss of the contribution
from these electrons. To account for a contribution of this magnitude requires two
spins per formula unit which are antiferromagnetically coupled, suggesting that
the [CuBr4 ]2− and [CuCl2 Br2 ]2− salts are just on the insulator side of the Mott–
Hubbard transition. In such a case, semiconducting behavior is not due to a gap in
the one-electron density of states, but arises because the holes on the BEDT-TTF
stacks localise due to the strong Coulomb interaction. The 3:2 charge stoichiometry
of these salts requires two holes per three BEDT-TTF sites and, as noted above, the
bond lengths show that two of the BEDT-TTF molecules are charged and that one
is neutral. The transport properties are therefore those of a “magnetic” semicon-
122       4 Molecular Materials Combining Magnetic and Conducting Properties




Fig. 4.10. Magnetic susceptibilities of (BEDT-TTF)3 [CuBr2 X2 ]: (a) X = Br; (b) X = Cl. The
dashed lines are fits to the quadratic layer Heisenberg antiferromagnetic model.

ductor, with an activation energy Ueff /2, where Ueff is the on-site Coulomb energy
associated with the transfer of a charge to place two charges on a single site.
    In contrast to metallic (BEDT-TTF)3 [CuCl4 ]·H2 O only a single EPR line is seen
in the bromo-salts, though the g values above the 55–60 K transition are intermedi-
ate between those expected for a Cu(II) moment and for spins on BEDT-TTF sites.
Hence the two spin systems interact significantly, in contrast to the other magnetic
anion salts [20, 43]. The antiferromagnetic transition in (BEDT-TTF)3 [CuBr4 ] has
also been confirmed by solid state proton NMR [53], in which T1−1 shows a diver-
gent anomaly at 8 K that is still present under high pressure (about 10 K at 9 kbar)
when the compound is metallic. The latter shows that the localised Cu2+ moments
are still present when the lattice is metallic. An isostructural compound containing
[NiCl4 ]2− has also been reported. In contrast to the Cu salt it has a metal–insulator
transition at 100 K [54].
    Among other tetrabromocuprate(II) salts of derivatives of TTF, (TTM-
TTF)[CuBr4 ] (TTM-TTF = tetra-methyl-thio-TTF) contains (TTM-TTF)2+ that
are very strongly distorted away from planar and a linear Br· · ·C· · ·S· · ·Br net-
work [55]. As expected for a compound containing a +2 donor cation, this salt is a
good insulator and a Curie–Weiss paramagnet with a Weiss constant less than 1 K.


4.3.1.2     Hexahalo-anions
Although quite a number of charge transfer salts containing organo-chalcogen
donor cations have been prepared with hexahalo-anions which are diamagnetic,
such as [PtCl6 ]2− , [SnCl6 ]2− , etc. [56], rather few have been reported with param-
agnetic anions (see Table 4.1). In fact, the only examples appear to be α-(BEDT-
TTF)4 [ReCl6 ]·C6 H5 CN [57], (BEDT-TTF)2 [IrCl6 ] [57], and a salt of dibenzo-TTF
                              4.3 Magnetic Ions in Molecular Charge Transfer Salts           123

with ReCl2− [58]. They are semiconductors, and the magnetic properties are dom-
           6
inated by the paramagnetism of the anions. Nevertheless they present a number of
interesting structural features.
   The structure of α-(BEDT-TTF)4 [ReCl6 ]·C6 H5 CN contains alternate layers of
BEDT-TTF and [ReCl6 ]·C6 H5 CN. The donor layers consist of two crystallograph-
ically independent stacks, in one of which the BEDT-TTF all carry a charge of
+1 while in the other they are all neutral. Correspondingly in the anion layers
are rows of [ReCl6 ]2− alternating with rows of C6 H5 CN. Interaction between the
cation and anion layers appear to be determined largely by Coulomb forces, since
the stacks of (BEDT-TTF)+ are adjacent to the [ReCl6 ]2− while the (BEDT-TTF)◦
are closest to the neutral solvent molecules. The compound is a semiconductor
with an activation energy that varies slightly with temperature and a relatively high
room temperature conductivity (3 S cm−1 ) parallel to the layers and about ten times
less perpendicular). The low temperature magnetic properties are dominated by the
Curie–Weiss behavior of the anion, but at higher temperatures a component due
to the BEDT-TTF is apparent. The latter was fitted successfully by a Heisenberg
antiferromagnetic alternating chain model with J1 /k = −16 K and J2 /k = −13 K
(Figure 4.11).
   Despite being electro-crystallised under the same conditions, the [IrCl6 ]2− salt
of BEDT-TTF has a completely different structure from that of the [ReCl6 ]2− one.
It contains no solvent of crystallisation, neither are there discrete layers of an-
ions and cations. Instead there are face-to-face dimers of BEDT-TTF forming a
three-dimensional network through end-to-end contacts, a relatively rare feature
in BEDT-TTF charge transfer salts. Despite this, the compound is a semiconduc-
tor with room temperature conductivity of 10−2 S cm−1 , a fact that is explained
by its formulation as (BEDT-TTF+ )2 [IrCl2− ], rather than the alternative (BEDT-
                                             6




Fig. 4.11. Susceptibility due to BEDT-TTF in α-(BEDT-TTF)4 [ReCl6 ]·C6 H5 CN at 250 G
(open circles) and 1000 G (filled circles). The data are fitted to the alternating chain AF model
(T > 8 K) and the Bleaney–Bowers dimer model (T < 8 K).
124       4 Molecular Materials Combining Magnetic and Conducting Properties

TTF1.5+ )2 [IrCl]3− ]. The formulation as an Ir(IV) salt is confirmed by the S = 1/2
                 6
Curie–Weiss magnetic behavior of the anion, combined with an exceptionally high
intra-dimer exchange constant of 670 cm−1 , fitted with the Bleaney–Bowers model
[48].



4.3.1.3     Pseudohalide-containing Anions
Apart from the high symmetry octahedral and tetrahedral halogeno-complexes of
transition metals, a variety of other monomeric anions have been incorporated into
charge transfer salts of TTF and its derivatives, in the search for combinations of
conducting and magnetic properties. Some are complexes of pseudo-halide ligands
such as CN− and NCS− , while others are of lower symmetry with mixed ligands
(see Table 4.2). Among the latter are the first examples of long range ferrimagnetic
order in an organic–inorganic charge transfer salt, where one of the sublattices is
furnished by the pπ electrons of a molecular radical cation and the other by the d-
electrons of the transition metal complex anions. In a number of cases, the anions
have been designed specifically to promote interaction between the organic and
inorganic components of the lattice by building into them S atoms of the molecular
donor.
    The first hexacyanometallate salt of TTF was formulated as (TTF)11 [Fe(CN)6 ]3
·5H2 O, an unusual stoichiometry that indicates a particularly complex structure
[59]. Eight of the TTF are present in dimerised stacks, and are assigned a charge
of +1 from the bond lengths. The remaining ones have their molecular planes
perpendicular to the stacks, two being neutral and the remaining one +1. Close
contacts are indeed found between the [Fe(CN)6 ]3− and the TTF (N· · ·S 3.09 Å),
but there is no report of cooperative magnetic properties, though the compound is
a semiconductor. In contrast, BEDT-TTF salts with [M(CN)6 ]3− (M = Fe, Co, Cr)
have more conventional structures with alternating layers of cations and anions.
Thus β-(BEDT-TTF)5 [M(CN)6 ]·10H2 O (M = Fe, Co) have the β-packing mode,
albeit with a pentamer rather than the more usual tetrameter repeat unit [60]. Both
compounds are semiconductors, although apparently there is appreciable Pauli
paramagnetism in the Co salt, suggesting the presence of conduction electrons.
A further series, κ-(BEDT-TTF)4 (NEt4 )[M(CN)6 ]·3H2 O (M = Fe, Co, Cr) has κ-
packing mode, and at room temperature all the BEDT-TTF have the same charge of
+0.5, as found in the superconducting salts with diamagnetic anions I− , Cu(NCS)− ,
                                                                       3          2
etc. [61]. Nevertheless, they are reported to be semiconducting in the neighborhood
of room temperature. The magnetic susceptibility corresponds to the sum of con-
tributions from the paramagnetic [Fe(CN)6 ]3− and the organic sublattice, with no
evidence for interaction between them. At 140 K, a sharp drop in susceptibility
arises from a charge disproportion among the dimers in the κ-structure, so that one
consists of BEDT-TTF+ and another of neutral molecules. The spin susceptibility
measured by EPR confirms the presence of the same transition in the isostructural
Table 4.2. Structures and physical properties of charge transfer salts containing pseudohalide complex anions.

Compound                               Packing                      Electrical Properties              Magnetic Properties     Ref.
(TTF)11 [Fe(CN)6 ]3 ·5H2 O        Dimerised Stacks orthogo- semiconductor                              –                       59
                                  nal monomers              (σRT ≈ 10−3 S cm−1 )
(BEDT-TTF)5 [Fe(CN)6 ]·10H2 O     β-donor packing;          semiconductor                              PM                      60
                                  pentamers                 (σRT ≈ 0.02 S cm−1 )
(BEDT-TTF)5 [Co(CN)6 ]·10H2 O     β-donor packing;          semiconductor                              Pauli paramagnet        60
                                  pentamers                 (σRT ≈ 0.5 S cm−1 )
(BEDT-TTF)4 NEt4 [Fe(CN)6 ]·3H2 O κ-donor layers            semiconductor                              PM; C = 1.3 emu K mol−1 60
                                                            (σRT ≈ 0.2 S cm−1 )
(BEDT-TTF)4 NEt4 [Co(CN)6 ]·3H2 O κ-donor layers            semiconductor                              PM                      60
                                                            (σRT ≈ 10 S cm−1 )
(BEDT-TTF)4 NEt4 [Cr(CN)6 ]·3H2 O κ-donor layers            semiconductor                              PM                      60
                                                            (σRT ≈ 0.15 S cm−1 )
(BEST)4 [Fe(CN)6 ]                β-donor packing           semiconductor                              PM                      62,63
                                                            (σRT ≈ 11 S cm−1 ;
                                                            Ea = 0.025 eV)
(BEST)3 [Fe(CN)6 ]2 ·H2 O         interpenetrated layers of semiconductor                              PM                      62,63
                                  cations 2+ and anions.    (σRT ≈ 10−6 S cm−1 )
(BET-TTF)4 (NEt4 )2 [Fe(CN)6 ]    κ-donor layers            semiconductor                              PM                      63
                                                            (σRT ≈ 11.6 S cm−1 ;
                                                            Ea = 0.045 eV)
(BEDT-TTF)2 Cs[Co(NCS)4 ]         α-donor layers            metal-insulator transition at 20 K                                 64
                                                            (σRT = 14 S cm−1 )
(BEDT-TTF)4 [Cr(NCS)6 ]·PhCN      α-donor layers            semiconductor                              PM                      67,68
                                                            (σRT ≈ 5 × 10−3 S cm−1 ;
                                                                                                                                       4.3 Magnetic Ions in Molecular Charge Transfer Salts




                                                            Ea = 0.26 eV)
(BEDT-TTF)5 NEt4 [Cr(NCS)6 ]·THF β-donor layers             semiconductor                              PM; C = 1.7 emu K mol−1 67,69
                                                                                                                                       125




                                                            (σRT ≈ 10 S cm−1 )                         |D| = 7.3 cm−1
Table 4.2. (Continued.)
                                                                                                                             126



Compound                               Packing                   Electrical Properties       Magnetic Properties     Ref.

(BEDT-TTF)5 [Cr(NCS)6 ]·(DMF)4         β-donor layers             semiconductor              PM; |D| = 2.8 cm−1      69
                                                                  (σRT ≈ 5 S cm−1 )
(BEDT-TTF)5.5 [Cr(NCS)6 ]            β-donor layers               semiconductor              PM; |D| = 4.7 cm−1      68,69
                                                                  (σRT ≈ 2 S cm−1 ;
                                                                  Ea = 0.03 eV)
(BEDT-TTF)4 [Fe(NCS)6 ]·CH2 Cl2      Cation and anion layers      semiconductor              PM;                     70
                                                                  (σRT = 7 × 10−3 S cm−1 ;   C = 4.926 emu K mol−1
                                                                  Ea = 0.7 eV)               θ = −0.19 K
(BEDT-TTF)4 [Fe(NCS)6 ]·(pip)        orthogonal                   semiconductor              –                       71
                                     dimers/monomers              (σRT = 4.2 S cm−1 ;
                                                                  Ea = 0.25 eV)
(BEDT-TTF)5 NEt4 [Fe(NCS)6 ]         β-donor layers               semiconductor              –                       71
                                                                  (σRT = 4.0 S cm−1 ;
                                                                  Ea = 0.03 eV)
(BMDT-TTF)4 [Cr(NCS)6 ]              –                            –                          –                       72
(BEDT-TTF)2 [Cr(NCS)4 (NH3 )2 ]      Dimerised, donor layers;     semiconductor              PM                      70
                                     anion layers                 (σRT = 30 S cm−1 ;
                                                                  Ea = 0.056 eV)
(BEDT-TTF)2 [Cr(NCS)4 bipym]0.25H2 O No π -stacking of anions and semiconductor              PM;                     73
                                     cations                      (σRT = 0.015 S cm−1 ;      C = 1.82 emu K mol−1
                                                                  Ea = 0.3 eV)               θ = −0.26 K
(TMTTF)[Cr(NCS)4 phen]               Donor dimers                 insulator                  AFM: TN = 3.0 K         75
                                     No close cation–anion        semiconductor              PM;                     75
                                                                                                                             4 Molecular Materials Combining Magnetic and Conducting Properties




(TMTSF)3 [Cr(NCS)4 phen
                                     contacts                     (σRT = 0.022 S cm−1 ;      C = 3.57 emu K mol−1
                                                                  Ea = 0.16 eV)              θ = −3.82 K
PM = Paramagnetic; AFM = antiferromagnetic
                           4.3 Magnetic Ions in Molecular Charge Transfer Salts   127

salt with diamagnetic Co(CN)3− as anion, indicating further that the anion plays
                                 6
little part [60].
    Three different salts of [Fe(CN)6 ]3− with the organic donors BEST-TTF and
BET-TTF (Scheme 4.1) have also been reported: β-(BEST-TTF)4 [Fe(CN)6 ],
(BEST-TTF)3 [Fe(CN)6 ]2 ·H2 O and κ-(BET-TTF)4 (NEt4 )2 [Fe(CN)6 ] [62, 63]. In
the 3:2 phase the structure shows an unusual interpenetration of the donor molecules
and the anions. This fact may be due to the +2 charge of BEST-TTF (very unusual
in any TTF-type donor and unprecedented with BEST-TTF). The magnetic proper-
ties of this salt correspond to the paramagnetic [Fe(CN)6 ]3− anions as the organic
sublatice does not contribute. The 4:1 salt of the BET-TTF donor presents the
typical alternating layers of anions and donors. The organic layers are formed by
only one BET-TTF molecule, with a charge of 1/4, packed in a κ-phase. The room
temperature conductivity is very high (11.6 S cm−1 ) although the thermal behavior
shows that this salt is a semiconductor with a low activation energy of 0.045 eV.
The high electron delocalisation of this salt is confirmed by the EPR studies on a
single crystal that show a Dysonian line when the magnetic field is parallel to the
organic layers [63].
    Because specific non-bonding interactions between chalcogen atoms in neigh-
boring molecules are such a common feature of the solid state chemistry of the
Group 16 elements, one strategy for promoting interaction between cation and an-
ion sublattices in TTF-type charge transfer salts is to incorporate Group 16 atoms
in the anion, preferably in a terminal position. The most convenient ligand for this
purpose is NCS− , which fortunately is bound to most transition metals through N.
A salt of BEDT-TTF with tetrahedral [Co(NCS)4 ]2− has the α-packing motif [64],
and is isostructural with the series of α-(BEDT-TTF)2 M[Hg(SCN)4 ] (M = NH4 ,
K, Rb), which has been much studied by physicists because of the interplay be-
tween superconducting and antiferromagnetic ground states [65, 66]. Nevertheless,
the compound α-(BEDT-TTF)2 Cs[Co(NCS)4 ] is a metal, but undergoes a metal–
insulator transition at 20 K, and in the crystal structure there are no close BEDT-
TTF· · ·SCN contacts. Such contacts are indeed found in several salts of BEDT-TTF
prepared with the paramagnetic anions [Cr(NCS)6 ]3− and [Fe(NCS)6 ]3− . With the
Cr(III) anion a 4:1 phase: (BEDT-TTF)4 [Cr(NCS)6 ]·PhCN, two 5:1 phases: β-
(BEDT-TTF)5 [Cr(NCS)6 ](DMF)4 and β-(BEDT-TTF)5 (NEt4 )[Cr(NCS)6 ](THF)
and a 5.5:1 phase: β-(BEDT-TTF)5.5 [Cr(NCS)6 ] have been prepared. Curiously,
this last phase is closely related to the two other 5:1 phases since the extra half
BEDT-TTF molecule is located in the anion layer, replacing the solvent molecules
of the other 5:1 phases [67]. All these salts are semiconductors with high room
temperatures conductivities in the range 1–10 S cm−1 . The magnetic properties
correspond to the sum of both sublattices with zero field splittings in the range 2.8–
7.3 cm−1 in the Cr(III) ion [68, 69]. With the Fe(III) anion two 4:1 phases: (BEDT-
TTF)4 [Fe(NCS)6 ]·CH2 Cl2 [70] and (BEDT-TTF)4 [Fe(NCS)6 ]·(piperidine) [71]
and one 5:1 phase (BEDT-TTF)5 (NEt4 )[Fe(NCS)6 ] [71] have been prepared. The
Cr(III) anion has also been used with the bis(methylene)dithio-TTF (BMDT-TTF)
128     4 Molecular Materials Combining Magnetic and Conducting Properties

donor in the salt (BMDT-TTF)4 [Cr(NCS)6 ] [72]. Most of these salts present short
anion–cation S· · ·S contacts despite having a layer structure with alternating an-
ions and cations. There are also close contacts between NCS groups on neighboring
anions, but despite these features the Fe(III) compounds remain paramagnetic to
1.5 K (as the Cr(III) salts) with very small Weiss constant (−0.19 K in the (BEDT-
TTF)4 [Fe(NCS)6 ]·CH2 Cl2 salt).
    Of much greater interest from a magnetic point of view are charge transfer
salts based on partially substituted pseudohalide complexes, of which the Rei-
necke’s anion trans-[Cr(NCS)4 (NH3 )2 ]− is a prototype. The salt of Reinecke’s an-
ion itself, (BEDT-TTF)2 [Cr(NCS)4 (NH3 )2 ], which contains alternating layers of
(BEDT-TTF)+ and anions, has magnetic properties dominated by the latter [70],
               2
but again no transition to long range magnetic order above 2 K, despite the pres-
ence of several cation–anion S· · ·S contacts less that 4 Å. When the NH3 is replaced
with an aromatic amine, however, the situation is transformed, because in favor-
able cases the planar amines form stacks with the donor cations, in addition to the
S· · ·S cation–anion contacts. Under those circumstances bulk ferrimagnetic order
is established, the first such case in charge transfer salts.
    That π–π cation–anion stacking is important for observing bulk magnetic order
in this class of compound is demonstrated in a negative sense by the example
of (BEDT-TTF)2 [Cr(NCS)4 (2,2 -bipyrimidine)]·0.25H2 O. Despite containing an
aromatic amine the structure does not have any π-stacking of the cations and
anions, although S· · ·S cation–anion contacts are present [73]. It is paramagnetic
down to 2 K, with a very small Weiss constant (−0.26 K).
    The first ferrimagnetic charge transfer salts with a donor pπ and an anion 3d
sublattice were based on the Reinecke’s anions with isoquinoline (C9 H7 N) as the
base [74]. In this case the anion [M(NCS)4 (C9 H7 N)2 ]− (with M = Cr or Fe) has
the trans-configuration. Charge transfer salts with 1:1 stoichiometry are formed
with BEDT-TTF (M = Cr, Fe) and TTF (M = Cr), the bulk magnetic proper-
ties in every instance being classically those of a ferrimagnet, showing full long
range order below a critical temperature Tc . The temperature dependence of χm T
has a shallow minimum decreasing from a room temperature value close to that
of donor spin SD = 1/2 and anion SA = 3/2 (for Cr3+ ). Below the minimum
χm T rises rapidly towards saturation at Tc , after which χm remains constant so
that χm T decreases linearly. Below Tc the isothermal magnetisation saturates at
2NµB for the Cr salt, corresponding to an antiferromagnetically alignment be-
tween SA and SD ; there is also a modest hysteresis. Typical magnetic data for these
compounds are shown in Figure 4.12, and the magnetic parameters are listed in
Table 4.3.
    When the isoquinoline is replaced by 1,10-phenanthroline, the anion necessar-
ily has the cis-configuration, but TTF, TMTTF and TMTSF salts have also been
obtained [75]. The TTF salt of [Cr(NCS)4 phen]− is a ferrimagnetic insulator with
Tc = 9 K (IV in Table 4.3), while the TMTTF salt is an antiferromagnetic insulator
(TN = 3 K). In both compounds there are close intermolecular contacts between
                            4.3 Magnetic Ions in Molecular Charge Transfer Salts         129




                                                        Fig. 4.12. Magnetic data for
                                                        the ferrimagnetic salt (BEDT-
                                                        TTF)[Cr(NCS)4 (C9 H7 N)2 ]. (a)
                                                                                   −1
                                                        χm T (filled squares) and χm ver-
                                                        sus temperature T (the inset shows
                                                        the minimum in χm T at 10 K); (b)
                                                        magnetisation versus field (inset
                                                        shows the hysteresis).

Table 4.3. Magnetic parameters for ferrimagnetic charge transfer salts D[M(NCS)4 B2 ].

                                   I      II     III    IV
Tc /K                              4.2    8.9    4.5    9.0
χm T (at 330 K)/emu K mol−1        2.26   2.18   4.75   2.22
Minimum χ − mT /emu K mol−1        1.7    0.99   3.97   1.2
Minimum T /K                       9.9    16.9   14.8   17.5
Coercive field/Oe                  338    75     18     ∼0
Remanent M/NµB                     0.42   0.74   0.38   ∼0
Msat at 7 T /NµB                   2.0    2.1    4.3    1.7
       D           M     B         Ref.
I:     BEDT-TTF    Cr    C9 H7 N   74
II:    TTF         Cr    C9 H7 N   74
III:   BEDT-TTF    Fe    C9 H7 N   74
IV:    TTF         Cr    phen      75
130     4 Molecular Materials Combining Magnetic and Conducting Properties




                                                      Fig. 4.13. Crystal structures of
                                                      (a) (TTF)[Cr(NCS)4 phen]; (b)
                                                      (TMTTF)[Cr(NCS)4 phen].




Fig. 4.14. Cation–anion π–π stacking in A[Cr(NCS)4 phen]; I, A = TTF; II, A = TMTTF.


the phenanthroline and the donor as well as S· · ·S contacts between the cations and
anions. The difference in the bulk magnetic properties appears to be the result of the
larger steric requirement of TMTTF, because the latter salt consists of dimerised
cations while in the TTF one there are stacks of alternating cations and anions
(Figure 4.13). The π -interaction between cations and anions is also disrupted in
the TMTTF compound compared to the TTF one (Figure 4.14) [76].
                           4.3 Magnetic Ions in Molecular Charge Transfer Salts     131

4.3.2     Metal Cluster Anions

One strategy for exploring the subtle structure–property relationships in molecular
charge-transfer salts by chemical means is to compare isostructural and isosym-
metrical series. Furthermore, forming solid solutions could also help to achieve
systematic variations of structure and properties, for which purpose it is of interest
to identify anion types that facilitate chemical doping. In this respect, metal clus-
ter anions show promise in forming extended isostructural series with TTF and
BEDT-TTF. The anion size may be finely tuned by substituting the terminal and
capping groups and, in addition, different solvent molecules may nest in the cav-
ities between the cluster anions without greatly altering the structure of the anion
layer. Finally, metal cluster salts are promising candidates for testing the feasibility
of anion layer doping, since the effects of structural and electrostatic disorder are
expected to be small when the dopant is embedded within a thick anion layer. Po-
tential doping mechanisms include mixed solvents (with the additional possibility
of including cations or anions in the cavity between the clusters) and mixed anions.



4.3.2.1    Dimeric Anions
In the quest for compounds exhibiting magnetic exchange interactions between
metal ions situated within the anion layers, it is logical to look for groups that
will bridge neighboring metal centers and transmit superexchange between them.
Ambidentate ligands like NCS− and (C2 O4 )2− are simple examples, and we begin
by mentioning a few charge transfer salts in which these ligands bridge discrete
pairs of metals.
   The dimeric anion [Fe2 (C2 O4 )5 ]4− , which contains high spin FeIII ions bridged
by one C2 O2− has been incorporated in TTF [77], TMTTF [77] and BEDT-TTF
              4
[78] salts. In every case the magnetic behavior is dominated by the magnetic anion.
In the TTF salt, which has the stoichiometry (TTF)5 [Fe2 (C2 O4 )5 ]·2PhMe·2H2 O,
there are chains of donors surrouded by the dimeric anions and orthogonal TTF
dimers while in the TMTTF salt (TMTTF)4 [Fe2 (C2 O4 )5 ]·PhCN·4H2 O there are
segregated stacks of donors and anions in a “checkerboard” arrangement. In the
BEDT-TTF salt (BEDT-TTF)4 [Fe2 (C2 O4 )5 ] there are closely spaced cation dimers,
so that the overall structure resembles the “checkerboard” arrangement found in
(BEDT-TTF)2 [Ge(C2 O4 )3 ]·C6 H5 CN [79]. The dimers of spin-paired monoposi-
tive cations therefore do not contribute to the magnetic properties, neither are there
layers of alternating anions and cations. The antiferromagnetic exchange between
the FeIII is quite comparable in magnitude to that found in other oxalate-bridged
FeIII dimers. Likewise containing oxalate-bridged dimeric anions are (BEDT-
TTF)5 [MM (C2 O4 )(NCS)8 ] where MM is either CrFe or CrCr [80]. Here the pres-
ence of NCS− is especially noteworthy because of the opportunity it presents for
cation–anion S· · ·S interactions. The latter compound does have a layer lattice of
132     4 Molecular Materials Combining Magnetic and Conducting Properties

alternating cations and anions, the former being related to (but crucially different
from) the κ-arrangement of orthogonal dimers. In this case the dimers are inter-
leaved by monomers, which are assigned charges close to zero by band structure
calculations. In agreement with those calculations the compounds are semiconduc-
tors, albeit with relatively high room temperature conductivity and low activation
energy. From the standpoint of magnetism, the principal features of interest is a
ferromagnetic intradimer exchange interaction in the CrFe compound, leading to
the S = 4 dimer ground state expected for S = 3/2 (Cr) and 5/2 (Fe). For the
CrCr anion a metallic 8:1 phase with BEDT-TTF has also been reported: (BEDT-
TTF)8 [Cr2 (C2 O4 )(NCS)8 ] [81]. The room temperature conductivity for this salt is
0.1 S cm−1 and increases with decreasing temperature to reach a value of 1 S cm−1
at 180 K [81]. The magnetic properties are dominated by the antiferromagnetic
behavior of the Cr–Cr dimer, as in the 5:1 phase.
   Dimeric anions containing only NCS− were first synthesised many years ago in
the form of [Re2 (NCS)10 ]n− (n = 2, 3) [82]. The structures of their BEDT-TTF salts
are quite different, although the anions themselves only vary slightly in geometry
with changing charge [83]. The structure of the n = 3 compound consists of layers
containing both cations and anions with several very short S· · ·S contacts between
them, but no continuous network of closely interacting BEDT-TTF (Figure 4.15).




                                                   Fig. 4.15. The crystal structure
                                                   of     (BEDT-TTF)3 [Re2 (NCS)10 ]
                                                   ·2CH2 Cl2 ; (a) along the BEDT-TTF
                                                   long axes; (b) along the a-axis.
                           4.3 Magnetic Ions in Molecular Charge Transfer Salts     133

The total susceptibility is modelled best as the sum of Curie–Weiss and dimer
contributions, the former attributed to the anions and the latter to one of the cations,
whose spin remains impaired while those of the remaining two cations in the unit
cell are paired.
   A special case of dimeric anion appears in the semiconducting salts
(TTF)2 [Fe(tdas)2 ] and (BEDT-TTF)2 [Fe(tdas)2 ] (tdas = 1,2,5-thiadiazole-3,4-
dithiolate). The structures of both salts show the typical layered structure with
dimerised chains in the anionic layer and β or α packings in the TTF [84] and
BEDT-TTF [85] salts, respectively. Both salts are semiconductors with room tem-
perature conductivities of 3 × 10−2 and 1 S cm−1 and activation energies of 0.18
and 0.10 eV, respectively. Due to the dimerisation of the [Fe(tdas)2 ]2− anions, the
Fe(III) ion has a square pyramidal coordination. Therefore, it has an S = 3/2
ground spin state as has been confirmed by magnetic measurements and Mössbauer
spectroscopy in the NBu+ salt of this anion [86, 87]. The magnetic data for both
                            4
salts are consistent with the formation of antiferromagnetic dimers (J /k = −154 K
for the TTF salt and −99 K for the BEDT-TTF salt). In the BEDT-TTF salt be-
sides the contribution of the Fe(III) dimers, there is a magnetic contribution from
the BEDT-TTF molecules that have been reproduced with a model of interacting
antiferromagnetic S = 1/2 chains [85]. There is also a 3:2 TTF salt with this anion
although the structure is not known and the magnetic properties show a Curie type
behavior, suggesting that in this case the anions are not dimerised [88].


4.3.2.2   Polyoxometallate Clusters
Polyoxometallates (POMs) have been found to be extremely versatile inorganic
building blocks for the construction of organic/inorganic molecular materials with
unusual electronic properties. A general review that provides a perspective of the
use of POMs in this area can be found in Ref. [89]. In the context of the present
article, these bulky metal-oxide clusters possess several characteristics that have
made them suitable and attractive as magnetic counter ions for new TTF-type
radical salts in which localised and delocalised electrons can coexist:
1. They are anions that can be rendered soluble in polar organic solvents.
2. They can incorporate one or more magnetically active transition metal ions at
   specific sites within the cluster.
3. Their molecular properties, such as charge, shape and size, can be easily varied.
   In particular, it is possible to vary the anionic charge while maintaining the
   structure of the POM.
A drawback of these bulky anions is that, although they often stabilise unusual
new packing arrangements of the organic ions, their high charges tend to localise
the charges of the organic sublattice, making it difficult to achieve high electrical
conductivities and metallic behavior for these materials. All the known radical salts
with magnetic POMs are based on the organic donor BEDT-TTF. The POMs used
134      4 Molecular Materials Combining Magnetic and Conducting Properties




Fig. 4.16. Types of magnetic polyoxometallates used as inorganic counter-ions for BEDT-TTF-
type radical salts: (a) Non substituted α-Keggin anions [Xn+ W12 O40 ](8−n)− (X = CuII , CoII ,
FeIII ,. . .); (b) Mono-substituted α-Keggin anions [Xn+ Zm+ (H2 O)M11 O39 ](12−n−m)− (X =
PV , SiI V ; M = MoV I , WV I ; Z = FeIII , CrIII , MnII , CoII , NiII , CuII ); (c) The Dawson–Wells
anion [P2 W18 O62 ]6− ; (d) The mono-substituted Dawson–Wells anion [ReOP2 W17 O61 ]6− ;
(e) The magnetic anions [M4 (PW9 O34 )2 ]10− (MII = Co, Mn).

to prepare these materials are depicted in Figure 4.16. The magnetic and electrical
properties of these materials are summarized in Table 4.4.


Keggin anions
α-Keggin anions of the type [Xn+ W12 O40 ](8−n)− (abbreviated as [XW12 ]; Fig-
ure 4.16(a)) were first combined with BEDT-TTF molecules to provide an extensive
series of radical salts having the general formula (BEDT-TTF)8 [XW12 O40 ](solv)n
(solv = H2 O, CH3 CN). Here, the central tetrahedral XO4 site may contain a dia-
magnetic heteroatom (2(H+ ), ZnII , BIII and SiI V ) [90, 91] or a paramagnetic one
(CuII , CoII , FeIII ,. . . ) [91]. The compounds crystallise in two closely related struc-
ture types, α1 and α2 , consisting of alternating layers of BEDT-TTF molecules
with an α packing mode, and the inorganic Keggin anions forming close-packed
pseudohexagonal layers in the ac plane (Figure 4.17). In the organic layers there
are three (α1 phase) or two (α2 phase) crystallographically independent BEDT-
TTF molecules which form two types of stacks: a dimerised chain and an eclipsed
one. The shortest interchain S· · ·S distances, ranging from 3.46 to 3.52 Å, are sig-
nificantly shorter than the intrachain ones (from 3.86 to 4.04 Å), emphasising the
two-dimensional character of the packing. Another important feature of this struc-
ture is the presence of short contacts between the organic and the inorganic layers
which take place between the S atoms of the eclipsed chains and some terminal O
atoms of the polyoxoanions (3.15 Å), and via hydrogen bonds between the ethylene
groups of the BEDT-TTF molecules and several O atoms of the anions (3.13 Å).
    From the electronic point of view, an inhomogeneous charge distribution in
the organic layer was found by Raman spectroscopy, in which the eclipsed chain
is formed by almost completely ionised (BEDT-TTF)+ ions, while the dimerised
chain contains partially charged BEDT-TTFs. This charge distribution accounts
for the electrical and magnetic properties of these salts. All of them exhibit semi-
Table 4.4. Structures and physical properties of BEDT-TTF charge transfer salts containing polyoxometallate anions.

Compound                           Packing                         Electrical Properties           Magnetic Properties                         Ref.

ET8 [MW12 O40 ]                    Layers of donors (α-packing)    Semiconductors;                 Regular AF chains of BEDT-TTF (J =          91
M = CoII , CuII , FeIII            made of regular and dimerized   σRT = 0.15–0.03 S cm−1          −60 cm−1 ) alternating with dimerized
                                   stacks                          Ea = 0.094–0.159 eV             AF chains (J = −310 cm−1 ) in coexis-
                                                                                                   tence with paramagnetic metal ions
ET8 [XW11 M(H2 O)O39 ]             Layers of donors (α-packing)    Semiconductors;                 Regular AF chains of BEDT-TTF (J =          93
M = CoII , CuII , NiII , FeIII ,   made of regular and dimerized   σRT = 0.15–0.03 S cm−1          −80 cm−1 ) alternating with dimerized
CrIII ; X = PIII , SiIV            stacks                          Ea = 0.094–0.159 eV             AF chains (J = −280 cm−1 ), in coex-
                                                                                                   istence with paramagnetic metal ions
ET8 [PM11 Mn(H2 O)O39 ]            Layers of donors (α-packing)    Semiconductors                  Regular AF chains of BEDT-TTF alter-        93
M = W, Mo                          made of regular and dimerized   σRT = 0.1 S cm−1                nating with dimerized AF chains in co-
                                   stacks;                         Ea ∼ 100 meV                    existence with paramagnetic manganese
                                   Chains of polyoxometallates                                     (II) ions
ET11 [ReOP2 W17 O61 ]              Layers of donors (β-packing)    Metallic. σRT = 11.8 S cm−1 ;   Paramagnetic behavior coming from           94
                                                                   M-I transition at ≈200 K.       noninteracting Re ions (S = 1/2)
                                                                   Ea = 27 meV
ET6 H4 [M4 (PW9 O34 )2 ]           Unknown                         Insulator                       The magnetic behavior corresponds to        96
M = CoII , MnII                                                                                    that of the ferromagnetic CoII cluster or
                                                                                                   to the antiferromagnetic MnII cluster
                                                                                                                                                      4.3 Magnetic Ions in Molecular Charge Transfer Salts
                                                                                                                                                      135
136     4 Molecular Materials Combining Magnetic and Conducting Properties




                                                   Fig. 4.17. (a) Structure of the radi-
                                                   cal salts (BEDT-TTF)8 [XW12 O40 ]
                                                   showing the layers of Keggin poly-
                                                   oxoanions and the two types of
                                                   chains, eclipsed and dimerized, in
                                                   the organic layers; (b) Projection
                                                   of the organic layer showing the
                                                   structural relationship between the
                                                   three crystallographic α-phases.



conducting behavior (σRT ≈ 10−1 –10−2 S cm−1 and Ea ≈ 100–150 meV), inde-
pendent of the charge in the organic sublattice (see inset in Figure 4.18). As far as
the magnetic properties are concerned, the localised electrons in the eclipsed chain
(one unpaired electron per BEDT-TTF) account for the chain antiferromagnetism,
and the delocalised electrons in the mixed-valence dimeric chain, account for the
                                4.3 Magnetic Ions in Molecular Charge Transfer Salts          137

0.014
                               14
                               12
                               10
0.012



                         L ρ
                                8




                         n
                                6

0.010                           4
                                2
                                    2    3   4     5    6 7     8   9
                                                 1000/T (K-1)
0.008


0.006
        0        50       100            150      200      250      300
                                        T (K)
Fig. 4.18. Plot of the magnetic susceptibility (χm ) vs. T for the (BEDT-TTF)8 [BW12 O40 ]
radical salt (filled circles). Open circles correspond to the corrected magnetic susceptibility
(after subtracting a paramagnetic Curie-type contribution. Solid lines represents the best fit to a
model that assumes an antiferromagnetic Heisenberg chain behavior (with J ∼ −30 cm−1 ; the
exchange hamiltonian is written as −2J Si Sj ) for the eclipsed chain, and an activated magnetic
contribution (with J ∼ −150 cm−1 ) coming from the dimeric chain. Inset: Semilogarithmic
plot of the electrical resistivity ( cm) vs. reciprocal temperature.


presence of an activated magnetic contribution at high temperatures and for a Curie
tail contribution at low temperatures (Figure 4.18).
    For those salts containing magnetic polyanions, the isolation of the magnetic
center (situated in the central tetrahedral cavity of the Keggin structure) precludes
any significant magnetic interaction with the organic spin-sublattice. In fact, the
electron paramagnetic resonance (EPR) spectra show both the sharp signal of the
radical cation and the signals associated with the paramagnetic metal ions. These
salts represent the first examples of hybrid materials based on polyoxometallates
in which localised magnetic moments and itinerant electrons coexist in the two
molecular networks.
    A salt containing the one-electron reduced polyoxometallate [PMo12 O40 ]4− has
also been reported [92]. It crystallises in the α1 structure, although some structural
disorder has been found. From the electronic point of view, this compound may be
of special interest as it contains delocalised electrons in the mixed-valence inorganic
sublattice. However, the magnetic properties of this compound, in particular the
EPR spectroscopy, indicate that these “blue” electrons do not interact with those
of the organic sublattice.
    With the aim of bringing the magnetic moments localised on the Keggin polyan-
ions closer to the π-electrons placed on the organic molecules monosubstituted
138      4 Molecular Materials Combining Magnetic and Conducting Properties

Keggin anions having one magnetic ion at the polyoxometallate surface have been
used [93]. These are of the type [Xn+ Zm+ (H2 O)M11 O39 ](12−n−m)− (X = PV , SiI V ;
M = MoV I , WV I ; Z = FeIII , CrIII , MnII , CoII , NiII , CuII , and ZnII ), (abbrevi-
ated as [XZM11 ]; Figure 4.16(b)). They can be considered as derived from the
non-substituted Keggin anions [Xn+ M12 O40 ](8−n)− by simply replacing one of the
external constituent atoms and its terminal oxygen atom by a 3d-transition metal
atom, Z, and a water molecule, respectively.
   This series of the semiconducting BEDT-TTF radical salts maintains the general
stoichiometry (8:1) and the structural characteristics of the previous family. In fact,
most of them crystallise in the α2 structure (Z = FeIII , CrIII , CoII , NiII , CuII and ZnII ).
However, an unexpected arrangement of the Keggin anions has been observed in
the Mn derivatives (BEDT-TTF)8 [PMnII M11 O39 ] (M = W, Mo). Here a related
structure namely α3 has been found in which the BEDT-TTFs are packed in the
same way as in the other two phases, while the Keggin units are linked through a
bridging oxygen atom in order to give an unprecedented chain of Keggin anions
that runs along the c axis of the monoclinic cell (Figure 4.19). The organic stacking
remains nearly unchanged for the three crystalline α-phases.




Fig. 4.19. Structure of the {(BEDT-TTF)8 [PMnW11 O39 ]}n radical salt showing the chains
formed by the Keggin units.
                                     4.3 Magnetic Ions in Molecular Charge Transfer Salts       139

     The magnetic properties of this series are similar to those observed in those with
  non-substituted Keggin anions. No magnetic effects arising from the d–π interac-
  tion between these localised d-electrons and the itinerant π-electrons are detected
  down to 2 K, even though the two sublattices are closer than in the salts of the non-
  substituted Keggin anions. For example in the FeIII derivative the magnetic behavior
  shows a decrease in the magnetic moment on cooling, which must be attributed, as
  before, to antiferromagnetic interactions in the organic sublattice, approaching the
  behavior of isolated paramagnetic metal ions at low temperature (Figure 4.20(a)).
  On the other hand, 4 K EPR measurements show signals characteristic of the two
  sublattices in all cases: a narrow signal at g ≈ 2 with line width of 25–40 G
  arising from the BEDT-TTF radicals, plus broad signals that closely match those
  observed in the t-Bu4 N+ salts of the corresponding paramagnetic Keggin anions
  (Figure 4.20(b)).


          6.0
                          BEDT-TTF
                          NBu4
          5.5
                                                  a
          5.0
χm(T 1)




                o




          4.5
                .
                .




          4.0
                0       50   100 150 200 250 300
                                 T (K)


            b
                                     BEDT-TTF              Fig. 4.20. Magnetic properties of the
                                                           (BEDT-TTF)8 [SiFeIII (H2 O)Mo11 O39 ]
                                                           compared      to    the    tetrabutylam-
                                                           monium       (NBu4 )    salt    of    the
                                                           [SiFeIII (H2 O)Mo11 O39 ]5−        anion:
                    x10       x10                          (a) Plot of the χmT product vs. T ; (b)
                                      NBu4                 Comparison between the EPR spectra
                                                           performed at 4 K. In the spectrum of
                                                           the ET salt we observe the coexistence
                                                           of the signal associated with the rad-
                                                           ical (sharp signal centered at 3360 G,
                                                           g = 2), with the low field signals
                    0         2500 H (G) 5000              coming from the FeIII ion (centered at
                                                           750 G (g = 8.9) and 1640 G (g = 4.1)).
140     4 Molecular Materials Combining Magnetic and Conducting Properties

The Dawson–Wells anion [P2 W18 O62 ]6−
The Dawson–Wells anion [P2 W18 O62 ]6− has also been used to prepare radical
salts. In this anion 18 WO6 octahedra share edges and corners leaving two tetrahe-
dral sites inside, which are occupied by PV atoms. Its external appearance shows
two belts of six octahedra capped by two groups of three octahedra sharing edges
(Figure 4.16(c)). Electrochemical oxidation of BEDT-TTF in the presence of this
polyanion leads to the new radical salt (BEDT-TTF)11 [P2 W18 O62 ]·3H2 O [94]. The
structure of this compound consists of layers of anions and BEDT-TTFs alternating
in the ac plane of the monoclinic cell (Figure 4.21(a)). Parallel chains of BEDT-
TTF molecules form the structural arrangement of the organic layer. The organic
molecules of neighboring chains are also parallel, leading to the so-called β-phase
(Figure 4.21(b)). What is remarkable in this structure is the presence of six crystal-
lographically independent BEDT-TTF molecules (noted as A, B, C, D, E and F in
Figure 4.21(c)) in such a way that each chain is formed by the repetition of groups of
11 BEDT-TTF molecules following the sequence . . .ABCDEFEDCBA. . . stacked
in an exotic zigzag mode. These unusual structural features illustrate well the abil-
ity of polyoxometallates to create new kinds of packing in the organic component.
But the most attractive characteristic of this salt concerns its electrical conductiv-
ity; it shows a metallic-like behavior in the region 230–300 K with an increase in




                                               Fig. 4.21. (a) Structure of the radical
                                               salt (BEDT-TTF)11 [P2 W18 O62 ]·3H2 O
                                               showing the alternating organic and
                                               inorganic layers. (b) View of the organic
                                               layer showing the β-packing mode. (c)
                                               View of the organic stacking showing the
                                               six different BEDT-TTFs (A–F).
                                         4.3 Magnetic Ions in Molecular Charge Transfer Salts   141

  the conductivity from ca. 5 S cm−1 at room temperature to 5.5 S cm−1 at 230 K.
  Below this temperature the salt becomes semiconducting, with a very low activa-
  tion energy value of 0.013 eV (Figure 4.22(a)). In view of this high conductivity,
  attempts to prepare a related compound containing a magnetic center on the sur-
  face of the Dawson–Wells polyanion have been carried out. As a result, a novel

               12

               10
                        a    [ReOP2W17O61]6-

               8
σ (S . cm−1)




               6

               4                                   [P2W18O62]6-
               2

               0
                    0       50    100      150      200    250     300
                                           T (K)



               b                 100 K
                                  50 K
                                                                      300 K
                                 40 K                                 280 K
                                                                      260 K
                                 30 K                                 240 K
                                 25 K                                 220 K
                                                                      200 K
                                 20 K                                 180 K
                                                                      160 K
                                 15 K                                 140 K
                                                                      120 K
                                                                      100 K
                                 10 K                                  80 K
                                                                       60 K
                                 4.5 K                                 50 K
                                                                       40 K
                                                                       30 K
                                                                       25 K
                                                                       20 K
                                                                       15 K
  1000 2000 3000 4000 5000                   3300 3350 3400 3450 3500
            H (G)                                      H (G)

  Fig. 4.22. (a) Thermal variation of the d.c. electrical conductivity σ for (BEDT-
  TTF)11 [P2 W18 O62 ] · 3H2 O and (BEDT-TTF)11 [ReOP2 ReW17 O61 ] ·3H2 O showing the high
  conductivity at room temperature and the metallic behavior above 230 K; (b) EPR measure-
  ments at 4 K for the ReVI derivative.
142     4 Molecular Materials Combining Magnetic and Conducting Properties

compound that contains a rhenium(VI) ion replacing a W in the Dawson–Wells
structure has been obtained ([ReOP2 W17 O61 ]6− , Figure 4.16(d)). It is isostructural
with the non-magnetic one and its electrical properties are also very close to those
observed in that compound (Figure 4.22(a)). From the magnetic point of view, no
evidence of interactions between the two electronic sublattices has been observed,
despite the fact that there are strong intermolecular anion–cation contacts. In fact,
the magnetic properties have indicated the presence of the spin S = 1/2 of the
ReVI , and EPR measurements show a spectrum very similar to that observed in the
tetrabuthylammonium salt of the polyoxometallate (Figure 4.22(b)). This novel
compound constitutes an illustrative example of a hybrid salt showing coexistence
of a high electron delocalisation with localised magnetic moments.




The magnetic anions [M4 (PW9 O34 )2 ]10− (M = Co2+ , Mn2+ )
Polyoxometallates of higher nuclearities have also been associated with organic
donors. Thus, the magnetic polyoxoanions [M4 (PW9 O34 )2 ]10− (M2+ = Co, Mn),
which have a metal nuclearity of 22, give black powders with TTF [95] and crys-
talline solids with BEDT-TTF [96]. These polyoxoanions are of magnetic inter-
est since they contain a ferromagnetic Co4 cluster or an antiferromagnetic Mn4
cluster encapsulated between two polyoxotungstate moieties [PW9 O34 ] (see Fig-
ure 4.16(e)). This class of magnetic systems is currently being investigated since
polyoxometallate chemistry provides ideal examples of magnetic clusters of in-
creasing nuclearities in which the exchange interaction phenomenon, as well as the
interplay between electronic transfer and exchange, can be studied at the molecular
level [97].
    The electrochemical oxidation of BEDT-TTF in the presence of these
magnetic anions affords the isostructural crystalline materials (BEDT-
TTF)6 H4 [M4 (PW9 O34 )2 ] which have four protons to compensate the charge. The
six BEDT-TTFs are completely charged (+1) and the compounds are insulators.
The magnetic properties of these salts arise solely from the anions. No influence
coming from the organic component on the magnetic coupling within or among
the clusters is detected down to 2 K. For example, in the Co derivative the χT
product shows a sharp increase below 50 K upon cooling and a maximum at ca.
9 K, which is analogous to that observed in the K+ salt and demonstrates that the
ferromagnetic cluster is maintained when we change K+ to BEDT-TTF+ . This
also indicates a lack of interaction between the two components. This conclusion
is supported by the EPR spectra performed at 4 K that show the same features for
both salts: a very broad and anisotropic signal which extends from 1000 to 4000 G
centered around 1620 G (g = 4.1) characteristic of the Co4 cluster. No signal from
the organic radical is observed, indicating a complete pairing of the spins of the
(BEDT-TTF)+ cations in the solid.
                          4.3 Magnetic Ions in Molecular Charge Transfer Salts       143

   The two above compounds have demonstrated the ability of the high nuclearity
polyoxometallates [M4 (PW9 O34 )2 ]10− to form crystalline organic/inorganic radical
salts with the BEDT-TTF donor. As such, they constitute the first known examples
of hybrid materials containing a magnetic cluster and an organic donor.
   To conclude this part we can say that the combination of magnetic polyoxomet-
allates with TTF-type organic donors has witnessed rapid progress in the last few
years. This hybrid approach has provided a variety of examples of radical salts
with coexistence of localised magnetic moments with itinerant electrons. This is
the critical step towards the preparation of molecular materials combining use-
ful magnetic and electrical properties. Thus far, however, the weak nature of the
cation/anion contacts as well as the low conductivities exhibited by most of the re-
ported materials have prevented the observation of an indirect interaction between
the localised magnetic moments via the conducting electrons.



4.3.3   Chain Anions: Maleonitriledithiolates

Planar metallo-complex anions of the type metal-bisdichalcogenelene tend to
form one-dimensional packings in the solid state when they are combined
with a suitable cation. In the context of the molecular conductors, the metal-
bismaleonitriledithiolates [M(mnt)2 ]− (M(III) = Ni, Cu, Au, Pt, Pd, Co and Fe)
(Figure 4.23) have been combined with perylene (see Scheme 4.1) to form the
charge-transfer solids Per2 M(mnt)2 . This organic molecule is one of the oldest
donors used in the preparation of highly conducting solids. Due to the absence
of any chalcogen atoms in the perylene molecule, all known charge-transfer salts
based on this donor have a strong one-dimensional character, which is at the origin
of the electronic instabilities exhibited by these salts. This feature contrasts with
the two-dimensional layered structures adopted by the BEDT-TTF derivatives. A
recent review that discusses the different perylene based compounds can be found
in Ref. [98].
   The structures and properties of the Per2 M(mnt)2 salts are summarised in Ta-
ble 4.5. They are all essentially isostructural and show similar lattice parameters
and diffraction patterns. In several cases (at least for M = Ni, Cu and Au) the crys-
tals have been obtained in two distinct crystallographic forms denoted as α and β.
The structure consists of segregated stacks of perylene and [M(mnt)2 ]− complexes
running along the b axis. In the α-phase each stack of [M(mnt)2 ]− is surrounded


NC          S       S       CN

                M
                                    Fig. 4.23. Metal-bismaleonitriledithiolate complexes
NC          S       S       CN      [M(mnt)2 ]− (M(III) = Ni, Cu, Au, Pt, Pd, Co and Fe).
Table 4.5. Structures and physical properties of perylene charge transfer salts.
                                                                                                                                                144



Compound          Packing                                      Electrical Properties             Magnetic Properties               Ref.
α-Per2 Pt(mnt)2   Segregated stacks of per and [Pt(mnt)2 ]− Metallic behavior along the stack- AF interactions between the spins 99, 100
                  complexes. Lattice distortion (tetrameriza- ing axis (σRT = 700 S cm−1 ) M–I S = 1/2 of the [Pt(mnt)2 ]− units
                  tion of the per chain and dimerization of transition at Tc = 8.2 K           (J ∼ −10 cm−1 ).
                  the inorganic chain) below the metal-to-                                     χ vanishes below Tc
                insulator (M–I) transition
α-Per2 Pd(mnt)2 Same as Pt salt                               Metallic behavior along the stack- AF interactions between the spins 98
                                                              ing axis (σRT = 300 S cm−1 ) M–I S = 1/2 of the [Pd(mnt)2 ]− units
                                                              transition at Tc = 28 K              (J ∼ −50 cm−1 ).
                                                                                                   χ vanishes below Tc
α-Per2 Ni(mnt)2   Same as Pt salt                             Metallic behavior along the stack- AF interactions between the spins 101, 102
                                                              ing axis (σRT = 700 S cm−1 ) M–I S = 1/2 of the [Ni(mnt)2 ]− units
                                                              transition at Tc = 25 K              (J ∼ −100 cm−1 ).
                                                                                                   χ vanishes below Tc
α-Per2 Fe(mnt)2   Segregated stacks of per and [M(mnt)2 ]− Metallic behavior along the stack- AF interactions between the spins 98
                  complexes. Lattice distortion (tetrameriza- ing axis (σRT = 200 S cm−1 ) M–I S = 3/2 of the [Fe(mnt)2 ]− units
                  tion of the per chain) observed below the transition at Tc = 58 K                (J ∼ −150 cm−1 ).
                  metal-to-insulator transition
α-Per2 M(mnt)2    Same as Fe salt                             Metallic behavior along the stack- Weak Pauli paramagnetism that 100, 101,
M = Au, Cu, Co                                                ing axis (σRT = 700 S cm−1 for Au vanishes below Tc                    102
                                                              and Cu; 200 S cm−1 for Co); M–I
                                                              transition at Tc = 12.2 K (Au), 32 K
                                                              (Cu) and 73 K (Co)
α-Per2 M(mnt)2    Segregated stacks of perylene and Semiconductors with                            Larger susceptibility than the α- 101, 102
                                                                                                                                                4 Molecular Materials Combining Magnetic and Conducting Properties




M = Ni, Cu        [Pd(mnt)2 ]− complexes. Structural dis- (σRT = 50 S cm−1 )                       phases. χ follows a T −α law with
                  order in the perylene chains.                                                    α = 0.75 (Ni) and 0.8 (Cu) that
                                                                                                   suggest random exchange AF in-
                                                                                                   teractions in the perylene chains
                          4.3 Magnetic Ions in Molecular Charge Transfer Salts      145




                                                          Fig. 4.24. The crystal struc-
                                                          ture of α-(Per)2 [M(mnt)2 ].


by six stacks of perylene molecules (Figure 4.24). The structure of the β-phase
is probably similar, although a full structural refinement does not exist due to the
presence of structural disorder.
   From the electronic point of view, the α-phase produced the first examples of
one-dimensional molecular metals where delocalised electron chains coexist with
chains of localised spins. In this respect it has been noticed that some of the prop-
erties of these compounds resemble those of Cu(Pc)I, a case where, as we have
mentioned in the Introduction, the delocalised electrons belonging to the Pc chain
interact with the paramagnetic Cu(II) ions. The properties of those derivatives con-
taining the paramagnetic metal complexes (M = Ni, Pd and Pt and Fe) are listed
in Table 4.5 and compared with those containing diamagnetic metal complexes
(M = Au, Cu, Co). The α-compounds are highly conductive along the stacking
axis b (∼700 S cm−1 for M = Au, Pt, Ni and Cu; ∼300 S cm−1 for M = Pd; and
∼200 S cm−1 for M = Fe and Co derivatives), showing a metallic regime at higher
temperatures. They undergo metal-to-insulator (M–I) transitions at lower temper-
atures, associated with a tetramerisation of the conducting perylene chains (2kF
Peierls transition) (Figure 4.25(a)). It is important to underline that the magnetic
character of the [M(mnt)2 ]− chain does not affect the transport properties and the
M–I transition occurs in the same way, irrespective of the paramagnetic or diamag-
netic nature of the metal complex. As far as the magnetic properties are concerned,
those compounds with S = 1/2 [M(mnt)2 ]− units (M = Pt, Pd and Ni) undergo a
spin-Peierls dimerisation of the localised spin chains at the same critical tempera-
ture where the M–I transition of the perylene chain takes place. Such a dimerisation
can be followed by the magnetic susceptibility. Thus, at temperatures well above
the transition the susceptibility indicates antiferromagnetic exchange interactions
within the chains with exchange constants of −15, −75 and −150 K for Pt, Pd and
Ni derivatives, respectively. This paramagnetic contribution vanishes at the M–I
transition (Figure 4.25(b)). The fact that a similar M–I transition also occurs in
compounds with diamagnetic [M(mnt)2 ]− units indicates that the Peierls instabil-
146                            4 Molecular Materials Combining Magnetic and Conducting Properties

                    10-2
a                                               Au α
                                                Pt α
                                                Pd α
                                                Ni α                       b
                                                Fe α
                    10-3                        Co α
                                                Cu α                  20                                                80
                                                                                   Pt
                                                                      15                                                60
resistivity (Ω.m)




                    10-4                                                                Ni




                                                          mu.mol -1
                                                                               .
                                                                                                      Pd
                                                                      10                                                40

                                                                      5                                                 20
                    10-5

                                                                      0                                                 0
                                                                           0       50   100   150     200   250   300
                    10-6                                                                      T (K)
                           3       10   30    100   300
                                        T (K)

Fig. 4.25. Transport and magnetic properties of the α-(Per)2 [M(mnt)2 ] (M(III) = Ni, Pt, Pd)
hybrids.

ity in the perylene chain is the dominant one and the that spin-Peierls transition
in the dithiolate chain is triggered by the perylene chain distortion. The existence
of an electronic coupling between the two kinds of chains is still controversial.
Clearly, the above picture does not require the presence of any exchange inter-
action between the itinerant electrons and the localised spins, since the structural
distortion in the perylene chains can be sufficient to induce the dimerisation in
the dithiolate chains. However, there are features in the EPR spectra that suggest
the presence of fast spin exchange between the two sublattices [99]. An additional
insight is provided by the proton NMR spin–lattice relaxation time in the Au and
Pt compounds which is indicative of a coupling of the proton spins of the perylene
molecules to the localised spin in the Pt compound [100].
   The β-compounds containing the diamagnetic Cu complex and the paramag-
netic Ni complex have also been reported [101]. Both are semiconductors with
an electrical conductivity at room temperature in the range 50–80 S cm−1 , that is
relatively high for semiconductors. They exhibit a significantly larger magnetic
susceptibility than the α-phases. Independently of the magnetic character of the
metal complexes, both follow a T −α behavior with α < 1, which is typical of a ran-
dom exchange antiferromagnetic chain. This similarity suggests that the structural
disorder of this phase is essentially associated with the perylene cations [102].


4.3.4                          Layer Anions: Tris-oxalatometallates

Over the last few years numerous examples have been found of two-dimensional
bimetallic layers containing dipositive cations, MII , and tris-Oxalatometallate (III)
anions, [MIII (C2 O4 )3 ]3− , in which the oxalato-ion acts as bridging ligand, forming
                           4.3 Magnetic Ions in Molecular Charge Transfer Salts    147

infinite sheets of approximately hexagonal symmetry, separated by bulky organic
cations [103, 104]. In view of the unusual magnetic properties of these compounds,
the synthesis of compounds containing similar anion lattices but interleaved with
BEDT-TTF molecules has been explored. A number of such compounds have
been characterised to date, and they prove to have a rich variety of structures
and properties. The first series is (BEDT-TTF)4 [AM(C2 O4 )3 ]·solvent (Table 4.6)
(A+ = H3 O, K, NH4 ; M(III) = Cr, Fe, Co, Al; solvent = C6 H5 CN, C6 H5 NO2 ,
C5 H5 N) [105–108]. While the stoichiometry is the same in all the compounds,
the structures fall into two distinct series with contrasting physical properties. One
which is orthorhombic (Pbcn) is semiconducting with the organic molecules present
as (BEDT-TTF)2+ and (BEDT-TTF)0 , while the other, which is monoclinic (C2/c)
                  2
has BEDT-TTF packed in the β arrangement [105] and is the first example of a
molecular superconductor containing a lattice of magnetic ions [109].
   The crystal structures of both series of compounds consist of alternate layers
containing either BEDT-TTF or [AM(C2 O4 )3 ]·solvent. The anion layers contain al-
ternating A and M forming an approximately hexagonal network (Figure 4.26). The
M are octahedrally coordinated by three bidentate oxalate ions, while the O atoms
of the oxalate which are not coordinated to Fe form cavities occupied either by A.
The solvent molecules occupy roughly hexagonal cavities in the [AM(C2 O4 )3 ] lat-
tice. Chirality is a further unusual feature of the anion layers. The point symmetry
of [M(C2 O4 )3 ]3− is D3 , and the ion may exist in two enantiomers. In the monoclinic
superconductors alternate anion layers are composed exclusively of either one or




                                                Fig. 4.26. Schematic view of the an-
                                                ion layer in (BEDT-TTF)4 [AM(C2 O4 )3 ]
                                                ·solvent (solvent = C6 H5 CN).
Table 4.6. Structures and physical properties of charge transfer salts containing tris oxalato-metallate anions: (BEDT-TTF)n [AM(C2 O4 )3 ]·
                                                                                                                                               148


Solvent.
A      M    Solvent       Packing                          Electrical Properties                         Magnetic Properties            Ref.

NH4    Fe   C6 H5 CN      Layers of pseudo-κ donors        semiconductor (σRT = 2 × 10−4 S cm−1 ,        PM: C = 4.37 emu K mol−1       105
                          anion layers                     Ea = 0.140 eV)                                θ = −0.11 K
K      Fe   C6 H5 CN      Same as above                    semiconductor (σRT = 10−4 S cm−1              PM: C = 4.44 emu K mol−1       105
                                                           Ea = 0.141 eV)                                θ = −0.25 K
NH4    Co   C6 H5 CN      Same as above                    semiconductor (Ea = 0.225 eV)                 DM                             106
NH4    Al   C6 H5 CN      Same as above                    semiconductor (Ea = 0.222 eV)                 DM                             106
H3 O   Cr   C6 H5 CN      Same as above                    semiconductor (Ea = 0.153 eV)                 PM: C = 1.73 emu K mol−1       106
                                                                                                         θ = −0.88 K
H3 O   Cr   C6 H5 CN      β donor layers                   superconductor (Tc = 6 K;                     PM: C = 1.96 emu K mol−1       119
                          anion layers                     Hc = 100 Oe)                                  θ = −0.27 K
H3 O   Fe   C6 H5 CN      Same as above                    superconductor (Tc = 8.3 K;                   PM: C = 4.38 emu K mol−1       105
                                                           Hc = 500 Oe)                                  θ = −0.2 K
H3 O   Cr   C6 H5 NO2     Same as above                    superconductor (Tc = 6 K;                     PM                             114
                                                           Hc = 100 Oe)
H3 O   Fe   C6 H5 NO2     Same as above                    superconductor (Tc = 4 K;                     PM                             114
                                                           Hc = 50 Oe)
H3 O   Fe   C 5 H5 N      Same as above; 1/4 donors dis-   metal–insulator transition at 116 K           PM                             107
                          ordered
H3 O   Cr   CH2 Cl2       Same as above; 1/4 donors dis-   metal–insulator transition at 200 K           PM                             108
                          ordered
Mn     Cr   –             β-donor stacks;                  metal (σRT = 250 S cm−1 )                     FM (Tc = 5.5 K)                117
                          bimetallic Mn(II)Cr(III) anion
                                                                                                                                               4 Molecular Materials Combining Magnetic and Conducting Properties




                          layers
                          4.3 Magnetic Ions in Molecular Charge Transfer Salts   149

the other, while in the orthorhombic semiconductors the enantiomers are arranged
in alternate columns within each layer.
   Although the anion layers are very similar, the molecular arrangements in the
BEDT-TTF layers are quite different in the orthorhombic and monoclinic series. In
the monoclinic phases there are two independent BEDT-TTF, whose central C=C
bond lengths differ markedly, indicating charges of 0 and +1. The +1 ions occur
as face-to-face dimers, surrounded by monomeric neutral molecules (Figure 4.27).
Molecular planes of neighboring dimers along [011] are oriented nearly orthog-
onal to one another, as in the κ-phase structure of (BEDT-TTF)2 X [110], but the
planes of the dimers along [100] are parallel. This combination of (BEDT-TTF)2+    2
surrounded by (BEDT-TTF)0 has also been observed in a BEDT-TTF salt with the
polyoxometallate β-[Mo8 O26 ]4− [111]. The (BEDT-TTF)0 describe an approxi-
mately hexagonal network, while the (BEDT-TTF)2+ are positioned near the ox-
                                                        2
alate ions, with weak H-bonding between the terminal ethylene groups and oxalate
O. Packing of the BEDT-TTF in the C2/c salts is quite different: there are no dis-
crete dimers but stacks with short S· · ·S distances between them, closely resembling




                                                 Fig. 4.27. Packing of the BEDT-TTF
                                                 in the orthorhombic series (BEDT-
                                                 TTF)4 [AM(C2 O4 )3 ]·solvent.
150     4 Molecular Materials Combining Magnetic and Conducting Properties




                                                 Fig. 4.28. Packing of the organic lay-
                                                 ers in the monoclinic series (BEDT-
                                                 TTF)4 [AM(C2 O4 )3 ]· solvent showing
                                                 the β -structure.


the β -structure in metallic (BEDT-TTF)2 [AuBr2 ] [112] and the pressure-induced
superconductor (BEDT-TTF)3 Cl2 ·2H2 O [113] (Figure 4.28).
    While the orthorhombic salts are semiconductors, the monoclinic ones are met-
als with conductivity of ∼102 S cm−1 at 200 K, the resistance decreasing mono-
tonically by a factor of about 8 down to temperatures between 7–8 K [105] (A =
H3 O+ ; M = Fe; solvent = C6 H5 CN) and 3 K [114] (A = H3 O; M = Cr; solvent =
C6 H5 NO2 ) where they become superconducting (Figure 4.29(a)).
    In line with their contrasting electrical behavior the magnetic properties of the
two series are also quite different. The susceptibilities of the semiconducting com-
pounds obey the Curie–Weiss law from 2 to 300 K with the M dominating the
measured moment. In particular, there is little contribution from the BEDT-TTF,
including those molecules whose bond lengths suggest a charge of +1. Hence
the (BEDT-TTF)2+ are spin-paired in the temperature range studied (the singlet–
                   2
triplet energy gap is expected to be >500 K), while the remaining BEDT-TTF do
not contribute to the paramagnetic susceptibility, in agreement with the assignment
of zero charge. On the other hand, the superconducting salts obey the Curie–Weiss
law from 300 to about 1 K above Tc , though with a temperature independent para-
magnetic contribution. The measured Curie constants are close to that predicted
for M3+ (Cr, Fe), while the Weiss constants (−0.2 K) signify very weak antifer-
romagnetic exchange between the M(III) moments. However, there is a strong
diamagnetic contribution in the superconducting temperature range, returning to
Curie–Weiss behavior above 10 K (Figure 4.29(b)). Whilst the EPR spectrum of the
semiconducting A = K, M = Fe compound consists of a single narrow resonance,
                            4.3 Magnetic Ions in Molecular Charge Transfer Salts       151




Fig. 4.29. Temperature dependence of (a) the resistivity; and (b) the magnetic susceptibil-
ity; of β -(BEDT-TTF)4 [(H3 O)Fe(C2 O4 )3 ]·C6 H5 CN. In (b) the susceptibility of (BEDT-
TTF)4 [KFe(C2 O4 )3 ]C6 H5 CN is also shown.


that of the A = H3 O, M = Fe compound consists of two resonances: a narrow
one assigned to the Fe(III) by analogy with the A = K compound, and a much
broader resonance from the conduction electrons. This situation is reminiscent of
that found in (BEDT-TTF)3 [CuCl4 ]·H2 O [43].
   In the series (BEDT-TTF)4 [AM(C2 O4 )3 ]·solvent, the lattice appears to be sta-
bilised by molecules included in the hexagonal cavities. The oxalato-bridged net-
152     4 Molecular Materials Combining Magnetic and Conducting Properties

work of A and M provides an elegant means of introducing transition metal ions
carrying localised magnetic moments into the lattice of a molecular charge transfer
salt. In the case of the A = H3 O, M = Fe compound, it led to the discovery of
the first molecular superconductor containing localised magnetic moments within
its structure, while the A = K, NH4 compounds are semiconducting. Clearly, it
would be advantageous to incorporate other transition metal ions at the A site to
create a two-dimensional magnetically ordered array between the BEDT-TTF lay-
ers as well as introducing a wider range of metal ions. A first step towards building
such an array produced a salt containing alternating layers of TTF and a trinu-
clear anion containing a central Mn(II) with trans-oxalate-bridges to two Cr(III).
The salt (TTF)4 Mn(H2 O)2 [Cr(C2 O4 )3 ]2 14H2 O contains strongly dimerised TTF+
and hence is not metallic. This compound exhibits an unprecedented packing in
the TTF layer similar to a κ-phase, although the interdimer distances are differ-
ent in the two directions. Its magnetic susceptibility is nicely fitted by a Heisen-
berg exchange model for a linear trimer [115]. Quite similar compounds occur
for all the combinations of MII = Mn, Fe, Co, Ni, Cu; MIII = Cr, Fe [116]. The
only known salt of TTF with tris-oxalatometallates is a 7:2 phase formulated as
(TTF)7 [Fe(C2 O4 )3 ]2 ·4H2 O where the TTFs are packed in chains surrounded by
four orthogonal dimers of TTF molecules and four paramagnetic [Fe(C2 O4 )3 ]3−
anions [77].
    The goal of creating a magnetically ordered array between the BEDT-TTF lay-
ers has recently been reached by the synthesis of a BEDT-TTF salt containing
both Mn(II) and Cr(III) in the oxalate layer [117]. The compound β-(BEDT-
TTF)3 [MnCr(C2 O4 )3 ] has a structure related to the paramagnetic superconductors
above, but with Mn(II) replacing H3 O+ within the honeycomb anion layer and
without incorporating molecules inside the hexagonal cavities. Furthermore, the
anion layer is orientationally disordered with respect to the BEDT-TTF layer in
which the molecules adopt a roughly hexagonal arrangement with face-to-face
stacks in the β-packing mode (Figure 4.30). Having two-dimensionally infinite
layers of Mn and Cr bridged by oxalate ions, the compound behaves as a ferromag-
net, with Tc of 5.5 K (Figure 4.31(a)), similar to A[MnCr(C2 O4 )3 ] salts where A
is a tetra-alkylammonium cation [103]. The saturation magnetisation and coercive
field are also similar. In dramatic contrast to the latter, however, which are insula-
tors, the BEDT-TTF salt is a metallic conductor, remaining so down to 2 K without
becoming superconducting (Figure 4.31(b)). It remains to be seen to what extent
the properties of this remarkable compound can be modified by further fine tuning
of the lattice through varying the metal ions, or by generating structures containing
other donor packing arrangements more commonly associated with superconduc-
tivity in BEDT-TTF salts, such as β or κ. Several new conducting molecular
magnets with either [MnCr(C2 O4 )3 ]− or [CoCr(C2 O4 )3 ]− layers and the donors
BEDT-TTF, BEST, BETS and BET-TTF (Scheme 4.1) have also been prepared. In
the MnCr derivatives the critical temperature is 5.5–6.0 K while in the CoCr ones
it is 9–10 K [118].
                                                                   4.4 Conclusions       153




Fig. 4.30. Packing of (a) the [MnCr(C2 O4 )3 ]− ; (b) the BEDT-TTF; (c) the organic and inor-
ganic layers, in (BEDT-TTF)3 [MnCr(C2 O4 )3 ].


4.4 Conclusions

It is clear from this chapter that compounds containing electron donor molecules of
the kind that form molecular metals and superconductors can be synthesised with a
wide variety of transition metal-containing anions, which introduce localised mag-
netic moments into the lattice. Correspondingly, whilst many of the compounds
consist of alternating layers containing cations and anions alone, they are formed
with many different packing motifs of the donor cations. Insulators, semiconduc-
tors, metals and superconductors are all represented. Examples also exist where the
anions interact with the cations through weak H-bonds, S· · ·S contacts shorter than
the Van der Waals distance or π · · ·π stacking contacts. Nevertheless, in the large
majority of cases it is fair to say that experimental evidence for exchange interac-
tions between donor π - and metal d-electrons, or metal d-electrons via a delocalised
donor π-system, is difficult to identify. Exceptions are (BEDT-TTF)3 CuBr4 [49],
(BET-TTF)2 [FeCl4 ] [42] and κ-(BETS)2 FeCl4 [34, 35], but the change in conduc-
tivity of the latter when the Fe(III) moments order antiferromagnetically could
well be due to magneto-striction. Whilst it is possible, too, that the failure of the
154           4 Molecular Materials Combining Magnetic and Conducting Properties

   30                                                              2.0

   25
                                                                   1.5
   20

   15                                                              1.0

   10
                                                                   0.5
      5

      0                                                            0.0
          2          3         4       5      6        7       8
                                      T (K)

      8
      6
      4
      2
      0
   -2
   -4
   -6
   -8
                -4         -2          0           2       4
                                      H (T)

0.005 3.0
                          H=0
0.004 2.9                 H = 1.5 T
              2.8
0.003 2.7

0.002 2.60                 5          10      15

0.001

0.000
          0          50        100    150      200     250     300
                                      T (K)

Fig. 4.31. Transport and magnetic properties of the (BEDT-TTF)3 [MnCr(C2 O4 )3 ] showing
the coexistence of metallic conductivity and ferromagnetism.
                                                                  4.4 Conclusions       155

metallic compound (BEDT-TTF)3 [MnCr(C2 O4 )3 ] to become superconducting at
low temperature may be the result of ferromagnetic order in the anion layer, there
is no unambiguous evidence that this is the case [117]. It is true that in those salts
where S· · ·S and π · · ·π stacking interactions occur between cations and anions,
transitions to long range ferromagnetic order occur, with one sublattice being fur-
nished by the cation π- and the other by the anion d-orbitals. However, in that
case the interactions are strong enough to break up the donor cation layers and,
since cations and anions are interdigitated, the resulting compounds are semicon-
ductors or insulators. Nevertheless, a rich harvest of novel molecular materials
has emerged, such as paramagnetic and antiferromagnetic superconductors, a fer-
romagnetic metal and ferromagnetic semiconductors. No doubt further synthetic
ingenuity will uncover more novelty in the future.


Acknowledgment

Financial support of the Spanish Ministerio de Ciencia y Tecnolog´ (Grant  ıa
MAT98-0880) and the European Union (TMR Network on Molecular Magnetism.
From Materials to Devices) are acknowledged. The writing of this article was
greatly facilitated by discussions with partners within the EC COST D14 003/99
Action. Peter Day thanks the IBERDROLA Foundation for a Visiting Professor-
ship at the University of Valencia, during which this chapter was written. He is also
grateful to colleagues in the University of Valencia for their warm welcome.



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5 Lanthanide Ions
  in Molecular Exchange Coupled Systems
     Jean-Pascal Sutter and Myrtil L. Kahn




5.1 Introduction

Molecular coordination compounds of rare earth ions attract increasing interest in
material science due to their luminescence and magnetic properties. As far as the
magnetic properties are concerned, the rather large and anisotropic moments of
most of the lanthanide ions make them appealing building blocks in the molecular
approach to magnetic materials. As early as 1976, Landolt et al. [1] used Ln(III)
ions for the preparation of a series of Prussian blue analogs which exhibited mag-
netic ordering and magnetic anisotropy with rather large hysteresis loops. Since,
numerous compounds containing a Ln ion associated with paramagnetic species
such as transition metal ions or organic radicals have been described [2, 3]. How-
ever, with the exception of the 4f 7 ion Gd(III) which has a spin-only ground state,
examples of molecular multi-spin systems involving Ln(III) ions are scarce and
more generally the magnetic interaction involving Ln ions remains rather poorly
understood.
   The aim of this chapter is to provide general information on the magnetic behav-
ior of molecular compounds where a Ln ion is in exchange interaction with another
spin carrier. Special attention is devoted to the Ln ions with a first orbital momen-
tum. But before considering such compounds and how recent advances permit one
to gain some insight into their magnetic interactions, it might be worth recalling
some generalities concerning the 4f elements.


5.1.1   Generalities

The electronic configuration of the rare-earth elements is (Xe)4fn 5d1 6s2 and the 14
elements of the series differ by a progressive filling of the f orbitals. In molecular
compounds, lanthanide ions are generally trivalent but for some elements a divalent
(Sm, Eu, and Yb) or a tetravalent (Ce) state can be stable when 4f0 , 4f7 or 4f14
configurations are attained. The coordination number for a Ln(III) ion may vary
from 3 to 12 and strong chemical similarity is found along the Ln series. Such
behavior underlines the poor participation of f orbitals in chemical bonds. For a
162        5 Lanthanide Ions in Molecular Exchange Coupled Systems

given ligand set, the difference in coordination number or geometry for a compound
of a Ln(III) ion from the beginning of the series as compared to one from the end of
the series is mainly due to the decrease in the ionic radii with the atomic number.
This contraction as electrons are added across the series reflects the inner nature
of the 4f orbitals.
    For the trivalent Ln series, all ions contain unpaired electrons and, consequently,
are paramagnetic, excluding La(III) (4f0 ) and Lu(III) (4f14 ) for which the 4f shell
is, respectively, empty or filled. For the Ln ions the orbital contribution is not
quenched, as is the case for some 3d ions for instance, interaction between the
spin angular momentum and the orbital angular momentum takes place. As a con-
sequence of this spin–orbit coupling, J, the quantum number associated with the
total angular momentum defined in Eq. (5.1), becomes a good quantum number to
describe the paramagnetism of a Ln ion. The expression allowing one to calculate
the value of χLn T for the free ion, where χLn stands for the molar magnetic suscep-
tibility for a Ln ion and T for the temperature, is given in Eq. (5.2). The calculated
value is usually in good agreement with the room temperature value of χLn T found
experimentally for paramagnetic Ln compounds without exchange interactions. In
this expression, N is the Avogadro number, k the Boltzmann constant, β the Bohr
magneton, and gJ the Zeeman factor given by Eq. (5.3). The value taken by J in
the ground state for the ions with a less than half-filled f-shell (f1 –f6 ) is given by
J = L − S whereas it is J = L + S for those with a more than half-filled shell
(f8 –f13 ).
    J=L+S                                                                               (5.1)
                   2
                 NgJ β 2
    χLn T =              J(J + 1)                                                       (5.2)
                  3k
                  J(J + 1) − L(L + 1) + S(S + 1)
    gJ = 1 +                                                                            (5.3)
                             2J(J + 1)
The symbol S corresponds to the spin quantum number and L represents the orbital
quantum number of the Ln ion. The values taken by S and L depend on the number
of unpaired electrons displayed by the ion. For instance, for Dy(III) which has a
4f9 configuration, the distribution of the nine electrons into the f orbitals following
Hund’s rules leads to five unpaired electrons (Figure 5.1). Consequently, for this ion
S = 5/2 and L = 5 (L = −1+0+1+2+3) yielding an angular momentum number
J = L + S = 15/2. The same S and L values are found for Sm(III) which has 4f5
configuration, but for this ion the angular quantum number is J = L − S = 5/2. As
l     -3    -2     -1   0     1     2   3



      Dy(III): 4f 9     S = 5/2
                        L=5                 Fig. 5.1. 4f-shell filling for Dy(III) and S and L
                        J = 15/2            values associated with the 4f9 configuration.
                                                                    5.1 Introduction   163

a general trend, the magnitude of the spin–orbit coupling for the Ln ions is larger
than for the 3d ions, and increases from the left to the right of the f-series.
    This orbital contribution and the ligand field have a dramatic effect on the mag-
netic properties. For the Ln ions displaying spin–orbit coupling the Curie law does
not apply. For such an ion the 4fn configuration is split by inter-electronic repul-
sion, in spectroscopic terms, the one with the highest spin multiplicity (2S + 1)
is the lowest in energy. Each of these terms is further split by the spin–orbit in-
teraction into 2S+1 LJ spectroscopic levels, with |L − S| ≤ J ≤ L + S. As already
mentioned, for a 4fn configuration with n < 7 the ground level has the lowest J
value, but for n > 7 the ground state has the highest J-value. For instance, for the
4f8 Tb(III) ion the ground level is 7 F6 . Each of these levels is further split into Stark
sublevels by the ligand field (Figure 5.2). This lifting is much smaller than for the d
ions because of the shielding of the 4f orbitals. Only a few hundred of cm−1 usually
separate the lowest from the highest sublevel resulting from the splitting of a 2S+1 LJ
level. The number of Stark sublevels depends on the site symmetry of the Ln ion.
For C1 symmetry, which is often the case in molecular compounds, 2J+1 sublevels
are expected when the number of 4f electrons is even and J +1/2 when it is odd [4].
For all paramagnetic Ln(III) ions, except Sm(III) and Eu(III), the ground 2S+1 LJ
level is separated by at least 1000 cm−1 from the next level. At room temperature,
only the Stark sublevels of the 2S+1 LJ ground state are thermally populated. As the
temperature is lowered, a depopulation of these sublevels occurs and consequently
χLn T decreases, the temperature dependence of χLn deviates with respect to the
Curie law.
   4f n-1 5d1




                    2 .104 cm-1



                                      2S+1
  4f n                                   LJ
                    2S+1
                        L                         104 cm-1

                                                                       102 cm-1

 Electronic      Spectroscopic    Spectroscopic
                                                         Stark sublevels
configuration       terms            Levels

Fig. 5.2. Schematic energy diagram showing the relative magnitude of the interelectronic
repulsion, the spin–orbit coupling, and ligand-field effects
164     5 Lanthanide Ions in Molecular Exchange Coupled Systems

   When the Ln(III) ion is in exchange interaction with another paramagnetic
                                             Ln                          Ln
species, the temperature dependence of χM T for the compound (χM stands for
the molar magnetic susceptibility) is due to both the variation of χLn T and the mag-
netic interaction between the Ln(III) ion and the second spin carrier. Consequently,
information about the nature of the magnetic interactions between such a Ln(III)
ion and the second spin carrier may not be deduced unambiguously from only the
                Ln
shape of the χM T versus T curve. Moreover, theoretical analysis of the magnetic
data of such a compound is impeded by the lack of a general theoretical model to
describe the χLn behavior of a Ln(III) ion in its ligand field.
   In the following, we will consider the cases where a Ln ion is associated with
another spin carrier. We will highlight the behavior encountered for these ions
through examples of molecular compounds reported so far.



5.2 Molecular Compounds Involving Gd(III)

Among the lanthanide ions, Gd(III) is unique because of its half-filled f7 configura-
tion. As a consequence this ion has no orbital contribution (L = 0), its ground state
is 8 S7/2 , and its magnetic behavior is governed only by the spin contribution. Thus,
when this ion is in an exchange interaction with another paramagnetic species it
behaves like a 3d ion. Its magnetic behavior can be analyzed by a Heisenberg–
Dirack–van Vleck phenomenological spin hamiltonian. The magnetic behavior of
an exchange coupled system involving Gd(III) can be considered as straightforward
and numerous compounds for which Gd(III) interacts with a second spin carrier
have been reported.


5.2.1   Gd(III)–Cu(II) Systems

The pioneering work in this area was performed by Gatteschi et al. who found
that in a series of {Cu(II)–Gd(III)} species the interaction between these ions was
ferromagnetic, irrespective of the details of the molecular structure [5–7]. The
ferromagnetic nature of the {Gd–Cu interaction} has since been confirmed for
a large number of compounds comprising discrete molecules based on Schiff’s
bases [8–15] and an extended network based on oxamato linkers [16, 17]. Long
range magnetic ordering has been reported for {Gd(III)–Cu(II)} coordination poly-
mers, but Tc for these ferromagnets is found at very low temperatures (Tc < 2 K)
[18, 19]. For a very few compounds the {Gd(III)-Cu(II)} interaction was found to
be antiferromagnetic [20, 21].
   To account for the ferromagnetic interaction between these ions, a mechanism
involving a charge transfer from Cu(II) to Gd(III) has been proposed [7, 8, 22].
                                   5.2 Molecular Compounds Involving Gd(III)      165

Following this mechanism, a fraction of the unpaired electron is transferred from
Cu(II) into an empty 5d or 6s orbital of Gd(III). While the transfer in the Gd orbital
takes place, the spin of the electron remains the same as in the starting orbital.
According to Hund’s rules, the f electrons are expected to be aligned parallel to that
in the 5d or 6s orbital, thus a ferromagnetic interaction is established. A thorough
discussion of the theoretical foundations of this mechanism has been developed by
Kahn et al. [23] and summarized recently by Gatteschi et al. [3].



5.2.2   Systems with Other Paramagnetic Metal Ions

Compounds for which Gd(III) has exchange interaction with other paramagnetic
metal ions are less documented but it seems that the sign of the exchange is mainly
governed by the nature of the chemical link between the spin carriers. For instance,
in a series of Schiff’s base derivatives where a Gd(III) is linked to transition metal
ions through an oxygen atom, ferromagnetic interactions were observed for Mn(III)
[24], Fe(II) [25], Co(II) [26], and Ni(II) [27–29]. However, for V(IV) both ferro- and
antiferromagnetic interactions were found [30, 31]. Antiferromagnetic interactions
were reported for compounds comprised of a Gd(III) ion linked to Cr(III) or Fe(III)
by a CN bridge [1, 32–34]. Oxalate or related bridging ligands have been envisaged
as well and lead to ferromagnetic {Gd(III)–Ni(II)} interaction [35], whereas for a
{Gd(III)-Cr(III)} system the observed interaction was too weak to yield a conclusive
result [36].
   The case where Gd(III) is interacting with a second f-ion has also been consid-
ered. In all cases reported so far the exchange interaction is weak and antiferromag-
netic [37–43], except one for which a ferromagnetic Gd(III)–Gd(III) interaction
was found [44].



5.2.3   Gd(III)-Organic Radical Compounds

Several compounds for which organic radicals act as ligands for a Gd(III) ion
have been reported. The appealing feature of such compounds is the direct contact
that exists between the two paramagnetic centers. This is a favorable situation to
improve somewhat the strength of the exchange interaction which is weak with
the Ln ions. Interestingly, the magnetic behavior appears greatly influenced by the
chemical nature of the organic moiety.
    The adduct formed between Gd(III) and a nitronyl nitroxide radical
(Scheme 5.1), an organic S = 1/2 spin carrier, was found to lead to ferromag-
netic interaction [45–49]. An example of such a compound where the Gd(III) ion
is linked to two nitronyl nitroxide units by means of NO groups is depicted in Fig-
ure 5.3. For this compound, {Gd(NitTRZ)2 (NO3 )3 }, the Gd(III) is surrounded by
166         5 Lanthanide Ions in Molecular Exchange Coupled Systems

                                                                O
                                                                    -
                                                                            .
                                                                        O




                    .




                                                .
    O   N       N   O               N       N   O
                                                         t              t
                                                          Bu            Bu
            R                           R
                                                          t
Nitronyl nitroxide radical   Imino nitroxide radical   3,5- Bu-semoquinonato
          (Nit-R)                    (Im-R)                    (SQ)                  Scheme 5.1



                                                                                              X O




                                                                                     .



                                                                                                    .
                                                                                         O
                                                                                 N                  N
                                                                            N                            N
                                                                                              Gd             O
                                                                    O
                                                                                      N     N
                                                                                                        N Me
                                                                        Me N            X X N
                                                                                      N
                                                                                Me                      Me
                                                                                              2
                                                                                         X=    -NO3




Fig. 5.3. View of the molecular structure of {Gd(NitTRZ)2 (NO3 )3 }.


two N,O-chelating nitronyl nitroxide subtituted triazole ligands and three nitrato
anions [48].
    The magnetic behavior of {Gd(NitTRZ)2 (NO3 )3 } is shown in Figure 5.4 in the
form of the χM T versus T plot, χM being the molar magnetic susceptibility. At
room temperature, χM T is equal to 8.90 cm3 K mol−1 , which is close to the value
of 8.62 cm3 K mol−1 expected for the isolated spins SGd = 7/2 and two Srad = 1/2.
For lower temperatures, χM T increases, reaching a maximum at 7 K before de-
creasing rapidly. The profile of the curve indicates that the {Gd-aminoxyl radical}
interactions are ferromagnetic, the decrease in χM T at low temperature was at-
tributed to weak intermolecular interactions among molecules in the crystal lattice.
The S = 9/2 ground state for this compound was confirmed by the field depen-
dence of the magnetization recorded at 2 K. The experimental behavior compares
well with the theoretical magnetization calculated by the Brillouin function for an
S = 9/2 spin (Figure 5.5).
                                                        5.2 Molecular Compounds Involving Gd(III)      167

                  11.5


                  11.0
T ( cm .K.mol )
-1




                  10.5
3




                  10.0
          M




                  9.50


                  9.00                                                    Fig. 5.4. Experimental ( ) and
                         0   20       40           60       80     100
                                                                          calculated (—) χM T versus T
                                           T (K)                          curve for {Gd(NitTRZ)2 (NO3 )3 }.


                   10


                  8.0


                  6.0
)
       B
M(




                  4.0

                                  Experimental data                      Fig. 5.5. Field dependence
                  2.0             Brillouin for S=9/2                    of the magnetization of
                                  Brillouin for S=7/2 + 2 S=1/2          {Gd(NitTRZ)2 (NO3 )3 } (•) at
                                                                         2 K. Calculated magnetization
                  0.0                                                    for three non-interacting spins
                         0   10       20       30          40      50
                                                                         (S = 7/2 + 2 × S = 1/2) ( ) and
                                       H ( kOe )                         for S = 9/2 ( ).


   The temperature dependence of the magnetic susceptibility for this compound
was analyzed using an expression for χM taking into account the intramolecular
interaction between the Gd(III) ion and the radicals, J , the intermolecular interac-
tion between the molecules, J , and an intramolecular interaction between the two
radicals, J . This latter interaction parameter considers the superexchange occur-
ring between two paramagnetic units linked by a lanthanide ion. This characteristic
will be illustrated in Section 5.3. Gadolinium(III) is a 4f7 ion with a 8 S7/2 ground
state and thus has no orbital contribution. Moreover the first excited states are very
168     5 Lanthanide Ions in Molecular Exchange Coupled Systems

high in energy. Consequently, the spin hamiltonian appropriate to the system may
be written as:
         ˆ     ˆ     ˆ       ˆ
  H = −J SGd · S − J SRad1 · SRad2                                             (5.4)
       ˆ   ˆ       ˆ         ˆ   ˆ   ˆ
taking S = SRad1 + SRad2 and S = S + SGd , H may be rewritten as
          J ˆ2        ˆ Rad ˆ Gd      J −J ˆ 2      ˆ Rad
  H=−         S − 2S2 − S2 −                  S − 2 S2                         (5.5)
          2                              2
and the energies E(s,s ) can be expressed as:
  E( 2 ,1) = 0
     9


             9
  E( 2 ,1) = J
     7
             2
  E( 2 ,1) = 8J
     5


              7
  E( 2 ,0) = J + J
     7                                                                         (5.6)
              2
The g(S,S ) Zeeman factors associated with these levels are:
             22       77
  g( 2 ,1) =
     9          gRad + gGd
             99       99
  g( 2 ,1) = gGd
     7


             4        59
  g( 2 ,1) =
     5          gRad + gGd
             63       63
               10       45
  g( 2 ,0) = − gRad + gGd
     7                                                                         (5.7)
               35       35
The molecular susceptibility is given by:
           Nβ 2 F
  χM =                                                                         (5.8)
         3kT − J F
where F is given by:
F =
                             +2J
   g 9 +126g 2 7 ,1 exp − 7J2kT +126g 2 5 ,1 exp − 2kT + 105 g 2 7 ,0 exp − 2kT
495 2                                               9J                       8J
 2 ( 2 ,1)   (2 )                    (2 )                 2 (2 )
                             +2J
           10+8 exp − 7J2kT +8 exp − 2kT +6 exp − 2kT
                                             9J            8J

                                                                             (5.9)
Least-squares fitting of the experimental data led to a ferromagnetic {Gd(III)-
aminoxyl} interaction of J = 6.1 cm−1 (gGd and grad were taken equal to 2.00)
[48].
   As a general trend, the {Gd(III)-nitronyl nitroxide} interaction is ferromagnetic
but for a very few compounds weakly antiferromagnetic interactions were found
                                   5.2 Molecular Compounds Involving Gd(III)       169




                                                  Fig. 5.6. ORTEP view of the molecular
                                                  structure for {Gd(o-ImnPy)(hfac)3 }.
                                                  Reproduced from Ref. [52] by permis-
                                                  sion of The Royal Society of Chem-
                                                  istry.


[49, 50]. When the nitronyl nitroxide radical is replaced by its imino nitroxide coun-
terpart (Scheme 5.1) the {Gd-radical} interaction becomes antiferromagnetic. For
{Gd(o-ImPy)(hfac)3 }, where o-ImPy stands for ortho-imino nitroxide substituted
pyridine, the paramagnetic moiety is linked to the Gd(III) ion through the N-atom
of the radical unit as shown in Figure 5.6. For this compound, a coupling constant
of J = −1.9 cm−1 (H = −2J S1 .S2 ) was found while for a related compound an
interaction parameter of J = −2.6 cm−1 was reported [51, 52].
   Antiferromagnetic interaction was also observed between Gd(III) and
semiquinonato radicals [53, 54]. For compound {Gd(Tp)2 (SQ)}, where Tp
stands for hydro-trispyrazolyl borate and SQ for 3,5-di-tert-butylsemiquinonato
(Scheme 5.1), the {Gd-semiquinone} interaction is characterized by a coupling
constant of J = −11.4 cm−1 (H = −2J S1 .S2 ). This substantial interaction has
been proposed to reflect a rather strong chemical link between the two paramag-
netic centers. As a result, an overlap may now exist between the single occupied f
orbitals of the metal center and the radical centered orbital. This would lead to the
observed antiferromagnetic {Gd(III)-SQ} interaction.
   The interaction between Gd(III) and tetracyanoethylene (TCNE) or tetracyan-
odimethane (TCNQ) radicals is also antiferromagnetic. Interestingly, the ability
of the latter paramagnetic ligands to act as bridges between metal ions leads to
extended structures, and magnetic order was observed for these compounds at low
temperatures [55, 56].
   The information gathered so far on the magnetic interaction occurring in molec-
ular compounds between Gd(III) and another spin carrier, either a metal ion or
an organic radical, suggests that the magnetic behavior of the compound depends
on the chemical link between the active centers. However, except for the Cu(II)
derivatives, the number of known compounds remains too limited to draw definite
conclusions. Further examples will be required to confirm and refine the present
trends.
170                  5 Lanthanide Ions in Molecular Exchange Coupled Systems

5.3 Superexchange Mediated by Ln(III) Ions

When two, or more, paramagnetic moieties act as ligands for a Ln center, a mag-
netic interaction may exist between these ligands which is superimposed on their
magnetic interaction with the Ln ion. Such combined contributions have been
observed for both {Gd-Cu} [5–7, 17] and {Gd-organic radical} [45, 48, 54, 57, 58]
systems. This superexchange among the paramagnetic ligands of the Ln center is
clearly evidenced with diamagnetic Ln ions, i. e. La(III), Lu(III), or Y(III) [46]
which is usually associated with the Ln series, as well as for Eu(III) which has
a non-magnetic ground state (see below). The magnetic behavior for the La(III)
compound, {La(NitTRZ)2 (NO3 )3 }, is depicted in Figure 5.7. The profile of this
curve indicates that an antiferromagnetic interaction takes place between the or-
ganic radicals, which tends to cancel the magnetic moment of the complex. Similar
behavior was found for the corresponding Y(III) derivative. Analysis by a dimer
model (H = −J S1 .S2 ) of their magnetic behavior yielded exchange parameters


                    0.80

                    0.70
                                                      0.06
                    0.60
T (cm 3 K mol -1)




                                 T ( cm 3 K mol -1)




                                                      0.05
          . 0.50
          .                                . 0.04
                                           .
            0.40
                                                      0.03

                    0.30
                                          M
        M




                                                      0.02

                    0.20                              0.01

                    0.10                                 0
                                                             0    10      20     30    40   50

                     0.0
                           0                 50                  100       150        200    250
                                                                       T (K)
Fig. 5.7. Experimental ( ) and calculated (—) temperature dependence of χM T for
{La(NitTRZ)2 (NO3 )3 }; Insert: detail of the variation of χM showing the maximum at 7 K.
                                                 5.3 Superexchange Mediated by Ln(III) Ions   171

of J = −6.8 cm−1 and J = −3.1 cm−1 respectively, for the La and Y derivative
[48]. The main difference between these two compounds is the nature of the dia-
magnetic metal centers. The observation of different J values thus corroborates
the hypothesis that the Ln ion is involved in the superexchange pathway between
the two paramagnetic ligands. The stronger exchange found for the La(III) deriva-
tive may be related to the spatially more diffuse orbitals for this ion as compared to
Y(III). This next-neighbor interaction is also expected to occur when Ln is a para-
magnetic ion. In that case, the sign and the relative magnitude of the {Ln-radical}
or {Ln-M} (M stands for a paramagnetic metal ion) interaction compared to the
{ligand-ligand} interaction will determine the ground state and the energy level
spectrum of the compound [9, 58].
   The case of Eu(III) compounds is somewhat peculiar. This 4f6 ion has a non-
magnetic 7 F0 ground state as a result of the canceling of its L and S components
having respectively, a value equal to 3. However, its first excited state, resulting
from the splitting of the ground term by the spin–orbit coupling, is sufficiently
low in energy to be thermally populated even below 300 K. Typical magnetic be-
havior for a Eu(III) ion is given in Figure 5.8, it corresponds to the behavior of
{Eu(Nitrone)2 (NO3 )3 }, a compound where the metal center is surrounded by dia-
magnetic ligands. At low temperature χEu T is equal to zero but increases with tem-
perature. This increase in the intrinsic magnetism for this ion is the consequence
of the population of its first excited state. In the temperature domain usually in-
vestigated for molecular compounds, i. e. 2 to 300 K, it is reasonable to assume

                    1.4                                            0.0065

                    1.2
                                                                   0.006
                    1.0
T (cm3.K.mol-1 )




                                                                            Eu




                                                                   0.0055
                                                                            (cm .mol )




                   0.80
                                                                                  3




                   0.60
                                                                   0.005
                                                                                  -1
          Eu




                   0.40
                                                                   0.0045
                   0.20

                    0.0                                            0.004
                          0   50   100    150     200    250    300
                                         T (K)

Fig. 5.8. Temperature dependence of χEu ( ) and χEu T ( ) for {Eu(Nitrone)2 (NO3 )3 }, the
solid line corresponds to the best-fit of the analytical expression of χEu T (Eq. (5.10) yielding
a spin–orbit parameter λ = 371 cm−1 .
172     5 Lanthanide Ions in Molecular Exchange Coupled Systems

that only two levels are concerned, the temperature dependence of χEu may thus
be analyzed in the free-ion approximation as a function of the spin–orbit coupling
parameter, λ [59]. The theoretical expression of χEu as a function of λ is given by
Eq. (5.10). The value taken by the g-factor for the ground term is g0 = 5 and for all
other terms gJ is equal to 3/2. χEu can thus be written as in Eq. (5.12). The analysis
of the experimental magnetic behavior of {Eu(Nitrone)2 (NO3 )3 } (Figure 5.8) by
this expression leads to a spin–orbit coupling value of λ = 371 cm−1 .
              6
                                         λJ(J + 1)
                   (2J + 1)χ (J) exp −
             J=0
                                           2kT
   χEu =      6
                                                                               (5.10)
                                     λJ(J + 1)
                 (2J + 1)χ (J) exp −
             J=0
                                       2kT

with
             Ng 2 β 2 J(J + 1) 2Nβ 2 (gJ − 1)(gJ − 2)
   χ (J) =                    +                                                (5.11)
                   3kT                   3λ

             Nβ 2 24+(27x/2−3/2)e−x +(135x/2−5/2)e−3x +(189x −7/2)e−6x
   χEu =
             3kT x    1+3e−x +5e−3x +7e−6x +9e−10x +11e−15x +13e−21x
             (405x −9/2)e−10x +(1485x/2−11/2)e−15x +(2457x/2−13/2)e−21x
       +
                    1+3e−x +5e−3x +7e−6x +9e−10x +11e−15x +13e−21x
                        λ
             with x =                                              (5.12)
                       kT

When the Eu(III) ion is surrounded by paramagnetic ligands, as for
{Eu(NitTRZ)2 (NO3 )3 }, the magnetic behavior of the compound can be attributed
to the contribution of the thermal population of the excited state of the Eu(III)
ion and the interaction between the paramagnetic ligands. Because the ground
state of the f-ion is non-magnetic, the low-temperature magnetic behavior for
{Eu(NitTRZ)2 (NO3 )3 } is governed by the intramolecular interaction between the
                                            Eu
two radical units. The rapid decrease of χM T below 20 K (Figure 5.9) can be at-
tributed to the antiferromagnetic interaction between the nitronyl nitroxide groups.
The occurrence of this antiferromagnetic interaction is demonstrated by the max-
                        Eu
imum exhibited by χM at 3 K (insert Figure 5.9), behavior reminiscent to that
observed for the corresponding Y(III) and La(III) derivatives. Provided that the
interaction between the paramagnetic ligands is weak enough to take place at
low temperature and that for this temperature only the nonmagnetic ground state
of Eu(III) is populated, the magnetic behavior of such a compound can be ana-
lyzed with the expression given in Eq. (5.13). The first term corresponds to the
interaction within a pair of S = 1/2 spins whereas χEu refers to the thermal
                                                       5.3 Superexchange Mediated by Ln(III) Ions     173

                   2.5


                   2.0
T ( cm 3 K mol )
-1




         . 1.5
                                                      0.14
         .
                                                      0.12

                                                      0.10
                                             mol )

                   1.0
                                            -1




                                                     0.080
        M




                                                 .
                                             3
                                             M (cm




                                                     0.060

                                                     0.040
               0.50
                                                     0.020

                                                       0.0
                                                             0   5   10   15   20   25   30
                   0.0
                         0         50       100               150     200       250       300
                                                             T (K)
                                                            Eu
Fig. 5.9. Experimental ( ) and calculated (—) χM T versus T curve for
                                                                   Eu
{Eu(NitTRZ)2 (NO3 )3 }; the insert shows the maximum exhibited by χM due to the
antiferromagnetic interaction between the paramagnetic ligands.


dependence of the intrinsic magnetic susceptibility of the Eu(III) ion given by
Eq. (5.12).

                                    2
                             2Nβ 2 gRad
           χM =
            Eu
                                            + χEu                                                   (5.13)
                         kT 3 + e− kT
                                        J




The analysis of the magnetic behavior of {Eu(NitTRZ)2 (NO3 )3 } by this expression
led to an intramolecular {radical-radical} interaction parameter J = −3.2 cm−1
(Figure 5.9) [60].
174     5 Lanthanide Ions in Molecular Exchange Coupled Systems

5.4 Exchange Coupled Compounds Involving Ln(III) Ions
    with a First-order Orbital Momentum

As mentioned above, the magnetic properties of a compound in which a paramag-
netic Ln(III) ion displaying spin–orbit coupling interacts with another spin carrier
is the superposition of two phenomena. The first originates from the thermal depop-
ulation of the so-called Stark sublevels of the Ln ion, and the second is the result of
the magnetic interaction between the magnetic centers. Usually, both become rele-
vant in the same temperature range. The first phenomenon, intrinsic to the Ln ion,
is modulated by the ligand field and the symmetry of the compound, and there is no
simple analytical model that can reproduce this magnetic characteristic for a given
compound. Thus, the analysis of the overall magnetic behavior for such a com-
pound by a theoretical model is not obvious. However, a rather simple experimental
approach may permit one to overcome the problem of the orbital contribution and
give some qualitative insight into the interactions occurring between a Ln(III) ion
displaying spin–orbit coupling and another spin carrier. It is based on knowledge of
the intrinsic contribution of the Ln ion in its ligand set, χLn . This approach requires
two compounds, one for which the Ln(III) is in exchange interaction with another
spin carrier, and an isostructural compound for which the coordination sphere of
the Ln center is identical but involves only diamagnetic ligands. The comparison
of the magnetic behavior of the two compounds reveals then the ferro- or antiferro-
magnetic nature of the interaction taking place in the former compound. Moreover,
a compound reproducing the intrinsic contribution of the Ln(III) provides access
to the crystal/ligand field parameters required to analyze the magnetic behavior of
the exchange coupled compound with a theoretical model. Quantification of the
interaction thus becomes possible.


5.4.1   Qualitative Insight into the Exchange Interaction

To illustrate this experimental approach, we will consider the investigation
of the {Ln(III)-aminoxyl} interaction in a series of isomorphous compounds,
{Ln(NitTRZ)2 (NO3 )3 }, comprising a Ln(III) ion (Ln = Ce to Ho) surrounded by
two N,O-chelating nitronyl nitroxide radicals. A view of the molecular structure
of these compounds is given in Figure 5.3 for the Gd derivative. For each com-
pound, the intrinsic paramagnetic contribution of the Ln ion, χLn , has been de-
duced from the corresponding {Ln(nitrone)2 (NO3 )3 } derivative where the Ln(III)
                                                                                  Ln
is surrounded by a diamagnetic ligand set. To allow a comparison between χM
and χLn , the ligand field for the compound used to determine χLn has to be the
same as for the exchange coupled system. The ligand chosen as a diamagnetic
counterpart to the nitronyl nitroxide radical is the N-tert-butylnitrone-substituted
triazole derivative, hereafter abbreviated as nitrone (Scheme 5.2). The nitrone
                                                 5.4 Exchange Coupled Compounds Involving Ln(III) Ions                     175


                               O X O                                                 X
                                                                                O         O
                           N                N                               N                  N
                  N                               N                                  Ln




                                                       .
                                    Ln                              H                                H
.



O                                                      O
                               N     N                                          N     N
     Me N                        X X            N Me            Me      N         X X              N Me
                               N     N                                          N     N
                      Me                    Me                          Me                      Me
                                     2                                                2
                               X=    -NO3                                       X=     -NO3


                      {Ln(NitTRZ)2(NO3)3}                               {Ln(Nitrone)2(NO3)3}               Scheme 5.2

and the nitronyl nitroxide-substituted triazole ligands are very much the same
as far as the moieties which are coordinated to the metal center are concerned,
i. e. the nitrogen heterocycle and the N-oxide unit. Moreover, the crystal struc-
tures of both {Ln(NitTRZ)2 (NO3 )3 } and {Ln(nitrone)2 (NO3 )3 } compounds display
essentially the same geometrical features. The difference between the magnetic
susceptibility of the {Ln(NitTRZ)2 (NO3 )3 } compound, χM and the correspond-
                                                              Ln

ing {Ln(nitrone)2 (NO3 )3 } derivative, χLn , then enables the contribution due to the
{Ln-aminoxyl} interaction to be revealed.
    For example, for the Ho(III) compound, {Ho(NitTRZ)2 (NO3 )3 }, χM T is found
                                                                         Ho

to decrease increasingly rapidly as the temperature is lowered (Figure 5.10).
                           Ho
As mentioned above, χM T results from the superposition of both the varia-
tion of the intrinsic susceptibility of the Ho(III) ion, χHo , and the {Ho(III)-
radical} interaction. The features of this magnetic behavior preclude any con-
clusion about the nature of the magnetic interaction between the metal center
and its paramagnetic ligands. However, when the intrinsic contribution, χHo T ,

                      16

                      14

                      12
T ( cm .K.mol )
-1




                      10
3




                  8.0
         M




                  6.0

                  4.0
                                                                                              Fig. 5.10. Temperature de-
                  2.0                                                                                         Ho
                                                                                              pendence of χM T ( ) for
                           0         50     100        150    200    250         300          {Ho(NitTRZ)2 (NO3 )3 } and χHo T
                                                      T (K)                                   (•) for {Ho(nitrone)2 (NO3 )3 }.
176                5 Lanthanide Ions in Molecular Exchange Coupled Systems

                  5.0
                                    6.0


                  4.0               5.0
T (cm 3 K mol )
-1




                                    4.0

                               B)
         .
         .        3.0         M (   3.0

                                    2.0

                  2.0               1.0
       M




                                    0.0
                                          0     10   20     30   40    50
                  1.0                                 H (kOe)




                  0.0
                        0    50           100    150     200     250    300
                                                T (K)
Fig. 5.11. Result of subtraction of the Ho(III) paramagnetic contribution, χHo T , from
 Ho
χM T for {Ho(NitTRZ)2 (NO3 )3 }. Insert: Field dependence of the magnetization at 2 K for
{Ho(NitTRZ)2 (NO3 )3 } ( ), {Ho(nitrone)2 (NO3 )3 } ( ), and the expected behavior for the
uncorrelated spin system (•).

deduced from the {Ho(nitrone)2 (NO3 )3 } derivative, is discounted, it appears that
  χHo T = χM T − χHo T increases at low temperature (Figure 5.11) clearly indi-
              Ho

cating that the {Ho(III)-aminoxyl} interaction is ferromagnetic. This is confirmed
by the field dependence of the magnetization of {Ho(NitTRZ)2 (NO3 )3 } which is
compared in Figure 5.11 (insert) to what would be the magnetization for the cor-
responding uncorrelated spin system. The latter was obtained by adding to the
magnetization of Ho(III) in {Ho(nitrone)2 (NO3 )3 } the contribution of two S = 1/2
spins, as calculated by the Brillouin function. For any value of the field the ex-
perimental magnetization determined for {Ho(NitTRZ)2 (NO3 )3 } is larger than that
expected for an uncorrelated system, confirming that in the ground state all the
magnetic moments of the magnetic centers are aligned in the same direction [61].
   An example of antiferromagnetic interaction is provided by the Ce(III) com-
pound, Figure 5.12. In this case, χCe T = χM T − χCe T decreases when
                                                     Ce

the temperature is lowered, behavior characteristic of an antiferromagnetic {Ce-
nitronyl nitroxide} interaction. The field dependence of the magnetization for
{Ce(NitTRZ)2 (NO3 )3 }, {Ce(nitrone)2 (NO3 )3 }, and the non-correlated magnetic
centers is shown in Figure 5.13. For any field, the experimental magnetiza-
                                   5.4 Exchange Coupled Compounds Involving Ln(III) Ions             177


                  1.4

                  1.2
T (cm .K.mol )




                  1.0
-1




                 0.80
3




                 0.60
        M




                 0.40

                 0.20

                  0.0                                                  Fig. 5.12. Temperature dependence
                        0   50   100     150         200   250   300        Ce
                                                                       of χM T ( ), χCe T (♦), and
                                        T (K)                            χCe T (•).

                  2.5


                  2.0


                  1.5
)
       B
M(




                  1.0


                 0.50                                                  Fig. 5.13. Experimental field de-
                                                                       pendence of the magnetization
                                                                       for {Ce(NitTRZ)2 (NO3 )3 } (•) and
                  0.0                                                  {Ce(nitrone)2 (NO3 )3 } (♦), and
                        0   10     20           30         40    50    calculated magnetization for a
                                       H ( kOe )                       non-correlated spin system (+).

tion of {Ce(NitTRZ)2 (NO3 )3 } is lower than that of a non-correlated system.
This comparison confirms that the magnetic moment of the ground state of
{Ce(NitTRZ)2 (NO3 )3 } results from antiferromagnetic interactions within the com-
pound. This procedure established that the correlation in the {Ln(NitTRZ)2 (NO3 )3 }
compounds is antiferromagnetic for the Ln(III) ions with 4f1 to 4f5 electronic con-
figurations, i. e. Ln = Ce, Pr, Nd, and Sm, conversely, this interaction was found to
be ferromagnetic for the configurations 4f7 to 4f10 , i. e. Ln = Gd, Tb, Dy, and Ho
[48, 60, 61]. Assuming that Hund’s rules dominate the ligand-field effects on the
Ln(III) ions, this would suggest that the {Ln-aminoxyl radical} spin-spin exchange
interaction is always ferromagnetic.
178     5 Lanthanide Ions in Molecular Exchange Coupled Systems

    The magnetic interaction between Ln(III) ions and semiquinone, another organic
radical, was also investigated. The tropolonate was chosen as the diamagnetic ana-
log for the semiquinone ligand and the first information available suggests that the
{Ln-semiquinone} interaction is antiferromagnetic for Ho(III) and ferromagnetic
for Yb(III), respectively 4f10 and 4f13 ions [62]. The {Gd-semiquinone} interaction
was also found to be antiferromagnetic (see Section 5.2.3) [53].
    The same approach has been applied to elucidate the {Ln–M} magnetic inter-
action between Ln(III) and paramagnetic metal ions in heterometallic compounds.
In that case, access to the intrinsic contribution of the Ln center is obtained by
replacing the paramagnetic M by a diamagnetic ion. For instance, the {Ln(III)–
Cu(II)} interaction has been investigated in a series of Schiff’s base derivatives. By
replacement of the paramagnetic Cu(II) by diamagnetic Ni(II) in a square planar
environment, the corresponding χLn T contribution was obtained. In this series, the
{Ln–Cu} interaction was found to be antiferromagnetic for Ln = Ce, Nd, Sm, Tm,
and Yb, and ferromagnetic for Ln = Gd, Tb, Dy, Ho, and Er [63, 64].
    The {Ln(III)–Cu(II)} interaction was also studied in coordination compounds
containing Ln(III) and Cu(II) ions bridged by an oxamato-type ligand developing
in an extended ladder-type structure. The contribution arising from the Ln(III) ions
was deduced from the isomorphous compounds where the Cu(II) was replaced
by Zn(II) [65]. By comparison of the magnetic data, ferromagnetic {Ln–Cu} in-
teractions could be established for Ln = Gd, Tb, Dy, and Tm whereas for Ln =
Ce, Pr, Nd, and Sm an antiferromagnetic interaction is suggested to take place
[66]. The same chemical systems were also prepared with paramagnetic Ni(II) in-
stead of Cu(II), which permits one to investigate the {Ln(III)–Ni(II)} interaction in
oxamato-bridged systems. Ferromagnetic interactions were established with Ln =
Gd, Tb, Dy and Ho and antiferromagnetic interactions are suggested to take place
for Ln = Ce, Pr, Nd, and Er. The ferromagnetic {Ln(III)–Ni(II)} interaction for the
Ln ions with 4f7 to 4f13 electronic configurations has also been confirmed for an
oxygen-bridged system [27].
    The use of [Co(CN)6 ]3− as the diamagnetic counterpart to the paramagnetic
building block, [Fe(CN)6 ]3− , involved in the preparation of exchange coupled
{Ln(III)–Fe(III)} cyano-bridged systems permited to address the question of the
nature of the interaction between these ions. This interaction was found to be an-
tiferromagnetic for Ln = Ce, Nd, Gd, and Dy, whereas ferromagnetic interactions
were obtained for Ln = Tb, Ho, and Tm [67]. All these experimental determina-
tions of the ferro- or antiferromagnetic nature of the magnetic interaction involving
paramagnetic Ln(III) ions with a first-order angular momentum are summarized
in Table 5.1.
    It can be mentioned that this procedure has also been successfully applied to
investigate the nature of the interactions between f ions in homodinulear phtalo-
cyanine compounds of paramagnetic Ln(III) ions. The magnetic behavior for an
exchange coupled system, {Ln–Ln} was compared to that obtained for the cor-
responding {Ln–Y} compound where one paramagnetic Ln(III) was replaced by
Table 5.1. Nature of the interaction observed in exchange coupled systems involving Ln(III) ions with a first-order orbital momentum (selection).
F stand for ferromagnetic and AF for antiferromagnetic interactions.

                     Ln(III)         Ce      Pr     Nd      Pm     Sm      Eu     Gd      Tb     Dy     Ho      Er     Tm      Yb        Ref.

Spin carrier     Bridging ligand
aminoxyl                             AF      AF     AF             AF             F       F       F     F                              48, 60, 61
semiquinone                                                                       AF                    AF                      F       53, 62
Cu(II)                   -O-         AF             AF             AF              F      F       F     F        F     AF      AF       63, 64
                               R
                     O         N
Cu(II)                               AF      AF     AF             AF              F      F       F                     F                 66
                     O         O
                               R
                     O         N
Ni(II)                               AF      AF     AF                             F      F       F      F      AF                        35
                     O         O

Ni(II)                   -O-                                                       F      F      F       F       F                        27
Fe(III)                  CN          AF             AF                            AF      F      AF      F              F                 67
                                                                                                                                                    5.4 Exchange Coupled Compounds Involving Ln(III) Ions
                                                                                                                                                    179
180     5 Lanthanide Ions in Molecular Exchange Coupled Systems

the diamagnetic Y(III) ion. Their difference revealed that the {Tb–Tb}, {Dy–Dy},
and {Ho–Ho} interactions are ferromagnetic whereas the {Er–Er} and {Tm–Tm}
interactions are antiferromagnetic [68]. Finally, the experimental approach has also
been applied to investigate the magnetic interaction involving a 5f ion, U(IV), with
Cu(II) and Ni(II) [69].
   The experimental method provides qualitative information about the nature of
the magnetic interaction involving lanthanide ions with a first-order orbital mo-
mentum. It also underlines the importance of the ligand field effect in the overall
magnetic behavior of these exchange coupled compounds. It is worth recalling
that the procedure is reliable only if the ligand-field effect is the same for the
compound used to gain access to χLn as for the exchange coupled derivative. A
difference would induce significant differences for their respective χLn contribu-
tions, especially at lower temperatures, and thus lead to a distorted interpretation
of the contribution of the exchange interaction which is also revealed in the low
temperature domain.



5.4.2   Quantitative Insight into the Exchange Interaction

Accurate analysis of the magnetic behavior of a molecular compound containing a
Ln(III) ion displaying spin–orbit coupling and in exchange interaction with another
spin carrier requires that the intrinsic contribution arising from the Ln(III) ion
is properly taken into account. All the energy sublevels of the Ln involved in
the investigated temperature range have to be considered whem determining the
interaction parameter. If the symmetry is high (octahedral, cubic, or rhombic) the
crystal field is described by just a few parameters and modeling of the crystal field
effect is straightforward [70]. However, molecular compounds usually present low
site-symmetry, as a consequence the number of crystal-field parameters is much
more important. Moreover, for a Ln ion, the correct quantum number is the total
angular momentum, J, while the hamiltonian that has to be considered incorporates
operators acting either on the spin momentum, SLn , or on the orbital momentum,
LLn . Consequently, the quantitative treatment of this hamiltonian will then require
the use of Racah algebra, especially as the ligand-field effects on the Ln ion may
lead to the mixing of multiplets and spectral terms. This makes the analysis of the
magnetic behavior of compounds for which a Ln(III) ion with a first-order orbital
momentum is exchange coupled with another spin carrier more difficult. Such an
analysis has been performed for the {Ln(NitTRZ)2 (NO3 )3 } compounds with Ln
= Dy(III) and Ho(III), respectively a Kramers and a non-Kramers ion [71]. The
purpose here is not to enter into details of the procedure but to briefly comment on
the different steps of the analysis and report the results.
                       5.4 Exchange Coupled Compounds Involving Ln(III) Ions      181

5.4.2.1    Model and Formalism
The {Ln–radical} or {Ln–M} exchange interactions in molecular compounds
are much weaker than the ligand field effects on the Ln ion. There is thus
no need to simultaneously diagonalize the corresponding hamiltonians. The ap-
proach followed, to analyze the magnetic behavior of {Dy(NitTRZ)2 (NO3 )3 } and
{Ho(NitTRZ)2 (NO3 )3 }, consisted of two steps. First, the ligand field effect, i. e.
the intrinsic contribution of the rare earth ion, was modeled in order to determine
the energy diagram {ELn } of the Stark sublevels for the Ln ions and the associated
eigenfunctions {|χLn }. Then the exchange interactions were computed in the ten-
sorial product space {|χLn |SRad1 |SRad2 } of the state functions |χLn of the Ln ion
in its ligand field environment with the state functions |SRad1 and |SRad2 of the
two radicals with which the Ln ion interacts by exchange.



5.4.2.2    The Ligand-field Effect
The first step of the approach consists in computing the spectrum of the low-lying
states of the Ln ion in its ligand environment. Interestingly, both magnetic and opti-
cal properties of the Ln ions have their origin in the spectroscopic Stark sublevels.
Analytical models of the ligand field describing the optical properties of these
ions in different materials exist and they can be adapted to compute the spectrum
of the low-lying states of the molecular compounds considered. In the presented
case, the semiempirical Simple Overlap Model (SOM) [72] was used to calculate
the crystal-field parameters. These were obtained by reproducing the magnetic be-
havior of the Ln ion, χLn , measured experimentally for the {Ln(nitrone)2 (NO3 )3 }
derivative, compound for which only the Ln ion in its crystal field contributes to
the magnetism. The energy diagrams of the Stark sublevels determined by SOM
for the Dy(III) and Ho(III) compounds, respectively 4f9 and 4f10 ions, are depicted
in Figure 5.14. The degeneracy expected for both ions is well reproduced, the Stark
sublevels are doubly degenerate for the Kramers ion Dy(III). It can be noticed that
for Ho(III) the ground sublevel is just 5.5 K below the first excited state, whereas
for the Dy(III) the ground and first excited states are separated by ca. 60 K. The
corresponding eigenfunctions and eigenvalues can then be computed taking into
account all spectroscopic terms and multiplets of the Ln ion. These were used for
the analyses of the {Ln-aminoxyl} interaction.



5.4.3     The Exchange Interaction

The topology of the {Ln(NitTRZ)2 (NO3 )3 } compounds in terms of exchange in-
teractions is shown in Figure 5.15. Two interactions have to be considered: The
interaction between the Ln(III) ion and the organic radical, J , and the intramolec-
182      5 Lanthanide Ions in Molecular Exchange Coupled Systems

              E (K)
                              561.0
523.7
487.7                         468.1
                              442.8
                              393.5 ; 398.7
                              367.8
341.5
                              287.6
                              246.7
219.1                         223.7 ; 224.3
                              192.8
                              180.3
145.0                         110.5
 93.1                          88.4
 60.2
                                  5.5
  0.0                            0.0             Fig. 5.14. Energy diagrams of the Stark
                                                 sublevels for {Dy(NitTRZ)2 (NO3 )3 } and
        Dy(III)        Ho(III)                   {Ho(NitTRZ)2 (NO3 )3 }.


                  Ln (S3, L3, J3)


         J                J


                                              Fig. 5.15. Schematic representation of the exchange
Rad1 (S1)         J’          Rad2 (S2)       interaction in {Ln(NitTRZ)2 (NO3 )3 }


ular exchange interaction between the two organic radicals, J (see Section 5.3).
This radical-radical interaction has been taken into account in the analytical model.
   An exchange interaction takes place only between spin momenta, and the ex-
change hamiltonian, Hex , corresponding to this topology is as given in Eq. (5.14).
The susceptibility measurements were performed with an applied field, therefore
the Zeeman effect must also be taken into account (Eq. (5.15)). In this hamilto-
nian, HZ , the first and second terms correspond to the Zeeman effect acting on
the total angular momentum of each paramagnetic species present in the system
(one lanthanide ion and two organic radicals). The third term corresponds to the
intermolecular interactions introduced in the mean field approximation. In this ex-
pression B is the magnetic induction, µB the Bohr magneton, ge the Lande factor
for the electron and N the Avogadro number.
   The matrix elements (Eq. (5.16)) were calculated in the tensorial product space
{| Ln |SRad1 |SRad2 }. The main difficulty arises from the evaluation of the matrix
elements between states of different SLn , LLn , and J quantum numbers, of the
                              5.4 Exchange Coupled Compounds Involving Ln(III) Ions     183

components with respect to a given system of axis, of the spin momentum and of
the orbital momentum of the Ln ion.
   Hex = −J SLn · (SRad1 + SRad2 ) − J SRad1 · SRad2                                  (5.14)

   HZ = −µB B(LLn + geSLn )−µB B(ge SRad1 + ge SRad2 )−N < (LLn + ge SLn )
      − µB B(ge SRad1 + ge SRad2 ) > [(LLn + ge SLn ) − µB B(ge SRad1 + ge SRad2 )]
                                                                            (5.15)

      Ln |   SRad1 | SRad2 |Hex + HZ |         Ln   |SRad1 |SRad2                     (5.16)
Indeed, as already mentioned, the good quantum number of a Ln ion is the to-
tal angular momentum, J. But, both the Hex and HZ hamiltonians incorporate
operators acting either on the spin momentum, SLn , or on the orbital momen-
tum, LLn , of the Ln ion but they never act on J. Consequently, to calculate the
matrix elements describing the whole system the formalism described by Judd
must be used [73]. This formalism allows one to calculate the matrix elements
 γ , j1 , j2 , J , M |X|γ , j1 , j2 , J, M where X is an operator (Hamiltonian) acting on
both j1 and j2 (but not on J). In other words, X is an operator formed by two op-
erators, each of which acts on two different parts of the system, namely j1 and
j2 .
     Once these matrix elements have been evaluated the Hex and Hz hamiltonians
can be used to calculate the matrix elements associated with the magnetic mo-
mentum operator, which are required to calculate the magnetic susceptibility. The
isothermal susceptibility calculations were made using the Linear Response the-
                                                            T
ory. The isothermal initial magnetic susceptibility, χij , is given in Eq. (5.17) where
Mipq = p|Mi |q and Mjpq = p|Mj |q are the matrix elements of the magnetic
moment operator, Mi and Mj , respectively and with j and i the cartesian directions
x, y, and z.
               µ2             e−βEp             µ2
   χjTi = −     B
                                     Mipq Mjqp + B β                e−βEp Mipp Mjpp
               Z0   pq
                             Ep − Eq            Z0             p

              µ2
       =     − Bβ
               2
                              e−βEp Mipp        e−βEq Mjqq                            (5.17)
              Z0         p                 q

The experimental magnetic behavior for {Dy(NitTRZ)2 (NO3 )3 } and
{Ho(NitTRZ)2 (NO3 )3 } was simulated by this expression as a function of
the {Ln-aminoxyl} interaction parameter, J , and the {radical-radical} interaction
paramater J . The best simulated curve for the Dy derivative was obtained for
J = 8 cm−1 and J = −6 cm−1 , it is compared to the experimental χM T behavior
                                                                    Dy

in Figure 5.16. For the {Ho(NitTRZ)2 (NO3 )3 } compound the simulation also
yields a ferromagnetic {Ho-aminoxyl} interaction parameter J = 4.5 cm−1 and a
{radical-radical} interaction J = −6 cm−1 [71].
184                   5 Lanthanide Ions in Molecular Exchange Coupled Systems

                 16


                 15
T (cm .K.mol )
-1




                 14
3




                 13
         M




                 12


                 11
                      0     50     100    150    200    250    300
                                         T (K)

Fig. 5.16. Experimental ( ) χLn T versus T behavior for {Dy(NitTRZ)2 (NO3 )3 } and calcu-
lated curve ( ) obtained for J = 8 cm−1 , J = −6 cm−1 .


    Some discrepancies exist between the experimental and calculated thermal vari-
ation of χM that can be ascribed to the limitations of the SOM in evaluating the
ligand field effects. The very low site-symmetry of the Ln ion in molecular com-
pounds leads to a large number of crystal field parameters and it would be clearly
illusory to let them vary freely and fit them solely from the variations of χM . Differ-
ent physical characteristics may be used to determine the crystal-field parameters.
Usually optical data provide access to these parameters but magnetic behavior or
NMR shifts can also be used [74]. Improvements can be expected from fitting to
measurements of the magnetization vector for single crystals, as from this the full
                                                            T
static isothermal initial magnetic susceptibility tensor, χij can be obtained. Quasi-
elastic and inelastic neutron scattering on a powdered sample should also be very
useful, as this would allow one to accurately determine the magnetic energy levels
of the molecules, provided that deuterated samples are used to avoid the strong inco-
herent neutron scattering from hydrogen. Another interesting measurement would
be that of the magnetic density by polarized neutron scattering measurements on a
single crystal. This magnetic density can be computed from the eigenstates {|p }
of the molecules. Obviously, all these experimental measurements will essentially
allow greater knowledge of the ligand field effects.
                                                                       References      185

5.5 Concluding Remarks

For quite a while, the magnetic interaction between Gd(III) and another spin carrier
was thought to be always ferromagnetic. However, several recent examples show
that this is not the case, antiferromagnetic interaction with Gd(III) may also be the
dominant interaction. Compounds with other paramagnetic Ln(III) ions are much
less documented, but the first information available suggests that for all the para-
magnetic ions of the 4f series, there is yet no obvious and general trend to explain
their magnetic interaction with other spin carriers. These experimental observations
are supported by a recent theoretical investigation on the nature of the magnetic
interaction between rare-earth ions and Cu(II) ions in molecular compounds. This
study concludes that for a given spin system either ferromagnetic or antiferromag-
netic interactions may be encountered. The ground state does not depend solely on
the filling of the 4f levels of the Ln(III) ion but also on inter-orbital 4f repulsion
and crystal field parameters [75]. This strongly suggests that the nature of the mag-
netic interaction will depend on the chemical system, not solely the spin bearing
units but also the chemical link between them. More examples are needed to get
a deeper insight into the chemical parameters governing the magnetic behavior of
lanthanide ions in molecular exchange coupled compounds.
   For these compounds, the interpretation of the magnetic behavior is often not
obvious but the experimental method described above appears as a rather simple
way to characterize the nature of the magnetic interaction. It requires, however,
careful consideration of the derivative chosen as model compound to reproduce
the intrinsic behavior of the Ln ion in its ligand field. The crystal-field effect is also
a key point in numerical analysis of the magnetic interaction of exchange coupled
systems.
   The growing interest in Ln ions in exchange coupled systems will certainly yield
numerous new examples of compounds which will provide the required knowledge
for a better understanding and rationalization of their magnetic behavior. The elu-
cidation of the pathways for the exchange interaction with these ions is a further
question to be addressed. Information on the mechanisms involved will permit
rationalization of the design of new molecule-based magnetic materials.



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6 Monte Carlo Simulation: A Tool to Analyse
  Magnetic Properties
     Joan Cano and Yves Journaux




6.1 Introduction

The quest for molecular based magnets [1–3] and high-spin molecules [4–6], in
the wider context of molecular crystal engineering, has led to the synthesis of aes-
thetic extended networks [7] and high-nuclearity metal complexes [8, 9]. These
compounds give rise to interesting magnetic properties, such as spontaneous mag-
netization, or slow magnetic relaxation times and quantum tunnelling phenomena
[10–12]. Furthermore, the large majority of compounds belonging to these families
of materials often crystallise in novel topologies. In order to establish a correlation
between the structure and magnetic behavior of the compounds, it is essential to
develop suitable models for the description of the low lying and excited spin energy
levels. Unfortunately, the huge (or infinite) number of possible configurations in
these systems precludes the calculation of the exact partition function. As a conse-
quence, the derivation of important thermodynamic properties such as the magnetic
susceptibility and specific heat capacity cannot be done. This situation is typical
of systems studied by statistical physics which deals with systems with many de-
grees of freedom. Exact analytical theories are available in rare cases and in order
to tackle the calculation of thermodynamic properties, physicists have developed
approximate methods such as high temperature expansion of the partition function
[13], closed chain computational procedure [14, 15] or density matrix renormaliza-
tion group approach (DMRG) [16, 17]. However, all these approaches are of limited
application or lead to uncontrolled errors which make improvement of the accuracy
of the results difficult. Monte Carlo simulation is the obvious choice to overcome
these problems [18]. The sources of errors are well known and the accuracy of the
calculation can be increased, in principle, by using more sample configurations and
by expanding the size of the simulated systems [18]. Furthermore, this approach
can be used for systems where analytic methods do not work. However, although
the Monte Carlo approach can be applied to many magnetic systems with different
types of interactions between the magnetic centers, this method remains simple to
program and affordable in term of computer power only in the case of the Ising
model [19] and the classical spin approximation (S = ∞) [20]. Recent examples
190     6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties

in the literature provide interesting systems where these models can be applied.
In order to illustrate the power and the efficiency of Monte Carlo simulation in
molecular magnetism we will reduce the scope of this chapter to isotropic systems
with spin S = 5/2 for which the classical spin approximation is satisfactory.



6.2 Monte Carlo Method

6.2.1   Generalities

A classical problem in statistical physics is the computation of average macroscopic
observables such as magnetization M for a magnetic system. In the canonical
ensemble, the average magnetization M is defined as:
            ∞
                  Mi e−Ei /kT
            i=1
      M =     ∞                                                                 (6.1)
                       −Ei /kT
                   e
             i=1

It is generally not possible to compute exactly this quantity in Eq. (6.1) due to the
mathematical difficulties and the infinite or huge number of configurations. The
basic idea of Monte Carlo simulation is to get an approximation of Eq. (6.1) by
replacing the sum over all states with a partial sum on a subset of characteristic
states:
            N
                  Mi e−Ei /kT
            i=1
      M =     N
                                                                                (6.2)
                       −Ei /kT
                   e
             i=1

In the limit, as N → ∞, the sum formula of Eq. (6.2) equates to Eq. (6.1).
The first possible approach involved the random selection of the states for the
subset, i. e. adoption of the simple sampling variant of Monte Carlo simulation. This
approach however, has major drawbacks as the rapidly varying exponential function
in the Boltzmann distribution causes most of the chosen states to bring a negligible
contribution to Eq. (6.2). In order to get sensible results, the ideal situation would
be to sample the states with a probability given by their Boltzmann weight. As
will be shown below, this can be done by using the importance sampling approach.
Comparison between simple and importance sampling can be illustrated by the
fictitious system of 40 independent particles allowed to occupy 100 levels equally
                                                               6.2 Monte Carlo Method          191

         100

          80
                                               T=10 K
          60
Energy




          40
                                                            Fig. 6.1. Occupation at 10 K of 100 en-
          20
                                                            ergy levels equally spaced by 1 K using
           0                                                a random selection (horizontal bars),
               0           1          2          3      4   an importance sampling (dots) and a
                                  population                Boltzmann’s distribution (line).


spaced by 1 K. In Figure 6.1 is depicted the repartition of the independent particles
among the 100 levels at 10 K using a random selection and importance sampling
approach (Metropolis algorithm [21]). These two repartitions are compared to the
Boltzmann distribution.
   This plot clearly shows that the high energy particles are too numerous in the
random sample when compared to the ideal Boltzmann distribution and will bias
the calculation of the average quantities. This is not the case for the sample ob-
tained with the Metropolis algorithm. Even with a small number of configurations
(900) the repartition in the average sample is very close to the ideal Boltzmann
repartition. For a large number of configurations (900,000) the repartition of the
40 particles obtained by the Metropolis approach is indistinguishable from the
Boltzmann repartition.
   The calculated average energies are 10.15 and 10.58 K for the random and the
Metropolis samples respectively ( E = 10.50 K for the 900,000 configurations
sample). The average energy calculated with the simple sampling is a poor ap-
proximation to the real average energy E = 10.50 K. On the other hand, the
importance sampling approach gives sensible results, therefore it seems essential
to use this sampling method in Monte Carlo simulation [18]. In this approach,
the calculation of the average physical quantities is done by a simple arithmetic
average (Eq. (6.3))
                       N
                   1
         M =                 Mi                                                              (6.3)
                   N   i=1

But the configurations used in the arithmetic average are chosen according to
their Boltzmann weights. That is, for low temperature there are more low energy
configurations than high energy ones. Although the method looks reasonable, it
seems difficult to calculate the sampling probability p(Ci ) of a configuration Ci
which depends on the partition function (ZN , Eq. (6.5)), that we are unable to
calculate
            e−Ei /kT
   p(Ci ) =                                                                   (6.4)
               ZN
192      6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties
            N
   ZN =          e−Ei /kT                                                         (6.5)
           i=1

This tour de force can be accomplished by applying the Metropolis algorithm [21].


6.2.2     Metropolis Algorithm

The idea advanced by Metropolis et al. [21] is to generate each new configuration
Cj from the previous one Ci and to construct a so-called Markov chain [18]. The
probability of getting Cj from Ci is given by a transition probability W (Ci → Cj ).
It is possible to relate this transition probability W (Ci → Cj ) to the probability of
a configuration p(Ci ) by considering the dynamics of the process. At the beginning
of the process, the probability of a configuration depends on the computer time
(number of iteration). Therefore, it is possible to calculate the probability of a
configuration Ci at the time t + 1 through the following relation
   p(Ci , t + 1) = p(Ci , t)
                    +            W (Cj → Ci )p(Cj , t) − W (Ci → Cj )p(Ci , t)    (6.6)
                        Cj =Cj

After several iterations (thermalization process) the probability of a configuration
p(Ci , t) must be independent of the computer time, that is
   p(Ci , t + 1) = p(Ci , t)                                                      (6.7)
One possibility to cancel the second term of Eq. (6.6) is the so-called detailed
balance condition
   W (Cj → Ci )p(Cj , t) = W (Ci → Cj )p(Ci , t)                                  (6.8)
which can be rewritten in the case of the Boltzmann distribution for p(Ci ) as
   W (Ci → Cj )   p(Cj )  e−E(Cj )/kT /ZN  e−E(Cj )/kT
                =        = −E(C )/kT      = −E(C )/kT                             (6.9)
   W (Cj → Ci )   p(Ci )  e    i      /ZN  e    i


This condition gives a relationship between the ratio of the transition probabilities
and the ratio of the configuration probabilities. It is worth noting that Eq. (6.9) is
independent of the partition function ZN and that all the quantities in the last ratio
of Eq. (6.9) are known or can be calculated. The next step is to give arbitrary values
to W (Ci → Cj ) and W (Cj → Ci ) respecting the detailed balance condition. In
1953, Metropolis, Teller and Rosenbluth proposed the simple following choice for
W [21]
      W (Ci → Cj ) = e− E/kT if          E>0
                                                                                 (6.10)
                   = 1.0     if          E≤0
with     E = E(Cj ) − E(Ci )
                                                      6.2 Monte Carlo Method       193

   This choice satisfies the detailed balance condition and, more importantly, it can
be shown by simple arguments that a sequence of configurations generated by this
procedure represents a configuration sample according to the Boltzmann distribu-
tion [18]. Finally, the last step in a Monte Carlo simulation is to define whether the
new configuration is accepted to calculate average quantities from Eq. (6.3). Ac-
cording to the Metropolis algorithm, only the probability of the transition to a new
configuration is given, but no more direct information on this condition is provided.
So, the success of a transition is ruled by a comparison of its probability with a real
random number r uniformly distributed between zero and unity (r ∈ [0, 1]). Thus,
only when W (Ci → Cj ) ≥ r is the new configuration accepted. This option is
sensible since most of the high-energy configurations will be rejected, especially at
low temperatures, where the transition probability W (Ci → Cj ) reaches smaller
values than most random numbers r.
   Although Monte Carlo simulation using the Metropolis algorithm appears to
be a simple alternative for the calculation of average quantities, some points are
delicate and can lead to unreliable results. The main points to be checked in order
to obtain a robust simulation are: the thermalization process, the size of the model,
the number of MC iterations and the random number generators.


6.2.3   Thermalization Process

Before calculating a physical observable, it is necessary to check that the memory
of the initial state is lost and the equilibrium distribution is reached, that is, the
probability of a configuration must be independent of the “computer time” (the
number of Monte Carlo steps, MCS) and should only depend on its energy. The
necessary time to get closer to the equilibrium can be very large at temperatures
lower than that of the magnetic ordering temperature. Sometimes, 3 × 104 MCS
site−1 are not enough to reach equilibrium. When a sample is in equilibrium at
higher temperatures (300 K) and suddenly cooled, the initial configuration is frozen
and a very large time is required to reach equilibrium in the new conditions. Shorter
times are required when a gradual decrease in temperature occurs. For example, in
a 3D cubic lattice the equilibrium is not completely reached after 105 MCS site−1
at 0.1 K, see Figure 6.2.
   To avoid this problem of slow relaxation toward equilibrium, two key points must
be considered. First, at each temperature, the configurations found at the beginning
of the simulation (first Monte Carlo loops) must be excluded in the calculation of
the physical observable. Generally, we discard the first 10% of configurations
generated by the MC algorithm, where equilibrium has not been reached. Second,
starting from a high temperature, a low cooling rate must be chosen according to
the following equation:
   Ti+1 = kTi , with 0.9 ≤ k < 1.0                                              (6.11)
 194                 6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties


                 6
                                             2K
      eq
/ ( χT)

                                             1K
                 4                           0.25 K
      cal




                                             0.1 K
(χT)




                 2
                                                                             Fig. 6.2. Limit number of MCS to reach
                 0                                                           equilibrium as a function of the temper-
                                4       4          4          4          5
                     0       2 10    4 10   6 10       8 10       1 10       ature in a 3D cubic lattice when it is sud-
                                      MCS / site                             denly cooled.

 From this equation, the points at low temperatures, where the relaxation time is
 large, get closer. Therefore, in the last Monte Carlo steps, when the sample has
 reached equilibrium, a configuration is chosen as the initial configuration for the
 next temperature. So, this configuration is placed close to the equilibrium condition.


 6.2.4                  Size of Model and Periodic Boundary Conditions

 Except in the case of high nuclearity complexes, which have a finite size, it is
 not possible to simulate real networks. Since the time of calculation is infinite in
 the last cases, finite models must be considered in order to study the extended
 network. On the other hand, it is necessary to use systems large enough to avoid
 finite size or border effects [18]. To illustrate this point, let us take the example of
 the antiferromagnetic S = 5/2 regular chain, where the exact law for a classical
 spin approach is known [20]. The results of the MC simulation of χ|J | (magnetic
 susceptibility) as a function of T /|J | for an increasing number of spins in the chain
 show that below 100 spins the simulations are not accurate enough, so it is necessary
 to reach 200 spins to avoid boundary effects at low temperatures (Figure 6.3).

                0.040

                                                                                  4
                                                                                  12
 -1




                0.035
 χ M / cm mol




                                                                                  20
 3




                                                                                  40

                0.030                                                             100
                                                                                  400
                                                                                  Fisher
                0.025
                         0      20      40      60        80         100      120
                                               T/K

 Fig. 6.3. χ |J | versus T /|J | plot for a series of linear systems with an increasing number of
 sites. The results are compared with Fisher’s law for a one-dimensional system of classical
 spin moments [20].
                                                            6.2 Monte Carlo Method        195




                                                    Fig. 6.4. Illustration of how periodic
                                                    boundary conditions are used to diminish
                                                    the model size without introducing border
                                                    effects.


   Although it is possible to simulate a chain of 200 spin moments within a reason-
able time, it would take too much time to simulate a 3D network on a 200×200×200
model. In fact, the threshold size to avoid finite size effects over a wide range for a
3D system is smaller, but the required size is still too large to allow an affordable
calculation time. The periodic boundary conditions (PBC) are used to diminish the
model size without introducing border effects [18]. Thus, for instance, the first and
last spin moments of a chain are considered as nearest-neighbours and, in conse-
quence, all spin moments become equivalents, see Figure 6.4. These PBC can be
extended to 2d and 3d networks as shown below.
   In a one-dimensional system, the PBC conditions reduce considerably the finite
size effects, so 20 spin moments are enough to obtain a nearly perfect simulation
of the magnetic behavior (Figure 6.5).



             0.035                              4 cyclic
                                                8 cyclic
                                                20 cyclic
/ cm3mol-1




             0.030                              40 cyclic
                                                Fisher
                                                                Fig. 6.5. χ|J | versus T /|J |
             0.025
      M




                                                                plot for a series of cycles
                                                                with an increasing number
                                                                of sites. The results are com-
             0.020                                              pared with Fisher’s law for
                     0   20   40   60    80   100      120      a one-dimensional system of
                                   T/K                          classical spin moments [20].
196     6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties

   In practice, the model size considered in the Monte Carlo simulations is double
the minimum size for which border effects are absent.


6.2.5   Random Number Generators

The use of random numbers is the core of Monte Carlo simulations. Thus, finding
a good random number generator (RNG) is a major problem. In an ideal situa-
tion the random numbers would be generated by a random physical process. In
practice, computers are used to carry out this function using mathematical sub-
routines. Actually, these generated numbers are not random and are referred to
as pseudorandom numbers. However, this difference is not very meaningful if a
RNG satisfies some important criteria. In general, RNGs supplied with compiler
packages are dirty generators, so it is necessary to find a proper subroutine. A good
introduction to RNGs is given in Ref. [22]. All mathematical RNGs supply a finite
number sequence, which must be reproducible in any computer. The period of this
sequence must be long and, at least, very much larger than the required random
numbers sequence to simulate a physical property at a certain temperature. On the
other hand, the number produced by a RNG must be apparently random, in other
words, they must present a homogeneous distribution, avoiding numbers turning up
as a series of sequences involving numbers of a similar magnitude. To summarize,
these RNGs must satisfy the statistical tests for randomness. Unfortunately, some
RNGs fulfil statistical tests but fail on real problems. Thus, it is necessary to check
the RNGs on real problems that have already been solved. Some authors suggest
testing the RNGs using the MC methods in the calculation of energy for a 2D Ising
network [23].


6.2.6   Magnetic Models

Although the nature of the interaction between the magnetic ions is electrostatic, the
magnetic data can be well described using effective spin hamiltonians reminding
of a magnetic interaction. Theoreticians have justified the use of such hamiltonians
for magnetic systems. Most of the studies have been based on the Heisenberg and
Ising Hamiltonians, which can be written in general as:
                                  ⊥             y   y
   H =−           Jij Siz .Sj + Jij (Six .Sj + Si .Sj )
                            z              x
                                                                                (6.12)
           j >i

                                                                ⊥
where Sik are components of the spin vectors Si , and Jij and Jij are the exchange
coupling constants. The Ising and Heisenberg models correspond to cases where
  ⊥                      ⊥
Jij = 0 and Jij = Jij , respectively. The Ising model is adapted to strongly
anisotropic ions, but in spite of its mathematical simplicity nobody has been able
                                                              6.2 Monte Carlo Method     197

to solve it exactly beyond the 2D square lattice [19]. On the other hand, the Heisen-
berg model is adapted to isotropic systems, but it is not possible to solve it except
for some finite systems. However, Monte Carlo simulation is a useful tool to de-
scribe the magnetic properties of systems where exact solutions are not known. We
have shown that the Metropolis algorithm allows one to sample the configurations
according to the Boltzmann distribution. The core of the algorithm is the compar-
ison of a random number with the quantity e− E/kT . In theory, it is necessary to
diagonalize the full energy matrix built from the Heisenberg hamiltonian to know
the energies of the configurations that allow the calculation of e− E/kT . Thus, ap-
parently, it seems that we have gone back to the starting point. It is possible to
overcome this problem by using a Quantum Monte Carlo approach but this is be-
yond the scope of this chapter [24–27]. There are many interesting compounds that
contain ions with spins S ≥ 2 (Mn(II) or Fe(III)), where there is another possibility.
It has been shown that these spins can be considered as classical vectors. How-
ever, in order to compare the calculated values with experimental observations, the
classical spin vectors are scaled according to the following factor:
    Si =     Si (Si + 1)                                                               (6.13)
With this approximation, the Heisenberg hamiltonian is reduced to
   H =−           Jij ·      Si (Si + 1) ·   Sj (Sj + 1) · cos θij                     (6.14)
           j >i

which allows one to easily calculate the configuration energies requested for the
Metropolis algorithm (CSMC method). Thus, this chapter focuses on the S = 5/2
systems, where the classical spin approach can be used.


6.2.7   Structure of a Monte Carlo Program

All the ingredients to write a Monte Carlo program are available. An abstract of
this program is shown in Figure 6.6.
    Two remarks must be made: (a) the initial spin configuration of the network or
cluster is chosen randomly, but other choices are possible; and (b) the sites of the
network are not explored randomly for the spin orientation update but systemati-
cally through a loop. It has been shown that this approach gives good results for
equilibrium configurations.
    After the generation of the sample using the Metropolis algorithm all the ther-
modynamic quantities can be calculated. It has been shown that the magnetization
is calculated as the simple arithmetic average
                  N
       1
   M =                  Mi                                                             (6.15)
       N          i=1

And it is also possible to calculate the average energy:
198     6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties

                       Initialisation of the network
                     Random orientation for the spins

                                 T=T initial

                                  istep = 0           No            T =Tend           Tnew = T x K

                               istep =istep+1                            Yes
                                  site i= 0
                                                                     STOP
                                   i = i +1

                        The new spin components
                      S x(i) , S y(i), S z(i) are choosed
                                   randomly

                               Calculate E

             E≤0                                      E>0

                                                random number R

                                                    R ≤ e-   E/kT


                                              Yes                   No

            take the new spin orientation                     keep the old spin orientation



                                                    i = maxsite


                                       No               Yes


                                                   istep >                            calculate average
                                              thermalisation steps                     quantities M

                                       No                                Yes

                                                                memorize configuration

                                        No                          istep = maxstep        Yes

Fig. 6.6. Flow chart of a Monte carlo program using the classical spin approach.
                 N
            1
      E =             Ei                                                                                  (6.16)
            N   i=1

as well as the magnetic susceptibility and specific heat, which are calculated as the
fluctuation of magnetization and energy, respectively.
      χ = M 2 − M 2 ; Cp = E 2 − E                                  2
                                                                                                          (6.17)
                                                  6.3 Regular Infinite Networks     199

6.3 Regular Infinite Networks

In order to fully understand and fine-tune the physical properties of magnetic
materials, it is necessary to gain as much information as possible, such as the g-
factors or the interaction parameter J between the magnetic ions. For a simple
system, it is possible to get the values of these parameters by fitting a theoretical
model to the experimental data. So, the calculation of the magnetic susceptibility
is often combined with a least-square routine allowing the determination of the
best parameters. In practice, a least-square fit by Monte Carlo simulation takes a
lot of computer time. Nevertheless, for networks with only one or two interaction
parameters, empirical laws using reduced variables can be established from Monte
Carlo simulations [28]. The magnetic susceptibility can be given by an expansion
function
        a            J
   χ=     f      b     + ε(H )                                                    (6.18)
        T            T
When the magnetic field is close to zero the ε(H ) term is negligible and the mag-
netic susceptibility becomes field independent. In this case, there is only one χ|J |
versus T /|J | curve for all J values. So, it is possible to obtain empirical laws from
the Monte Carlo simulations which depend on the reduced temperature β = T /|J |.
These empirical laws, which have been derived for several regular networks (1D,
square and honeycomb 2D and cubic 3D), take the form:
                          k
                 a0 +          ai β i
            g2           i=1
   χ |J | =             k+1
                                                                                  (6.19)
            4
                 1+           bj β j
                       j =1

The coefficients associated with the highest degree of the polynomials for both
the denominator and the numerator are set so that they converge to the Curie law
at high temperatures (χ T = 4.375 cm3 K mol−1 , for g = 2). Furthermore, the
zero-grade terms in the numerator are fixed so that they converge to the finite
χ |J | values obtained by the simulations at low temperature. The exact numerical
coefficients associated with the empirical laws derived for cubic, diamond and 3-
connected 10-gon (10, 3) 3D networks are given in Table 6.1, and those for square
and honeycomb 2D networks are shown in Table 6.2. Empirical laws can also be
found for alternating systems with different magnetic interactions, but they present
a more complicated form. Equations for other systems that are not shown in the
present manuscript are available from the authors.
   A comparison is made with the high temperature series expansion of the partition
function (HTE) for 2D honeycomb and square and 3D cubic networks by Stanley
200        6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties

Table 6.1. Coefficients of the rational functions providing the thermal variation of the reduced
magnetic susceptibility χ |J | as a function of β = T /|J | for simple cubic, diamond and (10, 3)
cubic networks (J in K) (Eq. (6.19)) [36].

Coefficient          Cubic           Diamond          (10,3) Cubic
      a0           0.0815865           0.116             0.156
      b0               1                 1                 1
      a1               0                 0                 0
      b1               0                 0                 0
      a2        1.22599 × 10−5        1.85958      1.20777 × 10−4
      b2       −2.78782 × 10−3        11.7921      5.11803 × 10−5
      a3               0                 0                 0
      b3               0                 0                 0
      a4       −5.34657 × 10−7        324.872      6.12417 × 10−4
      b4        9.71169 × 10−6        2795.33     −2.47313 × 10−4
      a5               0                 0                 0
      b5               0                 0                 0
      a6        3.56382 × 10−8        2.5012      −1.0435 × 10−6
      b6        1.37954 × 10−9        18.033      −2.32108 × 10−4
      a7               0                 0                 0
      b7        8.14585 × 10−9           0                 0
      a8               0             0.264794       3.99986 × 106
      b8               0             0.816704      8.05117 × 10−6
      a9               0                0                 0
      b9               0            0.0605244      9.14253 × 10−7


et al., and Lines et al. and with Fisher’s law for a chain (Figure 6.7) [13, 20, 29–
33]. Agreement between MC simulations and the other approaches is excellent at
temperatures higher than that of the maximum value of χ|J |. Nevertheless, below
this temperature there is a noticeable discrepancy since the HTE method is not
applicable in this region, whereas there is a perfect agreement between the MC
simulation and Fisher’s law for a regular chain over the whole temperature range.
On the other hand, as expected, the maximum value of χ|J | increases and its
position is displaced towards lower temperatures when the dimensionality of the
network and the connectivity between the magnetic ions decrease, since the number
of spin correlation paths also decrease [28, 34]. It must be noticed that for the 3D
system the maximum corresponds to the antiferromagnetic ordering temperature,
whereas for the 1D and 2D networks it is well established that there is no magnetic
ordering for the Heisenberg model.
   We have tested the CSMC approach to fit the magnetic data for
[N(CH3 )4 ][Mn(N3 )3 ] [35, 36], which crystallizes in a regular cubic network
                                                       6.3 Regular Infinite Networks        201

Table 6.2. Coefficients of the rational functions providing the thermal variation of the reduced
magnetic susceptibility χ |J | as a function of β = T /|J | for square and honeycomb 2D
networks (J in K) (Eq. (6.19)).

Coefficient        Square         Honeycomb
    a0          −121201.0           2.82178
    b0        −1.05473 × 106       −582.803
    a1            311085.0          82.6317
    b1         2.72275 × 106        3830.22
    a2          −289512.0          −110.786
    b2        −2.56424 × 106       −8491.63
    a3           −117474.0         −248.245
    b3         1.07481 × 106        8711.63
    a4           −19202.0           626.252
    b4           −201403.0         −4401.53
    a5            358.413          −530.795
    b5            17648.1           982.435
    a6            428.864           220.820
    b6           −275.529          −34.5723
    a7           −73.9798          −47.0672
    b7           −39.9761          −12.2174
    a8             4.375            4.375
    b8            −5.4875          −2.11426
    a9              0.000             0.000
    b9              1.000             1.000



(Figure 6.8). Its magnetic behavior can be reproduced using J = −5.2 cm−1 and
g = 2.025 [36]. These values are close to those found with the HTE method
(J = −5 cm−1 ) [35]. It is worth noting that the agreement between the MC simu-
lation and the experimental data is very good, even at low temperatures, confirming
the classical behavior for this 3D network.
    An interesting comparison between the magnetic behavior of three different
antiferromagnetic regular 3d networks is shown in Figure 6.9. These 3D systems
correspond to primitive cubic, diamond and 3-connected 10-gon (10, 3) cubic
networks. As expected, the antiferromagnetic ordering temperature TN /|J | is dis-
placed toward a lower temperature as the connectivity between the magnetic sites
decreases [36]. Below TN /|J |, in an ordered phase, our results could be compared
to the less accurate mean field approximation. In this approach, as in our MC sim-
ulations, the expected limit of the χ |J | value at T /|J | = 0 is equal to 2/3 of its
maximum value. So the CSMC method is able to reproduce the physical behavior
in the paramagnetic and in the ordered phases, while the mean field approximation
202     6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties



                                                                          0.300
                                                                                           (a)


                                                                          0.250

                                                                                           (b)
           (a)                      (b)




                                                           -1
                                                                          0.200




                                                           |J| / cm mol
                                                                                                 (c)




                                                           3
                                                                          0.150
                                                                                                 (d)


                                                                          0.100



                                                                          0.050



                                                                                  0          10          20             30    40     50
                                                                                                              T / |J|
          (c)                       (d)

Fig. 6.7. χ |J | versus T /|J | plots obtained by MC simulation for 1D, 2D honeycomb, 2D
square and 3D cubic networks in a Heisenberg model. These plots are compared with those
obtained by the high temperature expansion method and Fisher’s law [13, 20, 29–33].



                                                          0.035


                                                          0.030
                                              -1
                                               / cm mol




                                                          0.025
                                              3




                                                          0.020


                                                          0.015


                                                          0.010
                                                                          0           50           100    150           200   250   300
                                                                                                         T/K


Fig. 6.8. Crystal structure and magnetic properties of [N(CH3 )4 ][Mn(N3 )] [35, 36]. The ex-
perimental data (circles) and the simulations by Monte Carlo methods (solid line) are shown.


leads to a large overestimation of the ordering temperature and the HTE method is
limited to the paramagnetic region [34].
    In [FeII (bipy)3 ][MnII (ox)3 ], a compound previously described by Decurtins et al.
                         2
[37], where bipy = 2, 2 -bipyridine and ox = oxalate, the Mn(II) ions are connected
via oxalate bridging ligands to build up a three-dimensional 3-connected 10-gon
network (Figure 6.10). From CSMC simulations, an antiferromagnetic interaction
is found for this compound with J = −2.01 cm−1 [36]. This value is in agreement
with those found in the literature for other dinuclear complexes and regular chains
incorporating oxalate groups as bridging ligands.
                                                                                             6.4 Alternating Chains               203




                                                                                0.25



                                                                                0.20




                                                            |J| /cm mol K
                                                                                           (c)
(a)                     (b)




                                                           -1
                                                           3
                                                                                0.15
                                                                                           (b)




                                                                      M
                                                                                0.10
                                                                                           (a)


                                                                            0.050
                                                                                       0         10     20             30    40     50
           (c)                                                                                               T / |J|


Fig. 6.9. MC simulations of χ|J | versus T /|J | plots for three different antiferromagnetic
regular 3D networks: (a) primitive cubic, (b) diamond and (c) 3-connected 10-gon (10, 3)
cubic networks [36]. The line without symbols represents the theoretical curve found by the
HTE method.



                                                          0.022
                                              -1
                                               / cm mol




                                                          0.018
                                              3
                                                    M




                                                          0.014



                                                          0.010
                                                                            0                     100                  200         300
                                                                                                        T/K

Fig. 6.10. Crystal structure and magnetic properties of [FeII (bipy)3 ][MnII (ox)3 ] [37]. The
                                                                          2
experimental data are shown as circles and the Monte Carlo and HTE simulation as bold and
normal lines, respectively [36].



6.4 Alternating Chains

Alternating S = 5/2 chains with two or more different exchange coupling constants
have also been investigated. An interesting example is that of a chain presenting
an interaction topology J1 J2 , that is, two different consecutive interactions (J1 and
J2 ) that repeat along the chain (. . .J1 J2 J1 J2 J1 J2 . . .). Drillon et al. have derived
an exact analytical law in the frame of the classical spin approach to analyse the
magnetic behavior of these systems [38]. On the other hand, the versatility in the
coordination of the azido ligand led to several interaction topologies. In the [MnII (2-
pyOH)2 (N3 )2 ]n compound (2-pyOH = 2-hydroxypyridine) the manganese(II) ions
are connected by µ-1,3-azido bridging ligands (Figure 6.11) [39]. It is well known
204      6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties




Fig. 6.11. Crystal structure and magnetic properties of [MnII (2-pyOH)2 (N3 )2 ]n [39]. The ex-
perimental data are shown as circles and the simulations by Monte Carlo method and Drillon’s
law as solid and dashed lines, respectively [38].




Fig. 6.12. Crystal structure and magnetic properties of [MnII (bipy)(N3 )2 ]n [40, 41]. The ex-
perimental data are shown as circles and the simulations by Monte Carlo method and Drillon’s
law as solid and dashed lines, respectively [38].

that this kind of bridge leads to antiferromagnetic interactions. However, a µ-1,1-
azido bridging ligand is also present in the [MnII (bipy)(N3 )2 ]n compound; so, a
ferromagnetic interaction is expected in this case (Figure 6.12) [40, 41].
   The experimental data were simulated by the CSMC method and Drillon’s law,
and a good agreement is found between both methods and the experimental data
(Table 6.3).
   The compound [Mn(Menic)(N3 )2 ]n (Menic = methylisonicotinate) represents a
more complex alternating 1D system. In this chain, a 1:4 ratio for the µ-1,3- and µ-
1,1-azido bridging ligands connecting the manganese(II) ions is found (Figure 6.13)
[42]. Nevertheless, a more complicated interaction topology than J2 J2 J2 J2 J1 is
observed for this compound. In this way, as there are two different MnNazido Mn
bond angle (α) values for the [Mn2 (µ-1,1-azido)2 ] entities (101.1o and 100.6o ,
Figure 6.13), a J2 J3 J3 J2 J1 interaction topology must be considered.
   In a recent paper, Drillon et al. conclude that several alternating ferro-
antiferromagnetic homometallic one-dimensional systems present similar mag-
netic behavior to that of the ferrimagnetic chains [43], which are described by
                                                              6.4 Alternating Chains        205

Table 6.3. Best parameters obtained by fitting a theoretical model to the experimental data
for [MnII (2-pyOH)2 (N3 )2 ]n and [MnII (bipy)(N3 )2 ]n . The fits have been performed using the
CSMC method and Drillon’s law [38–41].

       Compound             Method       g     J1 /cm−1    J2 /cm−1

[MnII (2-pyOH)2 (N3 )2 ]n    MC         2.04    −13.2       −12.3
                            Drillon     2.03    −13.8       −11.7
  MnII (bipy)(N3 )2 ]n       MC         1.98    −12.9       +4.9
                            Drillon     1.99    −12.9       +5.0

Kahn as systems that contain two different near-neighbour spin moments antifer-
romagnetically coupled [15].
   [Mn(Menic)(N3 )2 ]n constitutes a beautiful example of these systems. Thus, its
χ T versus T experimental curve presents a minimum. Moreover, a maximum is also
observed at lower temperature, which is characteristic of this particular interaction
topology. Only the J2 J3 J3 J2 J1 model provides a correct description of the magnetic
behavior, even at low temperatures (Figure 6.13). A good fit is obtained with the
set of parameters J1 = −15.6 cm−1 , J2 = 1.06 cm−1 and J3 = 1.56 cm−1 . These
results agree perfectly with those obtained from a proposed exact analytical law
[42]. As is known, the J parameter and the α angle are related. Thus, the J2 and J3
values are in agreement with the theoretical magneto-structural correlation found by
Ruiz et al. [44], supporting the consideration that two different exchange coupling
constants for the [Mn2 (µ-1,1-azido)2 ] entities has a physical meaning and is not
the result of a mathematical artifact.



         J2    J3    J3     J2     J1




        100.6o 101.1o


Fig. 6.13. Crystal structure and magnetic properties of [Mn(Menic)(N3 )2 ]n . The experimental
data are shown as circles and the simulations by Monte Carlo method and the exact analytical
law proposed by us as solid and dashed lines, respectively. The interaction topology is shown
in the picture of the crystal structure [42].

   The presence of a minimum and a maximum in the χM T versus T curve, can be
explained by considering instant spin configurations at several temperatures pro-
vided by the MC simulation process (Figure 6.14) [42]. In this way, the stronger
antiferromagnetic coupling promotes an antiparallel spin configuration and the
206      6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties




Fig. 6.14. Thermal variation of the spin configuration for an alternating J2 J3 J3 J2 J1 interaction
topology. The antiferro- and ferromagnetic interactions are represented by bold and dashed
lines, respectively.

χM T product decreases on cooling. At lower temperatures, in spite of the weak
character of the ferromagnetic interactions, as they are present in a greater propor-
tion (4:1), the ferromagnetic alignment of the resulting spins becomes efficient.
Finally, the strongest antiferromagnetic interaction dominates the magnetic behav-
ior, and χM T increases to reach a maximum then further decreases attaining a zero
value at 0 K.



6.5 Finite Systems

In a system where the local spin moments have an infinite value (Si = ∞) the
number of microstates (Sz values) is infinite, as in a classical spin approach where
the spin vector can be placed along infinite directions. Thus, the classical spin
approach is less correct when the value of the local spin moment decreases, since
the quantum effects become non-negligible. We have verified previously that the
classical spin approach can be used to analyse the magnetic behavior of periodic
systems. In a real non-periodic system the number of states is limited, especially
for small systems with a few paramagnetic centers, and the energy spectrum is
far from being a continuum, so the mentioned quantum effects could be more
important in these systems. The question is whether the magnetic behavior of these
non-periodic systems can be reproduced by MC simulation within the framework
of the classical spin approach. In other words, does the applicability of the classical
spin approach depend only on the values of the local spin moments or does the size
of the network have some influence? Moreover, is it possible to simulate a discrete
                                                                              6.5 Finite Systems       207

                    (a)                                                        (b)
                      J                                       0.500
1
                                                                                                   1
                                                                                                   2




                                             |J| / cm mol K
                                                              0.400                                3




                                            -1
               J




                                            3
2
                                                              0.300



         J
3                                                             0.200
                                                                      0   3      6         9   12       15
                                                                                     T/J

Fig. 6.15. A comparison between the theoretical χ|J | versus T /|J | plots simulated from the
exact quantum solution (symbols) and Monte Carlo methods (lines) for a series of small linear
models.


spectrum from a continuous energy spectrum? For any system at low temperatures
or for very small systems this task can be especially difficult since there are few
populated states. In this section, the limits where the classical spin approach can be
applied will be established. Thus, from the study of some systems where an exact
quantum solution is available (Figure 6.15), it is possible to check the validity of
the classical spin approach. In Figure 6.15, the curves for several linear systems
obtained by CSMC simulation are compared to those calculated from an exact
quantum method. The classical spin approach is not valid at low T /|J | values, due
to the small number of populated states, which can be considered as a quantum
effect. Also, from Figure 6.15 it can be concluded that the higher the number
of paramagnetic centers, the lower the quantum effect. Thus, for any system at
T /|J | > 4, the classical approach can be applied, and it is valid for a wider
range of T /|J | as the number of paramagnetic centers increases. So, for more
extended systems where the exact numerical solutions cannot be calculated, the
MC simulation in a classical spin approach will be a powerful tool to study their
magnetic behavior.
   The same comparison between MC simulations and exact quantum numerical
solutions has been made for spin topologies presenting more than one coupling
constant. Two examples are shown in Figures 6.16 and 6.17, where only interac-
tions of antiferromagnetic nature are present. χT versus T /|J | curves have been
simulated for different J /J values. MC simulations are valid for T /|J | values
higher than 1.5, for J > J , and similar conclusions as above are reached.
   Moreover, several real complexes have been studied by a CSMC method. As
an example, in Figure 6.18, two interesting clusters containing ten and eighteen
iron(III) ions respectively, with a ring structure, named ferric wheels, are shown
[45, 46]. From the magnetic point of view, these clusters are beautiful examples
of systems that can be used as models for the interpretation of the magnetic prop-
208       6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties

                                                 5.000


                                                 4.000




                                  T / cm mol K
                               -1
                                                 3.000
          J




                               3
               J'
                                                 2.000

                                                                                 0.0    0.6
                                                 1.000
                                                                                 0.2    0.8
                                                                                 0.4    1.0
                                                 0.000
                                                         0       5    10           15          20
                                                                     T/J

Fig. 6.16. A comparison between the theoretical χT versus T /|J | plots as a function of the
J /J ratio (α) for the model shown in the picture. The plots have been simulated by exact
quantum solution (symbols) and Monte Carlo methods (lines).

                                             8.000



                                             6.000                         0.0   0.6
                                                                           0.2   0.8
                            T / cm mol K




      J
                            -1




                                                                           0.4   1.0
                                             4.000
                            3




          J'                                 2.000



                                             0.000
                                                     0       5       10           15          20
                                                                     T/J


Fig. 6.17. A comparison between the theoretical χT versus T /|J | plots as a function of the
J /J ratio (α) for the model shown in the picture. The plots have been simulated by exact
quantum solution (symbols) and Monte Carlo methods (lines).

erties of linear chains. (versus T plots have been simulated by a CSMC method,
considering magnetic interactions only between nearest neighbours. The obtained
values of the coupling constants agree perfectly with those obtained by an exact
analytical classical spin law for 1D systems.



6.6 Exact Laws versus MC Simulations

In previous sections, it has been shown that the MC method is a high-performance
tool to simulate the magnetic behavior of many different systems. Notwithstanding,
in some cases exact classical spin (ECS) laws are also available, so experimental
data can more easily be processed. Thus, the question arises as to whether to use a
                                           6.6 Exact Laws versus MC Simulations         209



(a)

                                                                         g = 1.98
                                                                         J = -9.8 cm-1




(b)



                 …J1 J1 J2…
                                                        g = 1.985
                                                        J1 = -19.1 cm-1
                                                        J2 = -8.0 cm-1



Fig. 6.18. Crystal structure, experimental (circles) and MC simulated (lines) magnetic prop-
erties of: (a) [Fe(OCH3 )2 (O2 CCH2 Cl)]10 and (b) [Fe(OH)(XDK)Fe2 (OCH3 )4 (O2 CCH3 )2 ]6
(where XDK is the anion of m-xylylenediamine bis(Kemp’s triacid imide)) [45, 46].

MC method when an analytical law can be applied. At the moment, there are already
ECS laws for several 2D networks. It is very important to understand how these
laws are elucidated and what are their applicability limits and this is the subject of
the present section. First, a method to obtain an ECS law for a 1D system, that is
the Fisher’s law [20], is described.


6.6.1    A Method to Obtain an ECS Law for a Regular 1D System:
         Fisher’s Law

The evaluation of any physical property at a precise temperature requires the so-
lution of two integrals (Eq. (6.1)): (a) the value of this property as the sum of the
contributions from each of the possible states, and (b) the normalization factor, that
210       6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties




                                θι




                                                  Fig. 6.19. Illustration of the angle between two coupled
 i                        i+1                     vectors.

is given by the partition function (ZN ). Considering the spin moments as vectors,
the energy of any configuration is given by Eq. (6.14), where θij is the angle be-
tween two coupled vectors. In the case of a regular chain, the partition function
can be described as
            N         π
                          1
     ZN =                   sin θi e(x cos θi ) dθi                                                (6.20)
            i=1   0       2
x being equal to −J S(S + 1)/T . It must be pointed out that there is a term, sin θ,
that takes into account the different arrangements that can be generated at a constant
angle θ, that is, from a precession of the second vector referred to the direction of
the first one, see Figure 6.19.
   The next equation is found from solving this integral
                             N
             sinh(x)
     ZN =                                                                                          (6.21)
                x
The magnetic susceptibility in zero field can be calculated from the total spin pair
correlation function, which can be defined as the sum of the individual spin pair
correlation functions:
                            N        N
             g2 β 2
     χ=                                       z
                                         siz sj                                                    (6.22)
            (4kT )         i=0 j =0

   These functions, that provide the average arrangement of all spin moments
referred to one of them, can be evaluated in a similar way to the partition function.
Defining a pair correlation function by
                   3 z z
      si · si+1 =     s s                                                                          (6.23)
                  ZN i i+1
     In a 1D system the integrals may be factorised as before.
                                     π
                          1
     u = si · si+1 =        cos θi sin θi e(x cos θi ) dθi                     (6.24)
                       0  2
   This factorisation involves an independent character for the spin pair correlation
function concerning only two near-neighbour centers. However, this is not the case
                                        6.6 Exact Laws versus MC Simulations      211

for topologies other than a chain where this methodology cannot be so easily
applied. In this way, Langevin’s function is obtained, which describes how one
spin moment is placed with respect to its neighbours.
                    1
   u = coth(x) −                                                               (6.25)
                    x
Obviously, the spin correlation function of vector i with itself is unity. On the
contrary, the neighbouring vector i + 1 is correlated to vector i by Langevin’s
function (u). On the other hand, the neighbouring vector i + 2 is correlated to i
through vector i +1. Thus, the spin pair correlation function of vectors i +2 and i is
u2 . From the summation in Eq. (6.22) and considering the obtained individual spin
pair correlations, the series shown in Eq. (6.26) is constructed. The factor 2 that
appears in some of the terms of the equation comes from the fact that an infinite
chain grows in the two directions of the chain axis. By expanding the summation
over integer n values, the wellknown Fisher’s law is obtained (Eq. (6.27).
                                                                     ∞
   χ T = χ Tfree–ion (1 + 2u + 2u2 + 2u3 + . . .) = χTfree–ion 1 +         2un (6.26)
                                                                     n=1
                       1+u
   χ T = χ Tfree–ion                                                           (6.27)
                       1−u



6.6.2   Small Molecules

The simplest case that can be studied is a system with only two paramagnetic
centers. Following the methodology detailed in the preceding section, the next
ECS law can be deduced
   χ T = χ Tfree–ion (1 + u)                                                   (6.28)
The χ |J | versus T /|J | plots obtained from Eq. (6.28), from a CSMC simulation
and from the exact quantum solution are shown in Figure 6.20. A good agreement
between the three methods is found, and some discrepancies appear only at low
values of T /|J |. The MC method gives a better result than the ECS law for this
T /|J | region, since an approach has been made in the calculation of the partition
function.
    In this same way, several comparisons between the three methods have been
made for a series of similar models, and it can be concluded that there is a good
agreement amongst them. Nevertheless, there is no such agreement in systems
where the interaction topology presents closed cycles, as those shown in Fig-
ure 6.21. In some of these cases where the exact quantum solution is available,
it has been observed that ECS laws do not simulate the magnetic behavior of the
system properly. In the simplest case, that is, a triangle, vector 1 is correlated to
212                    6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties

                 0.6
                                                               Quantum result
                 0.5                                           ECS law
|J| / cm mol K



                                                               CSMC
-1




                 0.5
3




                 0.4


                 0.4


                 0.3
                       0              2      4         6          8             10
                                                 T/J
Fig. 6.20. Theoretical χ |J | versus T /|J | plots obtained by exact quantum solution, exact
classical law and CSMC simulation.

vector 3 either through the left or the right-hand ways, increasing the number of
correlation paths. Also, vector 1 can be correlated to itself through a correlation path
that involves a whole turn. This turn can be made clockwise or counter-clockwise,
but both paths are equivalent, so it must be considered only once in the ECS law,
as shown in the next equation.

            χ T = χ Tfree–ion (1 + 2u + 2u3 + u3 )                                       (6.29)

Notwithstanding, as vector 1 is correlated to itself through all other vectors, it is not
possible to split the spin correlation function in their individual spin pair correlation
functions. Thus, this methodology is not useful in these systems, and the derivation
of an ECS law is a hard and difficult task.


                           Series 1                              Series 2




Fig. 6.21. Systems where the interaction topology presents closed cycles.
                                                  6.6 Exact Laws versus MC Simulations                       213

a)                                                      b)
                                                                       20.0

             5.0                                                       18.0

                                                                       16.0
(T / J)lim




                                                          (T / J)lim
             4.0                                                       14.0

                                                                       12.0

             3.0                                                       10.0

                                                                        8.0
                   3    4    5        6   7   8                               2   3   4      5       6   7     8
                             Cycle size                                               Number of cycles


Fig. 6.22. The limit value of T /J for perfect agreement between the exact classical and
quantum solutions increasing: (a) the cycle size and (b) the number of cycles (see Series 1 and
2 in Figure 6.21). The condition to control the quality of the agreement is stricter in case (b)
than in case (a) in order to facilitate the analysis of the results.

    A study has been performed on the series of topologies shown in Figure 6.21.
From a comparison of the results of the ECS laws with those from MC simulations
it can be deduced that, by decreasing the number of triangular cycles (Series 2)
or increasing the size of the cycle (Series 1), the validity range of the ECS laws
increases and, consequently, the T /|J | threshold decreases (Figure 6.22). In the
first case, this effect is due to a decrease in the number of correlation paths involving
one or more closed cycles. In the second case, when the cycle size increases, the
value of the spin correlation function involving a closed cycle path becomes lower.
Therefore, this kind of correlation path is negligible in an infinite size ring, as a
result again obtaining Fisher’s law.


6.6.3                  Extended Systems

Two analytical laws have been derived to date for a 2D network. These ECS laws
                           e
have been deduced by Cur´ ly et al. for alternating square and honeycomb networks
[47–50], where there is only one magnetic interaction along a chain and a differ-
ent interchain interaction (Figure 6.23). From these equations, ECS laws can be
obtained for the corresponding regular networks. In this way, it could be expected
that more complex topologies or 3D networks could be solved, and that it would
not be necessary to use MC methods to simulate their magnetic behavior. On the
other hand, MC methods allow one to consider as many coupling constants and
g-factors as desired for any system, but this is not the only reason for continuing
to use MC methods.
                             e
   From an analysis of Cur´ ly’s law for an alternating 2D square network it can
be observed that the spin correlation function is, surprisingly, the product of the
one-dimensional spin correlation functions along each spatial direction [50, 51]. In
this topology, when ferromagnetic and antiferromagnetic interactions are present it
214        6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties

                                                  J
            J
                                            J'
      J'




                2d square                          2d honeycomb

Fig. 6.23. Alternating square and honeycomb networks.


is expected that χ T will reach a zero value at 0 K, whatever the magnitude of these
                                            e
two interactions. Nevertheless, from Cur´ ly’s law, in the case of a ferromagnetic
interaction stronger than the antiferromagnetic one, the χT product diverges on
cooling, and when both interactions are of the same magnitude, χT versus T
follows Curie’s law, that is, the system, surprisingly, behaves as if the spin moments
do not interact at all. Moreover, the coefficients of the high temperature expansion
         e
for Cur´ ly’s law do not agree with those obtained by Camp et al. or Lines [30,
33, 51]. These remarks, as some that will be made later, can also be extended
to Cur´ ly’s law for 2D honeycomb networks. Thus, for instance, [Mn(ox)2 (bpm)]n
       e
presents an alternating honeycomb network, where the oxalate (ox) bridging ligand
acts as an exchange pathway along one of the directions and the bipyrimidine (bpm)
ligand connects the chains (Figure 6.24) [52]. Excellent fits of the model to the
experimental data for this compound have been obtained both from MC simulations
and from Cur´ ly’s law [28, 49]. However, the J constant values obtained from MC
               e




Fig. 6.24. Crystal structure and magnetic properties of [Mn(ox)2 (bpm)]n [52]. The experi-
mental data (circles) and the simulations by Monte Carlo methods (solid line) are shown.
                                                6.6 Exact Laws versus MC Simulations           215

simulations agree much better with those found in dinuclear and one-dimensional
systems with oxalate or bipyrimidine as bridging ligands [28, 52].
   A more detailed analysis of the elucidation of an ECS law for a regular 2D
square network will allow one to find the limitations of this methodology. Thus,
as in this kind of network all paramagnetic centers are equivalent, only the total
spin correlation function referred to one spin moment must be evaluated. As has
been previously said, correlation of spin moment A to itself is 1, correlation of spin
moment B to A is given by the Langevin’s function (u), and correlation of spin
moment C to A is u3 (Figure 6.25). In this way, the summation in Eq. (6.30) is
                                           e
generated, and its resolution leads to Cur´ ly’s law.
                                                                
                                 ∞                  ∞            ∞    ∞
   χ T = χ Tfree–ion 1 + 2            ui + 2           uj + 4              ui+j 
                                 i=1            j =1             i=1 j =1
                                  2
                       1+u
       = χ Tfree–ion                                                                        (6.30)
                       1−u
   Notwithstanding, three short correlation paths exist between the A and C spin
moments (1, 2 and 3), so the u3 term must be computed three times. An analytical
law can easily be deduced from the summation generated by computing all these
paths (even for the alternating case), but an infinite number of correlation paths
such as 4 and 5, and a finite number such as 6, have been omitted from this rea-
soning. These longer correlation pathways are not so important for a wide range of
T /|J | values, but they are numerous and the contribution from all of them can be
significant and must not be disregarded. Therefore, the calculation of ECS laws for
more than 1D becomes impossible. In Table 6.4, the number of different spin cor-


           B
                             4
                                       C
       A
                   2

       1
                                 A
               C
                         5                      C

                                  C             6

                                           A
                                           3

                                                C
                                                             Fig. 6.25. Illustration of correlation
                                                             paths to spin moments.
216                          6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties

Table 6.4. Number of individual spin correlation paths (λ) as a function of the correlation path
length (n) in a 2D square network, obtained by SPPA method.

n                    λ           n         λ             n                     λ
0                1               8      6674             16       22155058
1                4               9     18600             17       60555564
2               12               10     51480            28       165126324
3               36               11    142412            29       450294176
4              104               12    391956            20      1225587036
5              300               13   1078612
6              848               14   2956928
7             2392               15   8105796


(a)                                                                                        (b)
                     0.250                                                                                    0.300
                                                              SPPA         =4 and 5                                                      SPPA         =4 and 5
                                                                     max                                                                        max
                                                              SPPA     =10 and 11                                                        SPPA         =10 and 11
                                                                     max                                                                        max
                     0.200                                    SPPA     =14 and 15                             0.250                      SPPA     =14 and 15
                                                                     max                     J| / cm3mol-1K                                     max
    |J| / cm mol K




                                                              SPPA         =18 and 19                                                    SPPA         =18 and 19
    -1




                                                                     max                                                                        max

                                                              CSMC                                                                       SPPA     =24 and 25
                                                                                                                                                max
    3




                     0.150                                                                                    0.200                      CSMC



                     0.100                                                                                    0.150



                     0.050                                                                                    0.100
                                                                                                                      5   10     15             20                 25
                             5        10        15               20                   25
                                                                                                                               T / |J|
                                               T / |J|


Fig. 6.26. χ |J | versus T /|J | plots as a function of the length of the spin correlation path for
two antiferromagnetic regular 2D networks: (a) square and (b) honeycomb. The results are
compared with the CSMC simulation (dots).

relation paths as a function of the correlation path length is shown. In Figure 6.26,
simulated χ|J | versus T /|J | curves are shown where the number of spin correla-
tion paths considered is limited by a prefixed maximum length of these paths (spin
path progressive addition method, SPPA).
   These curves show better agreement with the MC simulation as this maximum
length increases, so in the infinite limit complete agreement is expected. However,
many of these spin correlation paths involve one or several loops. Thus, as has
been previously shown, these loops do not allow the factorisation of the partition
function and the total spin correlation function cannot be developed in individ-
ual contributions, which invalidates this methodology [51]. Nevertheless, as these
closed paths become relevant only at low T /|J | values, then the simulated curves
reach the best agreement with the MC simulation at T /|J | > 8.7 K. The threshold
T /|J | value for the applicability of the SPPA method is higher in a honeycomb
(6.6 K) than in a square networks, because the number of closed paths is lower
for a prefixed correlation path length in the first case. In Table 6.5, the temper-
                          e
ature expansion for Cur´ ly’s law and for results obtained by SPPA, CSMC and
                                                     6.7 Some Complex Examples       217

Table 6.5. Coefficients of the temperature expansion series for 2D square and 2D honeycomb
networks obtained by Curely’s law and by SPPA, CSMC and HTE methods [13, 30, 31, 49, 50].

n   Curely’s Law     SPPA       CSMC         HTE

                      Square 2D
0     1.00000      1.00000     1.00000    1.00000
1     2.66667      2.66667     2.65737    2.66667
2     3.55555      5.33333     5.22918    5.33333
3     2.84444      9.95556     9.59006    9.95556
4     1.26420      17.69877 16.81410      16.90864
5     0.06020      31.24374 29.8237       27.24044
6     0.28896      53.99729 52.41480      42.21216
                   Honeycomb 2D
0     1.00000      1.00000   1.00000       1.00000
1     2.00000      2.00000   1.99966       2.00000
2     1.77778      2.66667   2.65477       2.66667
3     0.94815      3.02222   2.98714       3.02222
4     0.63210      3.31852   3.20519       3.31852
5     0.46655      3.67972   3.41378       3.67972
6     0.14448      3.83925   3.56714       3.57587


HTE methods are compared. In the CSMC method, the coefficients are obtained
from empirical laws presenting maximum terms β 25 and β 27 for the square and
honeycomb networks, respectively. These empirical laws are obtained from a fit
of the MC simulation data (see Section 6.3), which entails some uncertainties that
lead to very small discrepancies in the first coefficients of the expansion series
(see Table 6.5). A good agreement is obtained between the SPPA, CSMC and HTE
                      e
methods, whereas Cur´ ly’s law is certainly not efficient at describing the magnetic
behavior of 2D systems. The SPPA method diverges from the CSMC and the HTE
methods when the path length is long enough to consider loop diagrams. Differ-
ences found between CSMC and HTE methods are due to the limitations of this
last method at low T /|J | values.



6.7 Some Complex Examples

The first example is a one-dimensional system with the formula
[{N(CH3 )4 }n ][Mn2 (N3 )5 (H2 O)}n ], which, from a magnetic point of view,
can be considered as a chain where there are magnetic couplings between near and
second neighbours (Figure 6.27) [53]. The interaction topology of this system has
been simplified by considering only two different exchange coupling constants. A
218     6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties




Fig. 6.27. Crystal structure and magnetic properties of [{N(CH3 )4 }n ][Mn2 (N3 )5 (H2 O)}n ]
[53]. The experimental data (circles) and the simulations by Monte Carlo methods (solid line)
are shown.

good agreement between the experimental and simulated data is obtained using
two different sets of parameters: g = 2.001, J1 = 1.57 cm−1 and J2 = 0.29 cm−1
or g = 2.007, J1 = 0.66 cm−1 and J2 = 1.07 cm−1 . However, a careful analysis
of the structure (angles, bond lengths), as already done in Section 6.4, does not
reveal the set of parameters with the best physical meaning. Furthermore, the
determination of ferromagnetic interactions is always fairly inaccurate and the
use of a simplified interaction topology does not permit unambiguous assignment
[53].
   Compound Csn [{Mn(N3 )3 }n ] is a 3D solid where three different magnetic inter-
actions occur (Figure 6.28) [53]. Regarding the interaction topology, this system can
be described as a stacking of alternating honeycomb planes. The magnetic behav-
ior has been simulated using the set of parameters: g = 2.029, J1 = 0.76 cm−1 ,
J2 = −4.3 cm−1 and J3 = −3.3 cm−1 . The J values found for the interaction
through a µ-1,1- or µ-1,3-azido bridge are similar to those found in simpler systems
[42, 53]. As in a previous example, the values of the J constants are corroborated by
the theoretical magneto-structural correlation performed by Ruiz et al. from DFT
calculations [44].




Fig. 6.28. Crystal structure and magnetic properties of Csn [{Mn(N3 )3 }n ] [53]. The experi-
mental data (circles) and the simulations by Monte Carlo methods (solid line) are shown.
                                                                                     6.7 Some Complex Examples                                             219


                                                                                                                                      64
                                                                     60




                                                                                                                             T
                                                                                                                                      62
                                                                                                                                                  (a)




                                                                                                                                  M
                                                      -1
                            J1




                                                      T / cm K mol
                                 J2
                                                                     50                          55                                   60
                                      J3




                                                                                         T
                                                      3
                                                                                                 40                                         0      30      60




                                                                                            M
                                                                                                               (b)                                 T/K
                                                                     40                          25




                                                               M
                                                                                                      0                    1400
                                                                                                               T/K
                                                                     30
                                                                                     0                          100                        200              300
                                                                                                                           T/K

Fig. 6.29. Crystal structure, interaction topology and magnetic properties of
[Fe10 Na2 (O)6 (OH)4 (O2 CPh)10 (chp)6 (H2 O)2 (MeCO)2 ] [54]. The experimental data
(circles) and the simulations by Monte Carlo methods (solid line) are shown.

    Compound [Fe10 Na2 (O)6 (OH)4 (O2 CPh)10 (chp)6 (H2 O)2 (MeCO)2 ] (chp = 6-
chloro-2-pyridonato) is an example of a high-nuclearity molecule (Figure 6.29)
[54]. This system is too big to be studied considering quantum spin moments, but
the CSMC method allows one to accurately simulate its magnetic behavior using
the coupling constant values: g = 2.0, J1 = −44 cm−1 , J2 = −13 cm−1 and
J3 = −10 cm−1 . Cano et al. rationalize the values of the the four coupling con-
stants taking into account the different bridging ligands, structural parameters and
some other data found in the literature. They conclude that the values found for the
four constants have a physical meaning.
    Compound {[(tacn)6 Fe8 (µ3 -O)2 (µ2 -OH)12 ]Br7 (H2 O)}Br·H2 O (tacn = 1,4,7-
triazacyclononane) is one of a few examples of a single molecule magnet (Fig-
ure 6.30) [12, 55–57]. There are many interesting potential applications of these
systems. Although the study of the magnetic behavior of these systems is very
important, in some cases it is not yet possible to perform. This system is situated
at the limit where exact quantum solutions can be found. The simulated and ex-
perimental χ T versus T curves are shown in Figure 6.30. The theoretical curves


                                                                                     50.0
                                                                                                                                      CSMC simulation
                                                 J4
                                                                     T / cm3mol-1K




                                                                                                                                      Quantum result
                                      J3   J2                                        40.0
                                                                                                                             O         Experimetnal data
                                            J1
                                                                                     30.0



                                                                                     20.0


                                                                                             0            50         100      150           200     250     300
                                                                                                                             T/K

Fig. 6.30. Crystal structure, interaction topology and magnetic properties of {[(tacn)6 Fe8 (µ3 -
O)2 (µ2 -OH)12 ]Br7 (H2 O)}Br·H2 O [12, 55–57]. The experimental data (circles), the CSMC
simulation (solid line) and quantum solution (dashed line) are shown.
220       6 Monte Carlo Simulation: A Tool to Analyse Magnetic Properties

have been obtained from the exact quantum solutions and from the CSMC method
using, in both cases, the same parameter values. In the CSMC simulation, in or-
der to better describe the magnetic behavior at very low temperatures, an extra
parameter (θ) has been added to consider the magnetic intermolecular interaction
(g = 2.0, J1 = −20 cm−1 , J2 = −120 cm−1 , J3 = −15 cm−1 , J4 = −35 cm−1
and θ = −2.2 cm−1 ).



6.8 Conclusions and Future Prospects

In this chapter it has been established that the classical spin approach allows proper
analysis of the magnetic behavior of systems with high local spin moments (S ≥ 2).
Nevertheless, this approach cannot easily be applied to a great variety of systems. In
these cases, it is possible to accomplish this objective using Monte Carlo methods,
which appears as a powerful tool in numerical integration to evaluate physical
properties. Thus, the Monte Carlo methods applied to a classical spin Heisenberg
model (CSMC) are able to study any system, whatever its complexity, and the
only limitation of this method is due to the classical spin approach. Unfortunately,
the simple CSMC method cannot be applied to systems that present small local
spin moments (S < 2). For such cases, it is possible to use alternative methods
although they are far more complicated. Among these methods are the Density
Matrix Renormalization Group and Quantum Monte Carlo. However, this is another
story, too long to be told in detail, and beyond the scope of the present chapter.



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7 Metallocene-based Magnets
     Gordon T. Yee and Joel S. Miller




7.1 Introduction

A wide variety of magnetically ordered solids derived from organic and
organometallic building blocks have been characterized in the past few years [1, 2]
These reports of bulk ferro-, ferri-, and antiferromagnetism follow those of super-
conductivity in organic solids [3] and extend the types of cooperative phenomena
observed in molecule-based materials. The great strength of this class of com-
pounds is that modification of their physical properties via conventional synthetic
organic and inorganic methods may lead to future generations of molecule-based
electronic devices including so-called ‘smart’ materials and systems [4]. The best
examples of this concept include the organic light emitting diode flat panel displays,
organic photoconductors and liquid crystal displays.
   One attractive approach to the generation of new magnetically interesting
phases is the synthesis of electron transfer (ET) salts with a general formula of
[donor]+ [acceptor]− , abbreviated D+ A− .1 This strategy has produced not only
isolated examples of magnets but families of structurally and electronically related
compounds from which systematic relationships are being deduced. An important
feature of this class of compounds is that the spin coupling between the build-
ing blocks is thought to be exclusively “through-space” as there are no covalent
bonds between D+ and A− . Also, the large anisotropy in these solids permits the
separate treatment of the relatively strong intrachain interactions and the weaker
interchain coupling. Understanding the mechanism of through-space interactions is
one of the most challenging problems in this field, and all but the three-dimensional
coordination polymers probably require some degree of this type of coupling to
achieve magnetic order, because magnetic ordering cannot occur for a 1D system
[5].
   In the role of the donor, decamethylmetallocenes, MCp*2 , where Cp* = de-
camethylcyclopentadienyl and M = principally Cr, Mn and Fe (Scheme 7.1) are
unsurpassed. The reasons for this are manifold and not altogether understood, but

 1 Also called “charge-transfer salts” in the literature.
224     7 Metallocene-based Magnets




      Fe


                   Scheme 7.1 Decamethylferrocene, FeCp*2 .


certainly include the electrochemical reversibility of their 0/+1 couples, their ten-
dency to π stack and the fact that their monocations all possess at least one unpaired
electron. They are also commercially available, which has facilitated their explo-
ration as a building block. The acceptor is generally an organic molecule with an
extended π system, substituted with electron withdrawing groups, especially ni-
triles and likewise is typically commercially available. However, in recent years,
much of the progress has been in synthesizing additional acceptors.
    This chapter summarizes the magnetic properties of the known ET salts based
on decamethylmetallocenium cations and related species paired with paramagnetic
anions. Electrochemical and magnetic properties of the neutral metallocenes are
summarized to introduce the subject. This is followed by families of ET salts
grouped according to the acceptor with olefinic acceptors treated first, quinone-
based acceptors second, and metal complex acceptors third. Magnetostructure–
property correlations will be discussed and the current state of theoretical models
will be considered. The chapter concludes with a brief examination of the research
opportunities that exist in this field. One group of paramagnetic acceptor anions,
namely, metal dithiolate complexes, will not be extensively reviewed herein as they
are the subject of Chapter 1.




7.2 Electrochemical and Magnetic Properties of Neutral
    Decamethylmetallocenes and Decamethylmetallocenium
    Cations Paired with Diamagnetic Anions

Metallocenes, MCp2 , where M is a first row transition metal in the 2+ oxidation
state and Cp is cyclopentadienide, and to an even greater extent, decamethylmet-
allocenes, MCp*2 , where Cp* is pentamethylcyclopentadienide, can be easily and
reversibly oxidized [6] (Figure 7.1) making them suitable as donors for electron
transfer salts. In general, the substitution of each H with Me on the periphery of the
Cp ring shifts the one-electron reduction potential more negative by about 0.05 V.
Except for ferrocenes, all the neutral donors shown in Figure 7.1 are easily oxidized
in the air, and Schlenk apparatus and/or glove box methods need to be rigorously
employed.
 7.2 Electrochemical and Magnetic Properties of Neutral Decamethylmetallocenes                                   225

                 Fe (C5MeH4)2          FeCp* 2
            FeCp2           Fe(C5Me 4H)2                       MnCp* 2     NiCp* 2                CrCp* 2   CoCp* 2




         0.5 V                   0V                            - 0.5 V                       - 1.0 V            - 1.5 V


C4 (CN)6 DClDQ         DCNQ TCNQ/TCNE            DMeDCF

           Me 2DCNQI


Fig. 7.1. Electrochemistry (vs. SCE) of some donors and acceptors (see text for abbreviations).


    The spin states, S, of metallocenium cations are a consequence of unpaired elec-
trons in metal d orbitals split by either the D5h or D5d ligand field.2 Vanadocenes
are 15 electron species and very reactive, hence relatively unexplored. Decamethyl-
cobaltocenium is an 18 electron species and hence diamagnetic. This leaves, as the
most important species, those based on chromium, manganese and iron, for reasons
explained below. Based on the information in Table 7.1, the Land´ g values for
                                                                       e
[MnCp*2 ]+ and [FeCp*2 ]+ are expected to be different from the free electron value
(2.0023), due to an orbital contribution to the magnetic moment. In fact, for M =
Fe(III) the g value is very anisotropic (g > 4; g⊥ ∼ 1.25) [7]. The anisotropic
g values for decamethylmanganocenium have not been determined because the
S = 1 species does not give an EPR signal. However, average g values from pow-
der magnetic measurements have placed it at between 2.2 and 2.4. Anisotropy is
important to the manifestation of hysteresis, a characteristic of some ferromagnets.
It is also the source of some of the variation in the values of magnetic properties of
compounds reported in the literature. For instance, due to anisotropy, two samples


Table 7.1. Electronic Ground State and Spin State (S), for MCp*2 , [MCp2 ]+ , MCp*2 , and
[MCp*2 ]+ .

M                                V          Cr            Mn             Fe          Co       Ni

Ground state, MCp2               4A         3A            6A             1A          2E       3A
                                      2g          2g           1g          1g          1g       2g
S, MCp2                          3/2        1             5/2            0           1/2      1
Ground state, [MCp2 ]+           3E
                                    2g
                                            4A
                                               2g
                                                          3E
                                                             2g
                                                                         2E
                                                                            2g
                                                                                     1A
                                                                                        1g
                                                                                              2E
                                                                                                   1g
S, [MCp2 ]+                      1          3/2           1              1/2         0        1/2
Ground state, MCp*2              4A         3A            2E             1A          2E       3A
                                    2g         2g            2g             1g          1g       2g
S, MCp*2                         3/2        1             1/2            0           1/2      1
Ground state, [MCp*2 ]+          3E
                                    2g
                                            4A
                                               2g
                                                          3E
                                                             2g
                                                                         2E
                                                                            2g
                                                                                     1A
                                                                                        1g
                                                                                              2E
                                                                                                 1g
S, [MCp*2 ]+                     1          3/2           1              1/2         0        1/2


 2 The point group symmetry is D
                                5h when the rings are eclipsed and D5d when they are
    staggered. Both geometries are found.
226     7 Metallocene-based Magnets

of the same compound, nominally randomly oriented, can exhibit different room
temperature values of χ T , if they are not truly random, but partially aligned to
different degrees.




7.3 Preparation of Magnetic Electron Transfer Salts

7.3.1    Electron Transfer Routes

The synthesis of ionic electron transfer salts typically involves the reaction of a
neutral donor capable of reducing a neutral organic acceptor. Fortunately, solution
electrochemistry may be used as a guide to predict reactivity. A distinct advantage
of the electron transfer strategy over other methods of preparing molecule-based
magnets [8] is that, with only this electrochemical constraint, the donor and accep-
tor may be varied independently to produce additional candidate magnets. Further-
more, by-products from this procedure, in general, are minimized. This translates
to the ability to investigate an array of related compounds from each new accep-
tor by pairing it with all available donors with which it is predicted to react. If
                                                  0
a newly synthesized acceptor is weak (i. e. E0/−1          0), it must be paired with a
strong donor to enable the pair to satisfy the electron transfer criterion. As a rule
of thumb, every acceptor on the scale above (Figure 7.1) will react by outer-sphere
electron transfer with every donor located to the right of it to yield an ionic product.
So, although TCNE reacts with both decamethylferrocene, FeCp*2 , and ferrocene,
FeCp2 , to give 1:1 complexes, only the former is a paramagnetic ionic salt at room
temperature.
    One caveat is that the solvent can play a role in the driving force for this reaction
and the structural phase obtained from this method and the metathetical route
described below. In some cases, incorporation of the solvent into the crystal lattice
leads to additional phases. For example, the reaction of FeCp*2 and TCNE in THF
yields [FeCp*2 ][TCNE], whereas in acetonitrile it yields [FeCp*2 ][TCNE]·MeCN.
Furthermore, as is the case with FeCpCp* and TCNE, more complex materials,
i. e. [FeCpCp*]2 [TCNE]3 ·x(solvent) form [9].



7.3.2    Metathetical Routes

An alternative way to synthesize ET salts involves the reaction of the cationic
oxidized donor and a reduced acceptor anion. Careful selection of the counter anion
and counter cation, respectively, allows the tuning of the solubilities and reactivities
of the components to a much greater degree, but at the sacrifice of simplicity. For
                                     7.4 Crystal Structures of Magnetic ET Salts     227

instance, this approach was used in the preparation of [MnCp*2 ][TCNQ] from
solutions of [MnCp*2 ]PF6 and NH4 [TCNQ] [10]. In some cases it is the only route
available if the neutral donor and/or acceptors are not available. This was the case
for the synthesis of the metal bis(dicyanodithiolate)metal-based (M[S2 C2 (CN)2 ]− ,
                                                                                  2
M = Ni, Pd, Pt) family of solids [11].



7.4 Crystal Structures of Magnetic ET Salts

All magnetically ordering electron transfer salts crystallographically characterized
to date have been shown to adopt an alternating · · ·D+ A− D+ A− · · · structure in
the π stacking direction to form 1D chains in the solid state [12a, 13b, d, 14],
Figure 7.2. This arrangement gives rise to the dominant magnetic interaction, which
is intrachain (Jintra ), and usually ferromagnetic for this class of materials.
    The unit cell typically contains four such chains (arranged as two pairs of two
chains, Figure 7.3, top) giving rise to four unique nearest-neighbor pairwise inter-
chain interactions. Within each pair the adjacent chains are in-registry with respect
to each other. The two pairs are out-of-registry with respect to each other. While
some of the various Jinter values might be similar in magnitude, it is important to
note that there is strong evidence that they are not all positive (i. e. not all indicate
ferromagnetic coupling). The effects of the competition between ferromagnetic
and antiferromagnetic coupling are evident in the results presented below in the
type of ordering phenomenon observed.




Fig. 7.2. Segment of the alternating D+ A− D+ A− linear chain structure observed for
[FeCp*2 ][TCNE] · MeCN [12a], and most other magnetic ET salts.
228      7 Metallocene-based Magnets




Fig. 7.3. Packing diagram for β and γ-[FeCp*2 ][TCNQ]. View down the chain axis showing the
inter chain interactions between chains I, II, III, and IV, top, and view parallel to the in-registry
chains I–II, and out-of-registry chains I–III and I–IV for ferromagnetic γ -[FeCp*2 ][TCNQ]
(right hand side) and metamagnetic β-[FeCp*2 ][TCNQ] (left hand side). Other ET salts exhibit
similar structures.
                         7.4 Crystal Structures of Magnetic ET Salts   229




Fig. 7.3. (Continued.)
230     7 Metallocene-based Magnets

7.5 Tetracyanoethylene Salts (Scheme 7.2)


NC       CN



NC       CN    Scheme 7.2 Tetracyanoethylene, TCNE.



7.5.1   Iron

The first electron transfer salt demonstrated to have a ferromagnetic ground state
was decamethylferrocenium tetracyanoethenide, [FeCp*2 ][TCNE] [14]. Single
crystal X-ray studies of [FeCp*2 ][TCNE]·MeCN and [FeCp*2 ][TCNE] have been
reported [14a]. Both pseudopolymorphs are composed of parallel chains of al-
ternating [FeCp*2 ]+ cations and [TCNE]− radical anions as illustrated in Fig-
ure 7.2. Monoclinic [FeCp*2 ][TCNE]·MeCN is a well-determined structure as
it lacks disorder, but does have layers of MeCN solvent separating the parallel
chains along the c-axis. In contrast, the structure of orthorhombic [FeCp*2 ][TCNE]
is not completely resolved due to disorder of the [TCNE]− anions. The intra-
chain Fe· · ·Fe separation is 10.415 Å for [FeCp*2 ][TCNE]·MeCN and 10.621 Å
for [FeCp*2 ][TCNE] [14a]. Nonetheless, due to the lack of solvent the interchain
separations are shorter for [FeCp*2 ][TCNE] than for [FeCp*2 ][TCNE]·MeCN. At-
tempts to determine the structure of the former at low temperature to minimize, if
not eliminate, the disorder in the structure were thwarted by two phase transitions
[14a, 46c] (Figure 7.4) that lead to the destruction of the crystals.
    A variety of physical measurements have confirmed that magnetic order exists
below a critical ordering temperature, Tc , of 4.8 K [14, 15] and its paramagnetic
properties above Tc have also been thoroughly examined. The high temperature
susceptibility of powder samples of [FeCp*2 ][TCNE] fits the Curie–Weiss expres-
sion with θ = +30 K indicating dominant ferromagnetic interactions [14]. The
calculated and observed room temperature susceptibility and saturation magne-




                                             Fig. 7.4. Excess heat capacity, [Cp (T )],
                                             for [FeCp*2 ][TCNE] [41c] Showing two
                                             structural phase transitions occurring be-
                                             low room temperature.
                                         7.5 Tetracyanoethylene Salts (Scheme 7.2)     231

Table 7.2. Summary of magnetic properties of ferromagnetic [FeCp*2 ][TCNE].

Formula                            C26 H30 N4 Fe
Formula mass                       454.4 Da
Structure                          1-D . . .D+ A− D+ A− . . . chains
Solubility                         Conventional organic solvents (e.g. MeCN, CH2 Cl2 , THF)
Critical/Curie temperature         4.8 K
Curie–Weiss Constant, θ            +30 K
Spontaneous magnetization          Yes, in zero applied field
Magnetic susceptibility (290 K)    0.00667 emu mol−1 (observed)
( to 1D chains)                    0.00640 emu mol−1 (calculated)
Magnetic susceptibility (290 K)    0.00180 emu mol−1 (observed)
(⊥ to 1D chains)                   0.00177 emu mol−1 (calculated)
Saturation magnetization (290 K)   16,300 emu-G mol−1 (observed)
( to 1D chains)                    16,700 emu-G mol−1 (calculated)
Saturation magnetization (290 K)   6,000 emu-G mol−1 (observed)
(⊥ to 1D chains)                   8,800 emu-G mol−1 (calculated)
Intrachain exchange interaction    27.4 K (19 cm−1 )
( to 1D chains)
Intrachain exchange interaction    8.1 K (5.6 cm−1 )
(⊥ to 1D chains)
Coercive field, Hcr (2 K)          1000 Oe


tization are in excellent agreement (Table 7.2) [14]. Spontaneous magnetization
is observed for polycrystalline samples below 4.8 K in the Earth’s magnetic field
[14] that is 36% greater than iron metal on a per iron atom basis. Hysteresis loops
characteristic of ferromagnetic materials are observed featuring a coercive field of
1 kOe at 2 K, Figure 7.5, [14]. Preliminary studies of the pressure dependence of




                                       Fig. 7.5. M(H ) for [FeCp*2 ][TCNE] at 2 K.
232     7 Metallocene-based Magnets

Tc reveal that it increases with applied pressure by 0.21 K kbar−1 and reaches 7.8 K
at 14 kbar applied pressure [16].


7.5.2    Manganese

The synthesis of [MnCp*2 ][TCNE] was more challenging because the solid is
not stable at room temperature unless completely dry and kept under an inert
atmosphere. For this reason, it must be synthesized and isolated at −40◦ C utilizing
Schlenk techniques [17]. [MnCp*2 ][TCNE] orders ferromagnetically at 8.8 K and,
although no single crystal structure analysis has been performed, IR (νCN = 2143,
2184 cm−1 ) and powder diffraction have been used to relate it to its iron analog. Like
[FeCp*2 ][TCNE], [MnCp*2 ][TCNE] exhibits hysteresis with a Hcr = 1.2 kOe at
4.2 K. Based on the McConnell model II (vide infra), this compound should also
exhibit ferromagnetic coupling, as is observed (θ = +22.6 K). There is evidence, in
the form of frequency dependent ac susceptibility data, that this compound exhibits
glassiness indicating that the compound is not fully long-range ordered [18].


7.5.3    Chromium

[CrCp*2 ][TCNE] was independently prepared by the groups of Hoffman and
Miller. It was reported to order ferromagnetically at 2.1 [19] and 3.65 K [20],
respectively, but does not exhibit hysteresis above 2 K. This is ascribed to the lack
of anisotropy at the Cr(III) center. The difference in Tc is thought to be due to differ-
ent phases of the material, with only the latter CH2 Cl2 -grown magnet being struc-
turally characterized. This material is not isomorphous to either [FeCp*2 ][TCNE]
or [FeCp*2 ][TCNE]·MeCN [12a], and belongs to the P 21 /n space group. Further-
more, the 2.1 K Tc magnet was made from MeCN and may contain some solvent.
Application of the aforementioned McConnell model II to [CrCp*2 ][TCNE] {and
[CrCp*2 ][TCNQ] (vide infra)} leads to the expectation of antiferromagnetic cou-
pling leading to ferrimagnetic behavior; however, ferromagnetic order, as evidenced
by the value of the saturation magnetization, is observed.


7.5.4    Other Metals

[NiCp*2 ][TCNE] has been prepared from the reaction of NiCp*2 and TCNE. It
exhibits antiferromagnetic coupling with θ = −10 K [21]. The CoIII analog,
[CoCp*2 ][TCNE], with S = 0 [CoCp*2 ]+ has also been prepared and exhibits es-
sentially the Curie susceptibility anticipated for S = 1/2 [TCNE]− (θ = −1.0 K)
[12a]. Attempts to prepare [MnIII Cp*2 ]+ (M = Ru, Os) salts of [TCNE]− have
yet to lead to suitable compounds for comparison with the highly magnetic FeIII
                                         7.5 Tetracyanoethylene Salts (Scheme 7.2)    233

phase [22]. Formation of [RuCp*2 ]+ is complicated by rapid disproportionation
to diamagnetic RuII Cp*2 and diamagnetic [RuIV Cp*(C5 Me4 CH2 )]+ [23]. The Os
analog has led to the preparation of a low susceptibility salt with TCNE; however,
crystals suitable for single crystal X-ray studies [22] have not as yet been isolated,
limiting progress in this area.



7.6 Dimethyl Dicyanofumarate
    and Diethyl Dicyanofumarate Salts

Two olefinic acceptors that are electronically very similar to each other and to
TCNE, dimethyl and diethyl dicyanofumarate (DMeDCF and DEtDCF, respec-
tively), Scheme 7.3, have been investigated. Given the related geometry of these
acceptors, the intrachain interactions in the resulting magnetic salts were theorized
to be similar and thus, any differences in bulk magnetic properties would be due
to modifications in interstack separations only, due to the additional ∼2–3 Å in the
lateral direction from the alcohol portions of the diester.

          O

RO                CN
                            R = Me, Et

     NC                OR

              O                          Scheme 7.3 Dialkyl dicyanofumarate, DRDCF.


   The synthesis of these molecules was previously reported by Ireland and co-
workers [24] who used the oxidative dimerization of commercially available α-
cyanoesters. Mulvaney and co-workers showed that they exhibit reversible one-
electron reductions at approximately −0.22 V vs. SCE [25]. As such, both de-
camethylmanganocene and decamethylchromocene react with each of these accep-
tors to give well-defined 1:1 ET salts, but decamethylferrocene is not sufficiently
reducing to react to give an ionic product.


7.6.1     Manganese

Like their TCNE analog, neither [MnCp*2 ][DMeDCF] nor [MnCp*2 ][DEtDCF] is
stable at room temperature when wet with solvent and so each must be prepared and
isolated at low temperature. Both are synthesized in dichloromethane and appear
as shiny brown-gold needles. Careful attempts to grow large single crystals have
been unsuccessful.
234     7 Metallocene-based Magnets

    The bulk magnetic properties of the DMeDCF salt are reminiscent of the corre-
sponding TCNE salt. Dominant ferromagnetic coupling (θ = +15 K) gives rise to
apparent ferromagnetic order below Tc = 10.5 K, including well-formed rectangu-
lar hysteresis loops with Hcr = 7 kOe at 1.8 K [26]. Ac Susceptibility measurements
on the compound show significant frequency dependence, indicative of glassiness.
The structure of this compound is believed to be isomorphous with its chromium
analog (vide infra) by powder diffraction.
    As expected, θ for [MnCp*2 ][DEtDCF] is also 15 K, consistent with similar in-
trachain coupling (Jintra ) in the π stacking direction [26]. In contrast, however, as the
temperature is decreased, [MnCp*2 ][DEtDCF] undergoes a 3D antiferromagnetic
phase transition at approximately 12 K. The nature of this transition is indicated
by low temperature ac susceptibility and magnetization vs. applied field measure-
ments. At 9 K, this compound is a metamagnet with critical field, Hc = 500 Oe.
Upon further cooling, this compounds appears to undergo a transition to a re-entrant
spin glass state that is accompanied by a large coercive field approaching 10 kOe.
Structure elucidation of the chromium analog suggests that the magnetic data re-
ported for this compound are on a crystallographically disordered solid due to loss
of solvent (vide infra).



7.6.2    Chromium

[CrCp*2 ][DMeDCF] is stable at room temperature in acetonitrile, permitting its
crystallization [27]. It exhibits the usual mixed stack structure (Figure 7.2). Above
50 K, the χ −1 vs. T data can be fitted to the Curie–Weiss law with θ = 23 K.
It also orders as a ferromagnet below 5.7 K, which is higher than its TCNE and
TCNQ analogs. Presumably because of the 4 A ground state of the cation, the com-
pound shows no hysteresis and the saturation magnetization (Msat =∼ 22,000 emu-
G mol−1 ) is the value expected for four unpaired electrons with g = 2. In contrast
to the Mn analog, it does not exhibit frequency-dependent ac susceptibility [27]
and hence, lacks glassy behavior.
   As expected, [CrCp*2 ][DEtDCF] is magnetically similar to its dimethyl analog,
but only up to a point. It exhibits Curie–Weiss behavior with θ = +22 K, again
showing that the intrastack interactions strengths are similar [28]. However, instead
of a ferromagnetic phase transition, there appears to be an antiferromagnetic phase
transition (peak in χ (T )) at 5.4 K, which is identified by a lack of a χ (T ) ac signal.
This suggests that, like its manganese analog, increasing the separation between
the stacks decreases the interchain ferromagnetic coupling, causing a change from
ferromagnetic to antiferromagnetic order.
   Instead of going to zero as the temperature is lowered still further, as expected
for an antiferromagnet, χ (T ) then begins to rise again, suggesting the onset of
some sort of frustration and glassiness. At 1.8 K and 5000 Oe, the magnetization
                   7.7 2,3-Dichloro-5,6-dicyanoquinone Salts and Related Compounds   235

is only ∼70% of its expected saturation value, in marked contrast to the behavior
of the dimethyl analog, which is fully saturated in this field.
   A crystal structure of this latter ET salt as its dichloromethane solvate,
[CrCp*2 ][DEtDCF] ·2CH2 Cl2 , which complicates the above analysis, was reported
recently [28]. That is, although the stacked . . .D+ A− D+ A− . . . motif is retained
as expected, the added methylenes in the acceptor create just enough space be-
tween the stacks for two solvent molecules to flank each donor. These additional
dichloromethane molecules act as spacers, changing the interstack interactions in
ways that are not yet understood. All of the above magnetic data on DEtDCF-based
salts were obtained on desolvated samples, implying that they possess intrinsic
structural disorder. No crystal structures of the desolvated salt have been reported.



7.7 2,3-Dichloro-5,6-dicyanoquinone Salts
    and Related Compounds

The effect of a subtle alteration in the structure on the magnetic properties has been
probed with the study of the isomorphous 2,3-dihalo-5,6-dicyanoquinone (DXDQ;
X = Cl, Br, I, Scheme 7.4)3 electron transfer salts of decamethylferrocene. At
−70◦ C there are minimal differences in their respective solid state structures [16]
and in the observed θ values which range from +10 to +12 K [21, 29] None of these
compounds exhibits ordering above 2 K. As Tc in a mean field model is proportional
to S(S + 1), [MnCp*2 ][DClDQ] was prepared anticipating that Tc might occur at
a higher and thus experimentally more accessible temperature [30]. The magnetic
susceptibility of [MnCp*2 ][DClDQ] can be fitted by the Curie–Weiss expression
with θ = +26.8 K This strong ferromagnetic interaction between adjacent radicals
within each chain coupled with a net weak antiferromagnetic interaction between
the chains leads to metamagnetic behavior below TN = 8.5 K [31]. Below ∼4 K
anomalous behavior with large hysteresis and remanent magnetization is observed
[31]. Similar complex metamagnetic behavior was observed for [MnCp*2 ][DXDQ]
(X = Br, I) at lower temperatures [21].

     X         X



O                    O



    NC         CN        Scheme 7.4 2,3-Dihalo-5,6-dicyanoquinone, DXDQ (X = Cl, Br, I).

 3 Usually DDQ in the literature, but DClDQ here to avoid ambiguity with other halogen-
    substituted acceptors.
236                               7 Metallocene-based Magnets

7.8 2,3-Dicyano-1,4-naphthoquinone Salts

The one-electron acceptor, 2,3-dicyano-1,4-naphthoquinone, DCNQ, Scheme 7.5,
has previously been explored in the context of organic metals [32]. Cyclic
voltammetry indicates that its reduction potential is between that of DDQ and
TCNQ. DCNQ is readily prepared from commercially available 2,3-dichloro-1,4-
naphthoquinone by cyanation with potassium cyanide and acid, followed by oxi-
dation of the resulting naphthohydroquinone with nitric acid [32].

                                    O

                                            CN



                                            CN

                                    O              Scheme 7.5 2,3-Dicyano-1,4-naphthoquinone, DCNQ.




7.8.1                             Iron

DCNQ readily reacts with decamethylferrocene to form an air-stable crystalline
electron-transfer salt that possesses the typical mixed stack architecture with
both in-registry and out-of-registry chains [33]. The magnetic properties of
[FeCp*2 ][DCNQ], Figure 7.6, are characteristic of a metamagnet with Hc of ap-
proximately 3 kOe. The magnetic order is believed to be ferromagnetic within the
chains with both ferromagnetic and antiferromagnetic coupling between the chains.
However, this compound is unusual as in the nominally antiferromagnetically or-
dered state, the moments are canted so that there is a net moment and hysteresis
observed that is centered about zero. Such an organization is known as a weak

                                             10000
Magnetization (emu-G/mol)




                                                 5000


                                                   0
                            -30000 -20000 -10000        0   10000   20000   30000

                                              -5000


                                            -10000                                  Fig. 7.6. M(H ) for
                                            Applied field (Oe)                      [FeCp*2 ][DCNQ] at 1.8 K [33].
                                                                   7.8 2,3-Dicyano-1,4-naphthoquinone Salts    237

ferromagnet or canted antiferromagnet [34]. This phase persists up to 4 K, from
M(T ) measurements, where a transition to a paramagnetic state occurs. Mössbauer
spectroscopy confirms the presence of a magnetic phase transition [33].


7.8.2                                Manganese

The plot of magnetization vs. applied field determined at 1.8 K, Figure 7.7, indi-
cates that [MnCp*2 ][DCNQ], like its iron analog, is also a metamagnet [35]. The
critical field, Hc , at this temperature is also approximately 3 kOe. In the nomi-
nally antiferromagnetically ordered state, the compound exhibits a coercive field
of approximately 1000 Oe and remanence of 500 emu-G mol−1 at 1.8 K. These
data show that, like [FeCp*2 ][DCNQ], the moments in this compound are also
canted slightly, again producing a weak ferromagnet. It is this condition that gives
rise to hysteresis centered at zero and a non-zero out-of-phase component to the
ac susceptibility (χ (T )). At 40 kOe, the magnetization is ∼13,000 emu-G mol−1 ,
approaching the expected value (18,400 emu-G mol−1 , assuming g = 2.3 for the
decamethylmanganocenium cation) consistent with ferromagnetic coupling of the
unpaired electrons. The low value of the saturation magnetization might indicate
canting in the ferromagnet-like state, as well.
   The ac susceptibility data obtained in zero dc bias are also consistent with
weak ferromagnetism. The peak in χ (T ) is accompanied by the onset of a small
non-zero χ (T ) component that is associated with the presence of hysteresis, not
characteristic of an uncanted (collinear) antiferromagnet. The ordered state persists
up to 8 K.
   However, unlike [FeCp*2 ][DCNQ], [MnCp*2 ][DCNQ] exhibits additional hys-
teresis centered near the antiferromagnetic to ferromagnet-like transition. At ±Hc
the sample does not switch back reversibly from ferromagnet-like to antiferromag-
netic order as the field is decreased from a high value toward zero [35].



                                                 15000
Magnetization (emu-G/mol)




                                                 10000

                                                  5000

                                                     0
                            -40000      -20000            0       20000    40000
                                                  -5000

                                                 -10000

                                             -15000                                  Fig. 7.7. M(H ) for
                                             Applied field (Oe)                      [MnCp*2 ][DCNQ] at 1.8 K [35].
238        7 Metallocene-based Magnets

7.8.3      Chromium

The magnetic properties of the chromium analog are consistent with ferromagnetic
coupling (θ = +6 K) within the chain and metamagnetism with a vanishingly small
critical field [35]. A peak in the ac and dc susceptibility at 4 K marks an antifer-
romagnetic phase transition. There is almost no out-of-phase ac signal, consistent
with the result that, unlike the iron and manganese analogs, there is essentially no
hysteresis. This is attributed to the absence of an orbital contribution to the magnetic
moment, and hence a source of anisotropy. The magnetization in an applied field
of 40 kOe is 20,400 emu-G mol−1 , approaching the expected spin-only saturation
value (22,340 emu-G mol−1 ).




7.9 7,7,8,8-Tetracyano-p-quinodimethane Salts

7.9.1      Iron

The reaction of FeCp*2 and TCNQ (TCNQ = 7,7,8,8-tetracyano-p-quino-
dimethane, Scheme 7.6) has been shown to yield three magnetic phases. Reaction
in acetonitrile at room temperature leads to the formation of the thermodynamic
phase, α-[FeCp*2 ][TCNQ], which contains [TCNQ]2− dimers and is better formu-
                                                      2
lated as {[FeCp*2 ]+ }2 [TCNQ]2− [36, 37], and a kinetic phase, β-[FeCp*2 ][TCNQ]
                                2
possessing a 1D structure [36, 38] of the type illustrated in Figure 7.2. Electro-
chemical synthesis also leads to α-[FeCp*2 ][TCNQ] [39]. Reaction in acetonitrile
at −40◦ C [38] leads to the formation of γ -[FeCp*2 ][TCNQ] [40], which also pos-
sesses a 1D structure of the type illustrated in Figure 7.2. α-[FeCp*2 ][TCNQ]
is a paramagnet with one spin per [FeCp*2 ][TCNQ] repeat unit, while both β-
and γ -[FeCp*2 ][TCNQ] have two spins per repeat unit and magnetically order.
β-[FeCp*2 ][TCNQ] is a metamagnet4 with Tc = 2.55 K and critical field, Hc , of
1 kOe at 1.53 K, while γ -[FeCp*2 ][TCNQ] is a ferromagnet with Tc = 3.1 K [40].
β- and γ -[FeCp*2 ][TCNQ] are structurally similar, differing only slightly in key
intra- and interchain interactions, Figure 7.3. The most significant of which is the
nearest N. . .N distance for TCNQ-TCNQ pairs that is 4.08 Å for the metamag-

NC                        CN



NC                        CN    Scheme 7.6 7,7,8,8-Tetracyano-p-quinodimethane, TCNQ.

 4 A metamagnet is an antiferromagnet in zero applied field that switches to ferromagnet-like
     alignment upon application of a sufficiently large magnetic field.
                            7.10 2,5-Dimethyl-N, N -dicyanoquinodiimine Salts     239

netic β phase and 4.34 Å for the ferromagnetic γ phase. This is consistent with the
proposed antiferromagnetic coupling associated with this interaction [12a].
   Specific heat data on β-[FeCp*2 ][TCNQ] reveal a sharp peak at 2.54 K consis-
tent with ordering. The low temperature data suggests an energy gap of 6.5 K and
like [FeCp*2][TCNE] is Ising-like [41c].


7.9.2    Manganese

[MnCp*2 ][TCNQ] was synthesized by Hoffman and coworkers utilizing a meta-
thetical route involving the mixing of solutions of [MnCp*2 ]PF6 and NH4 [TCNQ]
[10] The structure as determined by single crystal X-ray diffraction, was reported
to consist of the usual 1-D stacks (Figure 7.2) with four formula units per unit cell.
As predicted, the compound exhibits magnetic properties consistent with strong
ferromagnetic coupling in the stacking direction (θ = +10.5 ± 0.5 K) and a phase
transition to a three-dimensionally ordered solid at 6.2 K. [MnCp*2 ][TCNQ] also
exhibits significant coercivity of 3.6 kOe at 2 K.


7.9.3    Chromium

The chromium analog [CrCp*2 ][TCNQ] was synthesized [42] by combining
equimolar solutions of the neutral donor and acceptor in acetonitrile. Crystals grown
from acetonitrile are isomorphous with the manganese analog. This compound dis-
plays ferromagnetic coupling (θ = +11.6 K) and a transition to a ferromagnetically
ordered state below 3.1 K. From a historical perspective, this compound is impor-
tant because it provided the first counterexample to the McConnell model that, in
its original incarnation, predicted antiferromagnetic coupling for this compound.



7.10 2,5-Dimethyl-N, N -dicyanoquinodiimine Salts

7.10.1    Iron and Manganese

[FeCp*2 ][Me2 DCNQI] and [MnCp*2 ][Me2 DCNQI], where Me2 DCNQI is 2,5-
dimethyl-N, N -dicyanoquinodiimine, Scheme 7.7, have been prepared [43]. Both
exhibit ferromagnetic coupling with θs of +10.8 K and +15.0 K, respectively.
However, neither exhibits evidence for long-range ordering above 2 K.
   Rabaca and coworkers [44] have recently re-examined [FeCp*2 ][Me2 DCNQI]
         ¸
and report a single crystal structure as well as somewhat different magnetic prop-
erties. The structure confirms the presence of the expected 1D chains. For their
240      7 Metallocene-based Magnets

         CH3

                          CN

     N                N

NC
                                Scheme 7.7 2,5-Dimethyl-N, N -dicyanoquinodiimine,
                CH3             Me2 DCNQI.

sample, θ = +3.2 K and a transition to an antiferromagnetically ordered state at
occurs at 3.9 K. This state is metamagnetic with Hc = 5.5 kOe at 1.7 K.



7.11 1,4,9,10-Anthracenetetrone Salts

[FeCp*2 ][ATO] where ATO is 1,4,9,10-anthracenetetrone, Scheme 7.8, has been
prepared [45]. This acceptor is unusual because it supports magnetic order, but
does not contain a nitrile functional group. The as-prepared solid is a dark-green
microcrystalline materials, but above 0◦ C, it slowly changes to a red-brown pow-
der, presumably due to loss of solvent. Although there is dominant ferromagnetic
coupling (θ = 10 K) the bulk magnetic properties of this ET salt, as determined by
ac susceptibility, are those of a glassy canted ferromagnet with Tg ∼ 3 K, reflecting
the disorder caused by partial desolvation. A second transition at about 5 K appears
to be antiferromagnetic (no (χ (T )) and a small amount of hysteresis is observed
at 1.8 K.

           O      O




           O      O            Scheme 7.8 1,4,9,10-Anthracenetetrone, ATO.




7.12 Cyano and Perfluoromethyl Ethylenedithiolato
     Metalate Salts

Planar four coordinate metal dithiolate complexes of principally Ni, Pd and Pt,
Scheme 7.9, have also been investigated as radical anions. Although formally
metal(III) species, these complexes, as monoanions (n = 1), possess one unpaired
electron that is delocalized over the π system and the metal.
                  7.12 Cyano and Perfluoromethyl Ethylenedithiolato Metalate Salts   241

                              n–
  R       S              R
                  S
                                    R = CN, CF3
              M
                                    M = Ni, Pd, Pt
  R       S       S      R

Scheme 7.9 [M(S2 C2 R2 )2 ]n− , also [M(mnt)]n− when R = CN.



7.12.1    Iron

Although bulk magnetic order is not observed in any of the members of the de-
camethylferrocenium family of these acceptors where R = CN or CF3 , some 1:1
bis(dithiolato)metallate salts of decamethylferrocenium studied to date exhibit fer-
romagnetic magnetic coupling with θ constants as high as +27 K (Table 7.3). Of
the compounds studied only [FeCp*2 ]{M[S2 C2 (CF3 )2 ]2 } (M = Ni and Pt) have a
1D chain structure reminiscent of other molecule-based ferromagnets (Figure 7.2).
The Pt analog with θ = +27 K possesses 1D . . .D+ A− D+ A− . . . chains whereas
the Ni analog with α = +15 K possesses zig-zag 1D chains and longer M. . .M
separations (11.19 Å vs. 10.94 Å for the Pt analog). Thus, the enhanced magnetic
coupling appears to arise from the stronger intrachain coupling. Data on the palla-
dium analog have not been reported.
     In contrast, [FeCp*2 ]{Ni[S2 C2 (CN)2 ]2 } or [FeCp*2 ][Ni(mnt)2 ] where mnt2−
= maleonitrilodithiolate, possesses isolated D+ A2 D+ dimers, akin to α-
                                                          2−
[FeCp*2 ][TCNQ], and is paramagnetic with θ ∼ 0 [11]. This is consistent with
one spin per repeat unit. Intermediate between the 1D chain and dimerized chains
structures are the α- and β-phases of [FeCp*2 ]{Pt[S2 C2 (CN)2 ]2 } which have 1D
. . .D+ A− D+ A− . . . strands in one direction and . . .D+ A2− D+ . . . units in another
                                                             2
direction. For these materials, the magnetic properties are consistent with the pres-
ence of one-third of the anions having a singlet ground state. Data on the palladium
analog have not been reported.


7.12.2    Manganese

With these two anions, the analogous salts of decamethylmanganocenium exhibit
3D cooperative magnetic order. For example, [MnCp*2 ]{M[S2 C2 (CF3 )2 ]2 } (M =
Ni, Pd, Pt) [46], all exhibit very similar metamagnetic behavior with Tc = 2.5 ±
0.3 K and θ = +2.8 ± 0.9 K (Table 7.3). Critical fields of approximately 800 Oe
at 1.85 K are observed. Since the iron and manganese complexes are isomorphous,
greater ferromagnetic coupling (predicted in a mean field model) would be expected
for Mn as Tc ∝ S(S + 1) [47]. It is possible that [FeCp*2 ]{Ni[S2 C2 (CF3 )2 ]2 } is
also metamagnetic, but with a Tc below 2 K and thus a phase transition has yet to
be observed.
242     7 Metallocene-based Magnets

Table 7.3. Weiss constants, θ , and critical temperatures, Tc , of ferromagnetic coupled and
magnetically ordered decamethylmetallocenium-based magnets.

Compound                               θ        Tc      Magnetic    Hc or Hcr         Ref.
                                       (K)a     (K)b    Behaviorf   (T, K)c
[CrCp*2 ][TCNE]                        +22.2    3.65    FM          ∼0 Oe (2 K)      20
[CrCp*2 ][TCNE]                        +12.2    2.1     FM          ∼0 Oe (n.r.)     19
[MnCp*2 ][TCNE]                        +22.6    8.8     FM          1.2 kOe (2 K)    17
[FeCp*2 ][TCNE]                        +16.9    4.8     FM          1.0 kOe (2 K)    12a
[FeCp*2 ]0.955 [CoCp*2 ]0.045 [TCNE]   n.r.     4.4     FM          n.r.             69
[FeCp*2 ]0.923 [CoCp*2 ]0.077 [TCNE]   n.r.     3.8     FM          n.r.             69
[FeCp*2 ]0.915 [CoCp*2 ]0.085 [TCNE]   n.r.     2.75    FM          n.r.             69
[FeCp*2 ]0.855 [CoCp*2 ]0.145 [TCNE]   n.r.     0.75    FM          n.r.             69
[NiCp*2 ][TCNE]                        −10                                           21
[FeCpCp*][TCNE]                        +3.3                                          9
[Fe(C5 Me4 H)2 ][TCNE]                 −0.3                                          61
[Fe(C5 Et5 )2 ][TCNE]                  +7.5                                          60
[CrCp*2 ][DMeDCF]                      +23      5.7     FM          <50 (1.8 K)      27
[MnCp*2 ][DMeDCF]                      +16      10.6    FM          7 kOe (1.8 K)    26
[CrCp*2 ][DEtDCF]                      +22      5.4     MM          0 Oe             28
[MnCp*2 ][DEtDCF]                      +15.5    12      MM          10 kOe (1.8 K)   26
[CrCp*2 ][C4 (CN)6 ]                   +13.8                                         21
[MnCp*2 ][C4 (CN)6 ]                   +18                                           21
[FeCp*2 ][C4 (CN)6 ]                   +35                                           57
[MnCp*2 ][DClDQ]                       +26.8    8.5     MM          5 kOe (2.3 K)    30,31
[FeCp*2 ][DClDQ]                       +10.3                                         21
[MnCp*2 ][DBrDQ]                       +20              MM          n.r.             21
[FeCp*2 ][DBrDQ]                       +19                                           21
[MnCp*2 ][DIDQ]                        +19              MM          n.r.             21
[FeCp*2 ][DIDQ]                        +12                                           21
[CrCp*2 ][DCNQ]                        +6       4.0     MM          ∼0 Oe (1.8 K)    35
[MnCp*2 ][DCNQ]                        +11      8.0     MM          3 kOe (1.8 K)    35
[FeCp*2 ][DCNQ]                        +4.0     4.0     MM          3 kOe (1.8 K)    33
[FeCp*2 ][DCID]                        +1                                            35
[CrCp*2 ][TCNQ]                        +12.8    3.1     FM          ∼0 Oe            42
[MnCp*2 ][TCNQ]                        +10.5    6.5 c   FM          3.6 kOe (3 K)    10
[FeCp*2 ][TCNQ]                        +3.8     3       FM          n.r.             40
[FeCp*2 ][TCNQ]                        +12.3    2.55    MM          1.6 kOe (1.53 K) 36,38
[Fe(C5 Me4 H)2 ][TCNQ]                 +0.8                                          61
[Fe(C5 Et5 )2 ][TCNQ]                  +6.1                                          60
[FeCp*2 ][TCNQCl2 ]                    +4.3                                          55
[FeCp*2 ][TCNQBr2 ]                    +0.1                                          55
[FeCp*2 ][TCNQI2 ]                     +9.5                                          55
[FeCp*2 ][TCNQMe2 ]                    −6.2                                          55
[FeCp*2 ][TCNQ(OMe)2 ]                 +2.1                                          55
[FeCp*2 ][TCNQ(OPh)2 ]                 −1.5                                          55
[FeCp*2 ][TCNQMeCl]                    +0.1                                          66
                 7.12 Cyano and Perfluoromethyl Ethylenedithiolato Metalate Salts           243

Table 7.3. (Continued.)

Compound                             θ         Tc      Magnetic      Hc or Hcr             Ref.
                                     (K)a      (K)b    Behaviorf     (T, K)c
[MnCp*2 ][Me2 DCNQI]                 +15.0                                                 43
[FeCp*2 ][Me2 DCNQI]                 +10.8                                                 43
[FeCp*2 ][Me2 DCNQI]                 +3.1      3.9     MM            5.5 kOe (1.7 K)       44
[FeCp*2 ][ATO]                       +10       3       FM            1 kOe (1.8 K)         45
[FeCp*2 ][chloranil]                 +13.5                                                 21
[FeCp*2 ][bromanil]                  +19                                                   21
[FeCp*2 ][C5 (CF3 )4 O]              +15.1                                                 21
[FeCp*2 ]{Ni[S2 C2 (CN)2 ]2 }        0                                                     11
α-[FeCp*2 ]{Pt[S2 C2 (CN)2 ]2 }      +6.6                                                  21
β-[FeCp*2 ]{Pt[S2 C2 (CN)2 ]2 }      +9.8                                                  21
[MnCp*2 ]{Ni[S2 C2 (CF3 )2 ]2 }      +2.6      2.4     MM            ∼800 Oe (1.85 K)      46
[FeCp*2 ]{Ni[S2 C2 (CF3 )2 ]2 }      +15                                                   11
[MnCp*2 ]{Pd[S2 C2 (CF3 )2 ]2 }      +3.7      2.8     MM            800 Oe (1.85 K)       46
[MnCp*2 ]{Pt[S2 C2 (CF3 )2 ]2 }      +1.9      2.3     MM            ∼800 Oe (1.85 K)      46
[FeCp*2 ]{Pt[S2 C2 (CF3 )2 ]2 }      +27                                                   21
[FeCp*2 ]{Mo[S2 C2 (CF3 )2 ]3 }      +8.4                                                  53
[CrCp*2 ][Ni(bdt)2 ]                 −7.8                                                  48
[MnCp*2 ][Ni(bdt)2 ]                 n.r. d    2.3     MM            200 Oe (2 K)          48
[FeCp*2 ][Ni(bdt)2 ]                 −2.4                                                  48
[CrCp*2 ][Ni(edt)2 ]·2MeCN           −5.3                                                  48
[FeCp*2 ][Ni(edt)2 ]                 −9.8      3.2     MM            4 kOe (2 K)           48
[CrCp*2 ][Ni(tcdt)2 ]                −20.4                                                 48
[MnCp*2 ][Ni(tcdt)2 ]                −28.5                                                 48
[FeCp*2 ][Ni(tcdt)2 ]                −22.9                                                 48
[FeCp*2 ][Ni(dmio)2 ]                +2.0                                                  52
[MnCp*2 ]{Fe[dmit]2 }                <0                                                    51
[MnCp*2 ]{Ni[dmit]2 }                n.r.      +2.5    FM            n.r.                  51
[FeCp*2 ]{Ni[dmit]2 }                >0                                                    50
[NiCp*2 ]{Ni[dmit]2 }                +27 e                                                 51
[FeCp*2 ][Ni(bds)2 ]                 >0                                                    50
[CrCp*2 ][Ni(tds)2 ]                 −86.4                                                 54
[MnCp*2 ][Ni(tds)2 ]                 +24.6     2.1     MM            60 Oe (2 K)           54
[FeCp*2 ][Ni(tds)2 ]                 +10.6                                                 54
[FeCp*2 ][Co(HMPA-B)]                +10 e                                                 56
[Fe(η5 -C9 Me7 )2 ][TCNE]            −0.3                                                  63
[Fe(η5 -C9 Me7 )2 ][TCNQ]            +6                                                    63
[Fe(η5 -C9 Me7 )2 ][DDQ]             −4                                                    63
[Fe(η5 -C5 Me4 St Bu)2 ][Ni(mnt)]    +3                                                    66
[Fe(η5 -C5 Me4 St Bu)2 ][Pt(mnt)]    +3                                                    66
n.r. Not reported. a For polycrystalline samples. b Tc determined from a linear extrapolation of
the steepest slope of the M(T) data to the temperature at which M = 0. c Hcr = coercive field,
Hc = critical field. d Does not obey Curie–Weiss law. e Modeled coupling constant. f FM =
ferromagnet; MM = metamagnet.
244      7 Metallocene-based Magnets

7.13 Benzenedithiolates and Ethylenedithiolates

Da Gama and co-workers have reported ET salt families utilizing the acceptor
radical anions [Ni(bdt)2 ]− , where bdt2− = benzenedithiolate, [Ni(edt)2 ]− where
edt2− = ethylenedithiolate, Scheme 7.10, and [Ni(tcdt)2 ]− where tcdt2− = tetra-
chlorobenzenedithiolate and several donor decamethylmetallocenes [48]. Both 1D
and layered structures are observed in these compounds. All exhibit dominant an-
tiferromagnetic coupling with θ values of between −2.4 and −28.5 K (Table 7.3).
Two compounds, [FeCp*2 ][Ni(edt)2 ] and [MnCp*2 ][Ni(bdt)2 ] are found to order
as metamagnets at Tc = 3.2 and 2.3 K, respectively. Critical fields at 2 K for these
solids are reported to be 4 kOe and 200 Oe, respectively [48].


a)                                   b)
                             n–                                  n–
     H    S             H                           S       S
                  S

              M                                         M

          S       S                                 S       S
     H                  H

Scheme 7.10 (a) [M(edt)2 ]n− , (b) [M(bdt)2 ]n− .



    In a follow-up study of the above, the compounds [MCp*2 ][Ni(edt)2 ] where
M = Cr and Fe, have been examined. A single crystal structure of the latter showed
it to possess 1D chains and an arrangement of donors and acceptors similar to
that shown in Figure 7.3. The former compound is isostructural, based on powder
diffraction. θ values are reported to be −6.7 and −5 K, respectively, and the latter
orders as a metamagnet with TN = 4.2 K with Hc = 14 kG. It also exhibits a poorly
resolved Mössbauer hyperfine field of approximately 350 kG (vide infra) [49].
    The nickel complex of the analogous benzenediselenolate ligand, bds2− , has
also been explored [50]. The [FeCp*2 ]+ salt, synthesized via a metathetical route,
crystallizes in two-dimensional stacks of D+ D+ A− repeat units where the donors
are side-by side. These charged stacks are separated from each other by planes of
A− anions in the perpendicular direction. The magnetic properties of this solid are
consistent with ferromagnetic coupling down to the lowest measured temperature
(1.5 K), but no evidence for spontaneous magnetization or hysteresis was observed.
A value of θ was not reported.
                                              7.14 Additional Dithiolate Examples   245

7.14 Additional Dithiolate Examples

The anion, bis(2-thioxo-1,3-dithiole-4,5-dithiolate)nickel(III), [Ni(dmit)2 ]− ,
Scheme 7.11, has been investigated as an acceptor anion. From a metathetical
route, [FeCp*2 ][Ni(dmit)2 ] forms unusual stacks arranged as D+ D+ A− A− where
stacks of side-by-side cations alternate with face-to-face pairs of anions [50].
The magnetic properties of this compound are consistent with dominant but
weak ferromagnetic coupling followed at low temperature by antiferromagnetic
interactions that lead to a low moment state. The analogous manganese compound
[MnCp*2 ][Ni(dmit)2 ] exhibits ferromagnetic coupling and a transition to a
ferromagnetic state below 2.5 K [51]. The structure of this latter compound has
not been determined.


                                         n–
        S        S        S   S
 E                   Ni              E

        S        S        S   S


Scheme 7.11 [Ni(dmit)2 ]− (E = S), [Ni(dmio)2 ]− (E = O).



    The iron analog of the above acceptor, bis(2-thioxo-1,3-dithiole-4,5-
dithiolate)iron(III), whose ET salt is formulated as [MnCp*2 ][Fe(dmit)2 ] has also
been reported. It exhibits evidence of antiferromagnetic coupling but no signs of
ferrimagnetic order that might be expected based on S = 1 Mn(III) and S = 3/2
Fe(III). Neither the structure, nor the value of θ was reported [51].
    The related oxo species, [Ni(dmio)2 ]− where dmio2− = 2-oxo-1,3-dithiole-4,5-
dithiolate, Scheme 7.11, has been investigated as an acceptor radical anion and
its decamethylferrocenium salt prepared [52]. [FeCp*2 ][Ni(dmio)2 ] is ferromag-
netically coupled (θ = +2.0 K) with weak antiferromagnetic interactions super-
imposed at low temperature. Long-range order was not reported. The complex
structure consists of mixed anion-cation layers and anionic sheets.
    One of the few examples of non-planar anions is a tris(dithiolato)metallate salt of
decamethylferrocenium, namely [FeCp*2 ]{Mo[S2 C2 (CF3 )2 ]3 } [53]. The salt only
possesses parallel out-of-registry 1D · · ·D+ A− D+ A− · · · chains with intrachain
Mo. . .Mo separations of 14.24 Å. The θ value is reduced to +8.4 K, which probably
reflects the reduced spin-spin interactions due to the bulky CF3 groups. 3D ordering
is not observed down to the lowest temperature studied (2 K) as expected for the
weak ferromagnetic intra- and interchain interactions. This salt-like structure is to
date the only structural motif that does not have parallel chains in-registry, avoiding
nearest neighbor antiferromagnetic A− /A− interactions.
246        7 Metallocene-based Magnets

7.15 Bis(trifluoromethyl)ethylenediselenato Nickelate Salts

In an effort to promote stronger intermolecular magnetic interactions, selenium
has been utilized in place of sulfur to form a homologous square planar dise-
lenate. Utilizing a metathetical route, the family of ET salts [MCp*2 ][Ni(tds)2 ],
Scheme 7.12, were prepared, where M = Cr, Mn and Fe and tds =
bis(trifluoromethyl)ethylenediselenato [54]. The three compounds are isostruc-
tural, as determined by single crystal X-ray diffraction, consisting of 1-D
. . .D+ A− D+ A− . . . chains. The Mn and Fe compounds exhibit dominant ferromag-
netic coupling, while the Cr compound shows strong antiferromagnetic coupling.
The data for the Fe salt have been fitted well by a 1D Ising model, but no evidence
for order has been found. In contrast, the Mn salt orders as a metamagnet with
Tc = 2.1 K (Table 7.3).


                                    n–
 F3C         Se               CF3
                       Se
                  Ni

 F3C         Se        Se     CF3
                                         Scheme 7.12 [Ni(tds)2 ]n− .




7.16 Other Acceptors that Support Ferromagnetic Coupling,
     but not Long-range Order above ∼2 K

The reactions of either 2,3,5,6-tetrachloroquinone (chloranil), Scheme 7.13, or
2,3,5,6-tetrabromoquinone (bromanil) with decamethylferrocene also give ferro-
magnetically coupled solids. The θ s for these compounds are +13.5 and +19.0 K,
respectively, although neither has been observed to exhibit ordering above 2 K. No
structural information has been reported, although the usual 1-D stack (Figure 7.2)
has been presumed [21].


      Cl          Cl



O                       O



      Cl          Cl        Scheme 7.13 2,3,5,6-Tetrachloroquinone, chloranil.
                            7.16 Other Acceptors that Support Ferromagnetic Coupling      247

   2,5-Iodo-7,7,8,8-tetracyano-p-quinodimethane, TCNQI2 ,55, Scheme 7.14, has
been investigated as an electron acceptor paired with decamethylferrocene. Struc-
tural characterization of this compound revealed D+ A− D+ A− stacking but where
the anion is significantly non-planar, perhaps due to the steric bulk of the io-
dine. Multiple close N· · ·I interstack interactions between adjacent acceptors are
observed. This compound exhibits Curie–Weiss behavior with θ = +9.5 K, but
does not show evidence of a phase transition to a ferromagnetic state. However,
Mössbauer spectroscopy at low temperature reveals hyperfine splitting that sug-
gests insipient magnetic order. Related compounds utilizing TCNQCl2 , TCNQBr2 ,
TCNQMe2 , TCNQ(OMe)2 , TCNQ(OPh)2 and TCNQMeCl have also been re-
ported with weak magnetic interactions and no evidence of magnetic order (Ta-
ble 7.3) [55].

                    I

NC                          CN



NC                          CN
                                     Scheme 7.14 2,5-Iodo-7,7,8,8-tetracyano-p-quinodimethane,
       I                             TCNQI2 .


    Hoffman and coworkers have reported [FeCp*2 ][Co(HMPA-B)] [56] where
HMPA-B = bis(2-hydroxy-2-methylpropanamido)benzene, Scheme 7.15. This ET
salt adopts the D+ A− D+ A− structure and, interestingly, has two unpaired electrons
on the acceptor, in contrast to all other metallocene-based magnets. The data were
fitted to a model that revealed significant zero-field splitting (D = +65 K) and
weak ferromagnetic intrastack interactions (J ∼ +10 K) precluding a magneti-
cally ordered ground state.


                                     1–




  O        N                     O
                        N
               Co

           O            O
                                          Scheme 7.15 [Co(HMPA-B]− .


   Hexacyanobutadiene, Scheme 7.16, was investigated quite early as a higher
homolog of TCNE. [FeCp*2 ][C4 (CN)6 ] 57 is found to adopt a 1D chain structure
with strong ferromagnetic coupling. The anion is disordered over two positions
involving rotation about the central C–C bond. The corresponding Cr and Mn ET
248         7 Metallocene-based Magnets

salts similarly exhibit ferromagnetic coupling, but evidence for long-range order
is lacking [21]. These compounds need to be re-investigated.


           NC           CN

NC

                        CN

NC              CN             Scheme 7.16 Hexacyanobutadiene, C4 (CN)6 .


   [FeCp*2 ][C3 (CN)5 ] with S = 0 [C3 (CN)5 ]− exhibits essentially the Curie sus-
ceptibility anticipated for isolated S = 1/2 [FeCp*2 ]+ (θ = −1.2 K) [12].
   2,3,4,5-tetrakis(trifluoromethyl)cyclopentadienone, Scheme 7.17, was investi-
gated as a possible acceptor and forms the desired one-dimensional chains in reac-
tions with FeCp*2 resulting in the expected ferromagnetic coupling (θ = +15.1 K).
However, this ET salt does not order above 2 K [21].

     F3C             CF3




F3C                     CF3

                O              Scheme 7.17 2,3,4,5-Tetrakis(trifluoromethyl)cyclopentadienone.


   An acceptor that is isomeric with DCNQ (vide supra) is 2-dicyanomethylene-
indan-1,3-dione (DCID), Scheme 7.18. Its relationship to DCNQ allows a com-
parison of essentially isostructural, but electronically different acceptors. DCID
reacts with FeCp*2 to give a structurally characterized ET salt that exhibits only
very weak ferromagnetic coupling (θ ∼ +1 K) and no evidence of order above
1.8 K. The arrangement of donors and acceptors in the solid state consists of the
usual mixed stacks.

                    O

                              CN



                              CN

                    O              Scheme 7.18 2-Dicyanomethyleneindan-1,3-dione.


  Parallel 1D chains of alternating radical [FeCp*2 ]+ cations and singly
deprotonated 2,5-dichloro-3,6-dihydroxy-1,4-benzoquinone (HCA− ) anions,
                         7.17 Other Metallocenes and Related Species as Donors    249

Scheme 7.19, is reported for [FeCp*2 ]+ [HCA]− ·H2 O, however, the magnetic prop-
erties for this compound were not reported [58]. Due to the diamagnetic nature of
the anion, magnetic ordering is not expected to occur. This work has been extended
to include the synthesis and structural characterization of the analogous bromanilic
and cyananilic acids [59].


    HO      Cl



O                O



    Cl      OH       Scheme 7.19 2,5-dichloro-3,6-dihydroxy-1,4-benzoquinone, H2 CA.




7.17 Other Metallocenes and Related Species as Donors

1,2,3,4,5-Pentamethylferrocene, and decaethylferrocene maintain the five-fold
symmetry necessary to form a cation with degenerate partially occupied molecular
orbitals and a Kramers doublet (2 E) ground state as reported for decamethylfer-
rocenium. FeCpCp* is a sufficiently strong donor to reduce TCNE and the simple
(1:1) 1D salt as well as three other phases were prepared [9]. This 1:1 phase exhibits
weak ferromagnetic coupling, as evidenced from the fit of its susceptibility to the
Curie–Weiss expression with θ = +3.2 K, but cooperative 3D magnetic ordering
is not observed down to the lowest temperature studied (∼2 K). A linear chain
structure is proposed for [Fe(C5 Et5 )2 ][TCNE], which also exhibits ferromagnetic
coupling, as evidenced from the fit of its susceptibility to the Curie–Weiss expres-
sion with θ = +7.5 K. It also did not exhibit cooperative 3D magnetic ordering
[60].
   To test the necessity of a 2 E ground state, the TCNE electron-transfer salt with
the lower- symmetry Fe(C5 Me4 H)2 donor was prepared [61]. The magnetic suscep-
tibility can be fitted by the Curie–Weiss expression with θ ∼ 0 K. The absence of ei-
ther 3D ferro- or antiferromagnetic ordering above 2.2 K in [Fe(C5 Me4 H)2 ][TCNE]
contrasts with the behavior of [FeCp*2 ][TCNE]. The 57 Fe Mössbauer data are in ac-
cord with the absence of significant magnetic coupling among the radical ions, and
show only nuclear quadrupole splitting for the [Fe(C5 Me4 H)2 ]+ salts and not the
zero-field Zeeman splitting observed for ordering solids such as [FeCp*2 ][TCNE]
[12a]. The lack of magnetic ordering is attributed to poorer intra- and intermolecular
overlap within and between the chains, leading to substantially weaker magnetic
coupling for [Fe(C5 Me4 H)2 ][TCNE], and suppressing the ordering temperature.
250     7 Metallocene-based Magnets

Alternatively, due to the essentially C2v symmetry of [Fe(C5 Me4 H)2 ]2+ the lowest
lying virtual charge transfer excited state may be a singlet, not a triplet, and the
admixture of a singlet excited state (a la McConnell II) should lead to antiferro-
magnetic, not ferromagnetic, coupling [61, 62] Since significant antiferromagnetic
coupling was also absent for [Fe(C5 Me4 H)2 ][TCNE], perhaps a reduced overlap
with neighboring radicals is the more important effect of modification of the cation.
   Bis(heptamethylindenyl)iron(II), [Fe(η5 -C9 Me7 )2 ], has also been investigated
as a donor [63]. This sandwich compound also lacks a five-fold axis and so will, at
best, possess accidentally degenerate metal d orbitals. ET salts pairing this donor
with TCNE, TCNQ and DDQ have been reported. Each forms a 1:1 complex with
one unpaired electron associated with the donor and one with the acceptor. The
TCNE and DDQ salts exhibit weak antiferromagnetic interactions, but the TCNQ
compound shows intriguing evidence of ferromagnetic coupling (θ = +6 K), in
contrast to predicted antiferromagnetic coupling based on the McConnell II mech-
anism (vide infra). [Fe(η5 -C9 Me7 )2 ][TCNQ] has been structurally characterized
by X-ray diffraction and found to possess · · ·D+ A− D+ A− · · · chains (Figure 7.2)
and the usual in-registry and out-of-registry interchain interactions characteristic
of solids that order magnetically. However, although the magnetization saturates
faster than predicted by the Brillouin function, no evidence of order was observed
above 2 K.
   Electron transfer salts and charge transfer (CT) complexes have been prepared
from octamethylferrocenyl thioethers, Fe(η5 -C5 Me4 SMe)2 , Fe(η5 -C5 Me4 St Bu)2 ,
and Fe(η5 -C5 Me4 S)2 S, and various acceptors. The latter CT complexes, character-
ized by non-integral charge transfer such as for [Fe(η5 -C5 Me4 SMe)2 ]3 [TCNQ]7 ,
exhibit complex crystal structures and significant degrees of electrical conductivity,
but are not the subject of this chapter [64]. Ionic ET salts with 2,3,5,6-tetrafluoro-
7,7,8,8-tetracyano-p-quinodimethane, TCNQF4 , exhibit dimerization of the radical
anion to give a diamagnetic dianion [64], as has been seen before with the analogous
FeCp*2 salt [65].
   One-to-one ET salts derived from [Fe(η5 -C5 Me4 SMe)2 ]+ or [Fe(η5 -
C5 Me4 St Bu)2 ]+ and [M(mnt)]− (where M = Co, Ni and Pt) vide supra) have
been characterized [66]. For most of these, θ values that were zero or slightly
negative were found. The exceptions were [Fe(η5 -C5 Me4 St Bu)2 ][M(mnt)] where
M = Ni and Pt, which form isomorphous . . .D+ A− D+ A− . . . chains and which
exhibit θ = +3 K, indicating weak ferromagnetic coupling, also in conflict with
the McConnell model prediction (vide infra).
   The reaction of 1, 1 -bis[(octamethylferrocenylmethyl)ferrocene, A
(M = M = Fe), Scheme 7.20, with TCNE leads to the isolation of
{Fe(C5 H4 CH2 )2 [Fe(C5 Me4 )(C5 Me4 H)]}2+ {[TCNE]− }2 (θ
                                          2                           =       −0.8 K)
[67]      and      {Fe(C5 H4 CH2 )2 [Fe(C5 Me4 )(C5 Me4 H)]}2+ [TCNE]− [C3 (CN)5 ]−
                                                             2
(θ = +0.1 K) [67, 68] while reaction of A (M = Fe, M = Co) forms
{Co(C5 H4 CH2 )2 [Fe(C5 Me4 )(C5 Me4 H)]}3+ {[TCNE]− }3 (θ = −5.8 K) [67]. The
                                           2
structures of these compounds have been reported.
                                                7.19 Mössbauer Spectroscopy      251




        M                M'              M




Scheme 7.20 1,1 -Bis[(octamethylferrocenylmethyl)ferrocene (M = M = Fe), A




7.18 Muon Spin Relaxation Spectroscopy

The static and dynamic magnetic properties of [FeCp*2 ][TCNE] have been studied
via the muon-spin-relaxation technique [70]. Spontaneous order is observed in
the ferromagnetic ground state below 5 K, while the muon spin relaxation rate in
the paramagnetic phase displays a gradual variation with temperature, indicating
that a slowing down of spin fluctuations occurs over a wide temperature range.
The temperature dependence of spin fluctuations between 8 and 80 K shows the
thermally activated behavior expected in a spin chain with Ising character.




7.19 Mössbauer Spectroscopy

The 57 Fe Mössbauer spectra of magnetically ordering electron transfer salts con-
taining decamethylferrocenium cations give insight into the development of the
local internal magnetic fields. Well above Tc , an unresolved quadrupole doublet
characteristic of [FeCp*2 ]+ is observed with an isomer shift of ∼ 0.5±0.1 mm s−1 .
Evolution of this signal to an atypical six-line Zeeman split spectra is observed in
zero applied magnetic field at low temperature as the compounds become long-
range magnetically ordered, either ferromagnetically or antiferromagnetically. For
example, a Zeeman split spectrum with an internal field (Hint ) of 379 kG is observed
for the [DCNQ]− salt at 1.63 K (Figure 7.8). These internal fields are substantially
greater than the expectation of 110 kG/spin/Fe [12a]. Mössbauer data for several
decamethylferrocenium ET salts are collected in Table 7.4.
252     7 Metallocene-based Magnets




Fig. 7.8. Mossbauer spectra of [FeCp*2 ][DCNQ] above and below Tc [33].

Table 7.4. Summary of 57 Fe Mössbauer parameters for [FeCp*2 ][acceptor] magnets.

Acceptor      Isomer Shift, δ, mm s−1   Internal Field, kG (at T , K)   Ref.

TCNE          0.58                      424.6 (4.23)                    12a
C4 (CN)6      0.51                      448 (4.34)                      57
DDQ           0.6                       440 (1.7)                       29b
β-TCNQ        0.53                      404,449 (1.4)                   71
TCNQI2        0.47                      270 (1.5)                       55
Me2 DCNQI     0.43                      448.5 (2.24)                    43
DCNQ          0.45                      379 (1.63)                      33
Ni(edt)2      0.48                      ∼350 (3.5)                      49
7.21 Dimensionality of the Magnetic System and Additional Evidence for a Phase Transition   253

7.20 Spin Density Distribution from Calculations
     and Neutron Diffraction Data

The spin density on [FeCp*2 ]+ has been determined by neutron diffraction at
low temperature. Experiments on [FeCp*2 ]+ paired with a diamagnetic polyox-
otungstate anion reveal that the iron atom carries 2.0 µB of spin density, the ring
carbons carry −0.005 ± 0.001 µB and the methyl carbons carry 0.008 ± 0.001 µB .
These values have been described as roughly consistent with ab initio DFT calcu-
lations [71].



7.21 Dimensionality of the Magnetic System
     and Additional Evidence for a Phase Transition

The single crystal susceptibility can be compared with different physical models to
aid our understanding of the microscopic spin interactions. For samples oriented
parallel to the field, the susceptibility above 16 K fits a 1D Heisenberg model
with ferromagnetic exchange of Jintra = +27 K (+19 cm−1 ) [12c]. Variation of
the low field magnetic susceptibility for an unusually broad temperature range
above Tc [χ ∝ (T − Tc )−γ ], magnetization with temperature below Tc [M ∝
(Tc − T )−β ], and the magnetization with magnetic field at Tc (M ∝ H 1/δ ) enabled
determination of the β, γ and δ critical exponents as 0.50, 1.2 and 4.4, respectively.
These values are consistent with a mean-field-like 3D behavior. Thus, above 16 K
1D nearest neighbor spin interactions are sufficient to understand the magnetic
coupling, but near Tc 3D spin interactions are dominant. At higher temperatures
the anisotropic magnetic susceptibility shows the dominance of 1D, Heisenberg-
like ferromagnetic exchange behavior in accord with the linear chain structure. A
fourth critical constant, α, obtained from heat capacity, Cp (T ), studies (Figure 7.9),
Cp ∝ (T − Tc )−α , gives α = 0.09 ± 0.02 [41a], consistent for an Ising-like system
as the excess entropy is approximately 2R ln 2 (R = gas constant) in value [41c].
   The low value of the 3D ordering temperature, Tc = 4.8 K, compared to the
1D exchange interaction (as indicated by Jintra = +27 K) for [FeCp*2 ][TCNE],
suggests the applicability of quasi-one-dimensional models governing the onset
of 3D cooperative ordering. For example, for a tetragonal lattice with interacting
nearest neighbor chains [72],
                √
          1.556 Jintra Jinter
   Tc =                                                                             (7.1)
                  kB
Solving this for Jinter using the above data gives a ratio of Jintra /Jinter = 77. Thus,
[FeCp*2 ]+ [TCNE]− and most of the other metallocene electron transfer salts are
in the 1D limit.
254     7 Metallocene-based Magnets




Fig. 7.9. Low temperature Cp (T ) for [FeCp*2 ][TCNE] [41a].


   To further test the applicability of the one-dimensional models, spin-
less S = 0 [CoCp*2 ]+ cations were randomly substituted for the cation
in the [FeCp*2 ]+ [TCNE]− structure. This leads to a solid solution of
[FeCp*2 ]x [CoCp*2 ]1−x [TCNE] that possesses finite magnetic chain segments
punctuated, at random, by isostructural, but diamagnetic interruptions [69]. This re-
sults in the dramatic reduction of Tc with increasing [CoCp*2 ]+ content (Table 7.3)
and is in excellent agreement with theoretical models [74].



7.22 The Controversy Around the Mechanism
     of Magnetic Coupling in ET Salts

Because of the many related examples of ET salts, several efforts to model the
magnetic properties have been made, though all have met with mixed success
and this remains a key unsolved problem. The first attempt, commonly known
as the McConnell-II model, involved the application of configurational mixing of
the lowest energy virtual charge transfer excited state with the ground state [75].
It makes the prediction that if the donor and acceptor each have non-degenerate
partially occupied molecular orbitals, then only antiferromagnetic coupling will
be observed, but that degeneracy can permit ferromagnetic interactions. Using
this approach, it is possible to rationalize the ferromagnetic intrastack coupling
observed in [FeCp*2 ][acceptor] and [MnCp*2 ][acceptor] families of compounds.
Extension of this simple model in the other two dimensions would, in principle,
                                                                   7.23 Trends      255

support bulk ferromagnetic order. However, for the analogous [CrCp*2 ][acceptor]
compounds, antiferromagnetic coupling is predicted and ferromagnetic coupling
is observed, casting doubt on the validity of this mechanism. Kollmar and Kahn
[76] have also argued that consideration of only the lowest CT excited state for
configurational mixing is an oversimplification for determining the preferred spin
state of the ground state and have challenged the general validity of this model.
    Kahn and coworkers have suggested that positive spin density on the metal can
induce negative spin density on the Cp rings via configurational mixing. Subsequent
overlap of regions of negative spin density on the Cp ring with regions of positive
spin density on the TCNE radical gives rise to significant net ferromagnetic cou-
pling between the metal and TCNE. Neutron diffraction, presented above, directly
addresses the appropriateness of this model, which only considers intrachain inter-
actions. However, the predictive ability of this mechanism, known as McConnell
I, has recently been called into question based on calculations on diradical para-
cyclophanes [77]. Again, a theoretical understanding of ET salt magnets has not
yet been achieved.



7.23 Trends

Although there is as yet no comprehensive theoretical treatment of the magnetic
behavior in this class of compounds, it is clear that there are trends that suggest such
an understanding is achievable. For example, with the exception of a few poorly
characterized cases of substituted TCNQs, when the acceptor is a purely organic
molecule and the donor is a Cr, Mn or Fe decamethylmetallocene, θ is positive,
indicating the dominant interaction, intrachain coupling, is always ferromagnetic
(for approximately 30 compounds). It is also the case that in all of the five known
families of ET salts that exhibit magnetic order utilizing the same acceptor with
two or more different decamethylmetallocenes, the critical temperature is always
highest for the [MnCp*2 ]+ salt and, where the data is available, roughly equal
for the [CrCp*2 ]+ and [FeCp*2 ]+ salts. It is interesting that Figure 7.10 includes
data from both ferromagnetic and antiferromagnetic (metamagnetic but well below
Hc ) phase transitions. Although not shown in Figure 7.10, it has also been noted
that, consistent with this trend, there are examples of [MnCp*2 ]+ salts that exhibit
magnetic order but where the corresponding [FeCp*2 ]+ salt does not and it has been
assumed that Tc for the latter is simply too low to be experimentally accessible (i. e.
below about 1.8 K, vide supra). These results show that critical temperature does
not scale in any simple way with S (which increases from left to right in the plot)
as would be expected based on a mean field model (i. e. Tc ∝ S(S + 1)). But it
also seems clear that the bulk magnetic properties are not so critically dependent
on the subtle variations of the crystal structures as to be beyond understanding.
256                                   7 Metallocene-based Magnets

                               12.5

                                                                    [DEtDCF] •-
Critical Temperature, T c, K


                               10.0                   [DMeDCF] •-


                                7.5


                                         [TCNE]•-
                                5.0


                                      [DCNQ] •-     [TCNQ]•-
                                2.5
                                             0.5               1                  1.5
                                             Fe                Mn                 Cr
                                                               S

Fig. 7.10. Trends in critical temperature for magnetic ordering ET Salts with the same anion
and different decamethylmetallocenium cations. Solid lines denote ferromagnets, dashed lines,
metamagnets.




7.24 Research Opportunities

The quest for s/p-orbital based ferromagnets remains the focus of intense interest
worldwide. The growth of this area of metallocene-based ET salts depends critically
on the identification of new donor and acceptor building blocks. Candidates need
to have favorable electrochemical and structural properties, including reversible
electrochemistry and probably π electrons for mediating coupling. The synthesis
of additional donors, other than decamethylmetallocenes, remains a vexing prob-
lem, particularly because some of the evidence above seems to indicate that high
symmetry is an important consideration.
   We conclude this chapter with a series of questions that we hope will spur
additional research, which, we have argued above, ET salts are well-suited to ad-
dress. Can the question of the mechanism of the intrachain magnetic coupling,
and through space coupling in general, be answered? A more subtle question, be-
cause its strength is orders of magnitude smaller, concerns the nature of interchain
coupling. Why is the net interchain coupling sometimes antiferromagnetic and
sometimes ferromagnetic? It seems quite likely that Tc is intrinsically limited by
weak interstack coupling. Can this be increased?
   Finally, this problem becomes one of crystal structure engineering. Is there
something special about the “usual” structure of these compounds? And if not,
can other structural classes be discovered and can structure be controlled? Can the
magnetic properties be predicted based on knowledge of the building blocks? As
molecular solids, these compounds are highly compressible. How does Tc vary with
                                                                           References        257

applied pressure? Although this was not specifically addressed, structural disorder
appears to contribute to spin glass behavior in some of the above examples. Is
this related to the known occurrence of glassiness in dilute metal alloys or is it an
example of new physics?


Acknowledgments

The authors gratefully acknowledge partial support by the Department of Energy
Division of Materials Science (Grant Nos. DE FG 03-93ER45504 and DE FG
02-86BR45271). We deeply thank our numerous co-workers, especially Arthur J.
Epstein and his group at The Ohio State University, for the important contributions
they have made over the years enabling the success of some of the work reported
herein.



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258       7 Metallocene-based Magnets

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8 Magnetic Nanoporous Molecular Materials
     Daniel Maspoch, Daniel Ruiz-Molina, and Jaume Veciana




8.1 Introduction

The exceptional characteristics of nanoporous materials have prompted their appli-
cation in different fields such as molecular sieves, sensors, ion-exchange and catal-
ysis. In this context, zeolites have been the predominant class of open-framework
materials. However, in the last two decades, the number of approaches to obtain
new porous materials that behave as zeolites has shown a spectacular increase. In
1982, Flanigen and coworkers initiated the synthesis of the first zeolite analogs,
the microporous aluminophosphate solids [1]. Immediately, this fascinating family
stimulated the discovery of new inorganic porous materials, most of them based
upon phosphates, nitrides [2], sulfates [3], sulfides [4], selenides [5], halides [6] and
cyanides [7] and a large list of metal ions (gallium [8], tin [9], iron [10], cobalt [11],
vanadium [12], indium [13], boron [14], manganese [15] and molybdenum [16],
among others). Together with the rapid development of inorganic-based porous
solids, a crucial innovation appeared at the beginning of the 90s, the introduction
of organic molecules as direct constituents of the porous structures. In essence, this
approach uses multifunctional organic linkers to connect “inorganic” frameworks.
   According to the dimensionality of the inorganic network, Férey has classified
these new porous materials into four different categories [17]: starting from a pure
inorganic framework (3-D inorganic system) [18] such as that shown in Figure 8.1a,
the introduction of organic moieties can induce pillaring between inorganic 2-
D layers (Figure 8.1b) or they can act as linkers between 1-D inorganic chains
(Figure 8.1c) [19]. Both, inorganic 1-D and 2-D structures are usually referred to
as hybrid inorganic-organic materials. Finally, organic ligands may arrange around
discrete clusters, containing one or several metal ions, as shown in Figure 8.1d.
These 0-D structures, as far as the inorganic part is concerned, will be referred to
from now on as coordination polymers [20, 21].
   At this point, it has to be mentioned that beyond the discovery of new open-
framework topologies and structures, development of new porous solids with open-
shell metal ions introduced the possibility of obtaining nanoporous materials with
additional magnetic properties. The synergism of both magnetic properties and the
262      8 Magnetic Nanoporous Molecular Materials




Fig. 8.1. Classification of the nanoporous structures as a function of the dimensionality of the
inorganic subnetwork. (a) 3-D pure “inorganic”-based framework; (b) Pillared 2-D “inorganic”
layers through multitopic organic linkers (hybrid materials); (c) 1-D “inorganic” chains linked
through multitopic organic linkers (hybrid materials); (d) “Inorganic” clusters or metal ions
connected through multitopic organic linkers (coordination polymers).



exceptional characteristics of nanoporous materials opens a new route to the devel-
opment of low-density magnetic materials, magnetic sensors and multifunctional
materials on the nanometer scale. For instance, magnetic zeotype structures offer
excellent conditions to encapsulate different functional materials with conducting,
optical, chiral and NLO properties, among others.
    Here, we will give a short overview of the different types of magnetic nanoporous
materials, although, due to the large number of examples so far described in the
literature, we will mainly focus on the analysis and study of magnetic nanoporous
coordination polymers, i.e., 0-D zeotype systems according to Férey’s classifica-
tion. Finally, indications and prospects for further investigations based on magnetic
nanoporous materials will be given.
             8.2 Inorganic and Molecular Hybrid Magnetic Nanoporous Materials       263

8.2 Inorganic and Molecular Hybrid Magnetic Nanoporous
    Materials

Before 1996, only a few examples of the magnetic properties of porous materials
based on vanadium [22], cobalt [23], copper [24] and molybdenum phosphates
and diphosphonates [25] had been described, most of them antiferromagnets with
ordering temperatures in the 2–50 K range. Then, important advances were intro-
duced by Férey, Zubieta and their coworkers who reported an extensive family of
porous iron (III) fluorophosphates and phosphates with antiferromagnetic ordering
in the temperature range 10–37 K [26] and iron phosphates with a three-dimensional
antiferromagnetic order at 12–30 K [27]. These results represented an important
breakthrough that was followed by an exponential increase in scientific publica-
tions devoted to the study and understanding of magnetic properties on porous
solids. Indeed, since then, new nanoporous systems that exhibit not only antifer-
romagnetic ordering [28] but also interesting ferri-/ferromagnetic ordering [29],
spin-crossover [30] and metamagnetic [31] properties, among others, have been
reported.
    For instance, the magnetic properties of several new 3-D inorganic magnetic
porous materials such as metal sulfates [3, 32] metal cyanides [33], oxochlorides
[34], fluorides [35] and selenites [36] have been described. Another important re-
sult in this field was reported by Long et al, who obtained a microporous cobalt
cyanide magnet of composition Co3 [Co(CN)5 ]2 showing long-range magnetic or-
dering with a critical temperature of 38 K [33]. Moreover, its microporosity was
confirmed by dinitrogen sorption measurements, with a Type I sorption isotherm af-
ter dehydration at 100 ◦ C under vacuum and a calculated surface area of 480 m2 g−1
(see Figure 8.2).
    Important contributions of 2-D and 1-D hybrid materials have also been
achieved. In 2003, Kepert et al. discovered a hybrid porous material formed by a
cobalt hydroxide layer structure pillared with trans-1,4-cyclohexanedicarboxylate
ligands that orders magnetically below 60.5 K, and has small one-dimensional
channels (3.7 × 2.3 Å2 ) that represent 13.4% of the crystal volume [37]. In the
field of porous antiferromagnets, the ordering temperature has been increased to
95 K for a hybrid vanadium carboxylate complex [38]. Finally, the hybrid nickel
glutarate open-framework shown in Figure 8.3, which behaves as a pure ferromag-
net below a temperature of 4 K, has been recently described [39].
    All the examples previously mentioned belong to 3-D, 2-D and 1-D hybrid
inorganic–organic systems. However, one of the approaches that has been more
intensively explored in the last few years is the preparation and characterization of 0-
D nanoporous coordination polymers. The advantage of this approach is threefold.
First, the endless versatility of molecular chemistry provides chemists with a huge
variety of polyfunctional ligands, most of them carboxylic-based and nitrogen-
based molecules. Second, these ligands have been proved to be good superexchange
264      8 Magnetic Nanoporous Molecular Materials




Fig. 8.2. (a) Dinitrogen sorption isotherm for evacuated Co3 (Co(CN)5 )2 at 77 K, where (◦) and
(•) indicate the absorption and desorption, respectively. (b) Field-cooled magnetization data
for evacuated Co3 (Co(CN)5 )2 at H = 10 G. Inset, magnetic hysteresis loop at 5 K. (Reprinted
with permission from [33]. Copyright 2002 American Chemical Society.)


pathways for magnetic coupling. And, last but not least, it may profit from crystal
engineering techniques to arrange transition metal ions within a wide variety of
open-framework structures that favor magnetic exchange interactions, since they
coordinate in a predictable way.
               8.2 Inorganic and Molecular Hybrid Magnetic Nanoporous Materials                265




Fig. 8.3. (a) Illustration of the nanoporous structure of [Ni20 (C5 H6 O4 )20 (H2 O)8 ]·40H2 O. (b)
Temperature-dependence of the χ T value, showing ferromagnetic ordering at 4 K. (Repro-
duction with permission from [39].)
266     8 Magnetic Nanoporous Molecular Materials

8.3 Magnetic Nanoporous Coordination Polymers

As previously mentioned, the design of coordination polymers may profit from
crystal engineering techniques to yield a large variety of open-framework struc-
tures, since organic ligands coordinate to transition metal ions in a more or less
predictable way. This situation is very advantageous where the challenge is often
to increase and modulate the pore sizes for selective adsorption and other appli-
cations. For instance, Yaghi et al. have already described a systematic approach
(reticular synthesis) based on the use of different dicarboxylic acids for the design
of open-framework structures with controlled pore sizes and functionalities [40].
   In this section we will review representative examples of magnetic nanoporous
coordination polymers. All these examples combine relevant magnetic properties
(the presence of strong magnetic exchange interactions and/or any type of mag-
netic ordering) and a contrasted porosity. First, examples of magnetic nanoporous
frameworks based on carboxylic ligands and different transition metal ions will be
reviewed. The second section will be devoted to metal-organic open-framework
structures based on N,N -ligands and the third to a new approach, developed in
our group, based on the use of paramagnetic organic radicals as polytopic ligands.


8.3.1   Carboxylic Ligands

Although 1,3,5-benzenetricarboxylic or trimesic acid (BTC) has been widely used
to obtain open framework structures, it was not until 1999 that Williams et al.
reported for the first time the magnetic properties of an open-framework struc-
ture based on the BTC ligand, the [Cu3 (BTC)2 (H2 O)3 ]n complex (referred to as
KHUST-1; see Figure 8.4) [41]. Structurally, KHUST-1 is composed of typical
paddle-wheel Cu(II) dimers connected by BTC ligands along the three crystallo-
graphic directions to create a three-dimensional network of channels with fourfold
symmetry and dimensions of 9 × 9 Å2 . Water molecules that fill the channels
can be easily removed at a temperature of 100 ◦ C without loss of structural in-
tegrity. Resulting voids give a surface area of 917.6 m2 g−1 , a calculated density
of 1.22 g cm−3 and an accessible porosity of nearly 41% of the total cell volume.
Interestingly, additional experiments with the non-hydrate KHUST-1 form showed
that it is possible to induce chemical functionalization without losing the overall
structural information.
   The structural porosity of KHUST-1 is accompanied by interesting magnetic
properties [42]. As shown in Figure 8.4, this porous coordination polymer shows a
minimum in its χ vs. T plot at around 70 K and an increase at lower temperatures.
Fitting to the Curie-Weiss law gave a Weiss constant of 4.7 K. This magnetic
behavior can be explained by the presence of strong antiferromagnetic interactions
within a Cu(II) dimer and weak ferromagnetic interactions between Cu(II) dimers.
                                8.3 Magnetic Nanoporous Coordination Polymers         267




Fig. 8.4. [Cu3 (BTC)2 (H2 O)3 ]n (HKUST) open-framework coordination polymer. (a) Paddle-
wheel CuII dimeric building-block. (b) Secondary building unit (nSBU). (c) Illustration of
the channel-like HKUST-1, showing nanochannels with fourfold symmetry. (d) Temperature
dependent magnetic susceptibility of as-synthesized HKUST-1 (•) and HKUST treated with
dry pyridine to give [Cu3 (BTC)2 (py)3 ]n ( ). (Reproduction with permission from [41] and
[42].)


   The paddle-wheel Cu(II) dimer motif (see Figure 8.5a) was also used by Za-
worotko et al. to obtain a molecular nanoporous Kagomé lattice [43]. In this case,
the authors proposed the use of such building blocks as molecular squares 120◦
linked by 1,3-benzenedicarboxylate ligands (BDC) to generate two different porous
frameworks, according to the self-assembly of the building units. The first of such
structures was: [(Cu2 (py)2 (BDC)2 )3 ]n [43], generated from the self-assembly of the
Cu(II) dimers with a triangular bowl-shaped topology to yield a Kagomé lattice
with hexagonal channels and dimensions of 9.1 Å (see Figure 8.5b). The second
structure [Cu2 (py)2 (BDC)2 ]n [44] was generated from the self-assembly of Cu(II)
dimers with a square bowl-shaped topology to give a two-dimensional network
with channels formed by narrowed windows (1.5 × 1.5 Å2 ) and large cavities with
maximum dimensions of about 9.0 × 9.0 × 6.5 Å3 (see Figure 8.5c).
268      8 Magnetic Nanoporous Molecular Materials




Fig. 8.5. Crystal structure of [(Cu2 (py)2 (BDC)2 )3 ]n and [(Cu2 (py)2 (BDC)2 )4 ]n . (a) Paddle-
wheel CuII dimeric building block. (b) A schematic representation of the triangular nSBU and
its arrangement in the Kagomé lattice, followed by a space-filling illustration of this open-
framework structure. (c) A schematic representation of the square nSBU and its arrangement in
the square lattice, followed by a space-filling view of this nanoporous structure. (Reproduction
with permission from [43] Wiley-VCH)



   As for KHUST-1, the Kagomé lattice shows a high rigidity in the absence of
solvent guest molecules and pyridine ligands, which can be removed at a temper-
ature of 200 ◦ C without loss of the crystalline character. From a magnetic point
of view, its most interesting feature is remnant magnetization [45]. Indeed, the χ
vs. T plot shows a maximum just below 300 K and a minimum at around 60 K,
increasing again at lower temperatures (see Figure 8.6). Fitting of magnetic data to
the Bleaney-Bowers model confirmed a strong intradimer antiferromagnetic inter-
action of −350 cm−1 , typical of discrete Cu(II) dimers [46], and weaker interdimer
antiferromagnetic interactions of −18 cm−1 . Even though interdimer interactions
are antiferromagnetic, their triangular lattice arrangement leads to a magnetic spin
frustration with a canted arrangement of spins and, therefore, to a geometrically
frustrated antiferromagnetic ordering. This is the origin of the unusual remnant
magnetization. In contrast, the two-dimensional framework with a square-like ar-
rangement of the dimeric units does not present any remnant magnetization due to
the lack of any geometrical frustration. In such a context, its magnetic behavior is
very similar to that observed for KHUST-1, with an intradimer antiferromagnetic
interaction of −380 cm−1 and interdimer interactions of −85 cm−1 .
                                   8.3 Magnetic Nanoporous Coordination Polymers              269




Fig. 8.6. Temperature dependence of the susceptibility (smooth line indicates the fitting to the
Bleaney-Bowers law) for (a) square [(Cu2 (py)2 (BDC)2 )4 ]n lattice and (c) triangular (Kagomé)
[(Cu2 (py)2 (BDC)2 )3 ]n lattice, respectively. Field-dependent magnetization for (b) square lat-
tice and (d) triangular lattice, respectively, showing the hysteresis loop for the latter. (Repro-
duction with permission from [45])


   Another rare example of spin-frustration is a vanadocarboxylate complex with
a magnetically frustrated framework described by Riou et al. [47]. Complex
[V(H2 O)]3 O(O2 CC6 H4 CO2 )3 ·(Cl·9H2 O) exhibits a three-dimensional framework
built up from octahedral vanadium trimers joined via the isophthalate anionic link-
ers to delimit cages where water molecules and chlorine atoms are occluded. Al-
though the trimeric clusters are connected along three directions, the 120◦ triangular
topology of V(III) ions in each cluster induces a spin-frustration of their magnetic
moments and, therefore, a lowering of the temperature for magnetic ordering.
   Finally, Kobayashi et al. have recently reported a 3-D nanoporous magnet
[Mn3 (HCOO)6 ]·(MeOH)·(H2 O) with a diamond framework containing bridging
formate ligands (see Figure 8.7) [48]. This is a short ligand with a small stereo
effect beneficial for the formation of coordination magnetic frameworks. The re-
sulting diamondoid framework exhibits one-dimensional channels of 4×5 Å2 (32%
of the total cell volume), where each node is occupied by a MnMn4 tetrahedral unit
270     8 Magnetic Nanoporous Molecular Materials

where the central Mn(II) ion is connected to four Mn(II) through six formate ligands
with one bidentate oxygen atom binding the central Mn(II) and one apical Mn(II)
and the other oxygen atom binding one neighbouring apical Mn(II) ion. This 3-D
network is thermally rigid up to 260 ◦ C, even after evacuation of guest molecules,
and exhibits a rich guest-modulated magnetic behavior. Indeed, magnetic measure-
ments of the as-synthesized or evacuated samples show characteristic ferrimagnetic




Fig. 8.7. [Mn3 (HCOO)6 ]·MeOH·H2 O diamantoid open-framework structure. (a) Mn-centered
MnMn4 tetrahedron. (b) Topological representation of the porous diamantoid framework
formed by the tetrahedral units as nodes sharing apices. (c) Temperature-dependent magnetic
susceptibility for as-synthesized and desolvated sample. ([48] – Reproduced by permission of
the Royal Society of Chemistry.)
                                  8.3 Magnetic Nanoporous Coordination Polymers             271

behavior and long-range magnetic ordering with critical temperatures close to 8 K.
Additional measurements of the magnetization (M) as a function of T indicate a
saturated magnetization close to 5 µB without a hysteresis loop, indicative of a soft
magnet. Fascinatingly, this critical temperature can be modulated at will from 5 to
10 K by the absorption of several kinds of guests molecules, thanks to the porosity
characteristics of this material.


8.3.2    Nitrogen-based Ligands

Although carboxylic ligands have been more extensively used, the use of polytopic
nitrogen-based ligands has also generated some nice examples of magnetic open-
framework structures. For instance, Kepert et al. recently reported a nanoporous
spin crossover coordination material based on the use of trans-4,4 -azopyridine
(azpy) as a ditopic ligand [49]. The crystal structure of the resulting complex
[Fe2 (azpy)4 (NCS)4 ·EtOH]n consists of double interpenetrated two-dimensional
grid layers built up by the linkage of Fe(II) ions by azpy ligands (see Figure 8.8). As
a result, two kinds of one-dimensional channels running in the same direction, filled
with ethanol molecules and exhibiting openings of 10.6 × 4.8 Å2 and 7.0 × 2.1 Å2 ,
are created. The evacuation of ethanol guest molecules takes place at 100 ◦ C and




Fig. 8.8. Schematic representation of the guest-dependent spin-crossover nanoporous
[Fe2 (azpy)4 (NCS)4 ·(EtOH)]n . X-ray crystal structures of the as-synthesized material at 150 K
and the evacuated sample at 375 K; and the temperature-dependent magnetic moment of (◦) the
as-synthesized [Fe2 (azpy)4 (NCS)4 ·(EtOH)]n , ( ) the evacuated [Fe2 (azpy)4 (NCS)4]n and
(♦) [Fe2 (azpy)4 (NCS)4 ·(1-PrOH)]n (evacuated structure exposed to 1-propanol). (Reprinted
with permission from [49]. Copyright 2002 AAAS.)
272     8 Magnetic Nanoporous Molecular Materials

is accompanied by several structural changes. The most significant modification
consists in an elongation and constriction of the one-dimensional channels, the
new dimensions being 11.7 × 2.0 Å2 . Furthermore, crystal changes by −6, +9,
+3% along the a, b and c axes, respectively, can also be macroscopically detected.
Interestingly, these structural modifications are accompanied by changes in the
macroscopic magnetic properties. The as-synthesized sample exhibits a constant
effective magnetic moment of 5.3 µB between 300 and 150 K. Below this temper-
ature, the magnetic moment decreases, reaching a constant value of 3.65 µB due to
a spin-crossover interconversion coming from a fraction of the Fe(II) ions. On the
contrary, the evacuated sample does not show spin-crossover behavior, exhibiting a
constant magnetic moment of around 5.1 µB , corresponding to two crystallographic
high-spin Fe(II) ions. Surprisingly, spin-crossover is recovered after re-absorption
of guest solvent molecules. Indeed, when an evacuated crystalline sample was im-
mersed in methanol, ethanol or propanol solvent, the magnetic properties were
similar to those observed for the as-synthesized sample.
    The use of the structural versatility of coordination polymers to obtain mag-
netic nanoporous molecular materials was once again demonstrated by You et al.
who reported a family of Co(II) imidazolates (im) complexes showing a variety of
open-framework structures with different magnetic behaviors [50]. In this case, the
rational use of solvents and counter-ligands plays a key role in obtaining a collection
of polymorphic three-dimensional nanoporous Co(II) structures: [Co(im)2 ·0.5py]n ,
[Co(im)2 ·0.5Ch]n , [Co(im)2 ]n , [Co(im)2 ]n and [Co5 (im)10 ·0.4Mb]n (where py, Ch
and Mb refer to pyridine, cyclohexanol and 3-methyl-1-butanol, respectively).
Complexes [Co(im)2·0.5py]n and [Co(im)2·0.5Ch]n are isostructural and formed
by Co(II) centers linked into boat- and chairlike six-membered rings connected in
an infinite diamond-like net. This conformation originates one-dimensional chan-
nels with dimensions 5.3 × 10.4 Å2 and 6.6 × 8.4 Å2 , respectively. The influence
of the reaction solvent and structure-directing agents was also evident in the other
three Co(II) imidazolate coordination polymers. The crystal structure of one of the
two compounds with formula [Co(im)2 ]n is formed by the self-assembly of four-
membered ring Co(II) units, which are doubly connected to wavelike or double
crankshaft-like chains. These chains intersect with those running along the per-
pendicular axis by means of the common four-rings at the wave peaks. Three such
frameworks are interwoven and linked by the imidazolates at the Co(II) ions. The
resulting 3-D framework shows one-dimensional helical channels with dimensions
3.5×3.5 Å2 . Similarly, the complex [Co(im)2 ]n is also formed by the self-assembly
of identical units connected into chains. These chains are linked to each other by the
imidazolate ligands along the other two directions to give a 3-D framework with a
pore opening of 4.0×4.0 Å2 . The fact that both structures crystallize in the absence
of solvent guest molecules gives them a highly structural rigidity up to 500 ◦ C. Of
special interest is the second complex [Co(im)2 ]n . In all polymorphous frameworks
the imidazolates transmit the antiferromagnetic coupling between the cobalt(II)
ions. However, the uncompensated antiferromagnetic couplings arising from spin-
                               8.3 Magnetic Nanoporous Coordination Polymers       273

canting phenomena are sensitive to the structures: compound [Co(im)2 ·0.5py]n is
an antiferromagnet with TN = 13.11 K; [Co(im)2 ·0.5Ch]n shows a very weak fer-
romagnetism below 15 K, [Co(im)2 ]n exhibits a relatively strong ferromagnetism
below 11.5 K and a coercive field (HC ) of 1800 Oe at 1.8 K, and [Co(im)2 ]n displays
the strongest ferromagnetism of the three cobalt imidazolates and demonstrates a
TC of 15.5 K with a coercive field, HC , of 7300 Oe at 1.8 K. However, compound
[Co5 (im)10 ·0.4MB]n seems to be a hidden canted antiferromagnet with a magnetic
ordering temperature of 10.6 K.


8.3.3   Paramagnetic Organic Polytopic Ligands

Magnetic coupling between transition metal ions in coordination polymers gener-
ally takes place through a superexchange mechanism involving the organic ligand
orbitals, a mechanism that is strongly dependent on their relative orientation and,
especially, on the distance between interacting ions. Therefore, the difficulty in
obtaining nanoporous materials with increasing pore size dimensions and simulta-
neous long-range magnetic properties remains a challenge. To overcome such in-
convenience, in our group we have developed a new efficient and reliable synthetic
strategy based on the combination of persistent polyfunctionalized organic radi-
cals, such as polytopic ligands, and magnetically active transition metal ions. The
resulting structures are expected to exhibit larger magnetic couplings and dimen-
sionalities in comparison with systems made up from diamagnetic polyfunctional
coordinating ligands, since the organic radical may act as a magnetic relay. This
so-called metal–radical approach [51] (combination of paramagnetic metal ions
and pure organic radicals as ligating sites) has already been used successfully by
several groups working in the field of molecular magnetism. However, even though
a large number of metal–radical systems have been studied, this is the first occasion
that this approach has been used to obtain magnetic nanoporous materials.
    Organic radical ligands must fulfil a series of conditions. Obviously, they must
have the correct geometry to induce the formation of open-framework structures.
Second, they must exhibit high chemical and thermal stability and, third, they
have to be able to interact magnetically with transition metal ions, which is an
indispensable condition to enhance the magnetic interactions of the nanoporous
material. To fulfil all three conditions we have chosen the tricarboxylic acid radical
(PTMTC) [52], shown in Figure 8.9.
    First, the conjugated base of the PTMTC radical can be considered as an ex-
panded version of the BTC ligand, where the benzene-1,3,5-triyl unit has been
replaced by an sp2 hybridised carbon atom decorated with three four-substituted
2,3,5,6-tetrachlorophenyl rings. Therefore, in accord with their related trigonal
symmetries and functionalities, PTMTC is also expected to yield similar open-
framework structures Second, polychlorinated triphenylmethyl (PTM) radicals
have their central carbon atom, where most of the spin density is localized, sterically
274     8 Magnetic Nanoporous Molecular Materials




                                                 Fig. 8.9. Plot and crystal structure of the
                                                 tricarboxylic perchlorotriphenylmethyl
                                                 radical (PTMTC).


shielded by encapsulation with six bulky chlorine atoms that increase astonishingly
the lifetime and thermal and chemical stability [53]. Third, a recently reported fam-
ily of monomeric complexes using a similar PTM radical with only one carboxylic
group (PTMMC) has confirmed the feasibility of this type of carboxylic-based
radicals to magnetically interact with metal ions [54].
   Following this strategy, we have recently reported the first example of a metal-
radical open-framework material [Cu3 (PTMTC)2 (py)6 (EtOH)2 (H2 O)] (referred to
as MOROF-1) that combines very large pores with magnetic ordering at low tem-
peratures [55]. As shown in Figure 8.10, crystal structure of MOROF-1 reveals a
two-dimensional honeycomb (6,3) network with the central methyl carbon of the
PTMTC ligand occupying each vertex, similar to those observed for some open-
frameworks obtained with the trigonal BTC ligand and a linear spacer [56]. In
our case, the linear spacer is composed of Cu(II) centers with a square pyramidal
coordination polyhedron formed by two monodentate carboxylic groups, two pyri-
dine ligands and one ethanol or water molecule. The correct arrangement of the
honeycomb planes leads to the presence of very large one-dimensional hexagonal
                                 8.3 Magnetic Nanoporous Coordination Polymers           275




Fig. 8.10. Illustration of the nanochannel-like structure of MOROF-1. The correct arrangement
of the honeycomb (6,3) layers creates large nanopores of dimensions 3.1 and 2.8 nm between
opposite vertices.


nanopores, each composed of a ring of six metal units and six PTMTC radicals,
which measure 3.1 and 2.8 nm between opposite vertices (see Figure 8.10). To
our knowledge, this is one of the largest nanopores reported for a metal–organic
open-framework structure. Moreover, complex MOROF-1 shows square and rect-
angular channels in a perpendicular direction with estimated sizes of 0.5 × 0.5 and
0.7 × 0.3 nm2 , respectively. Both pore systems give solvent-accessible voids in the
crystal structure that amount to 65% of the total unit cell volume.
   Paramagnetic Cu(II) ions are separated by long through-space distances of 15 Å
within the layers and 9 Å between them, for which non-magnetic coupling between
metal ions should be expected. However, each open-shell PTMTC ligand is able to
magnetically interact with all three coupled Cu(II) ions and, therefore, to extend
the magnetic interactions across the infinite layers. As shown in Figure 8.11, the
smooth decrease in the χ T value below 250 K is a clear sign of the presence of
antiferromagnetic coupling between nearest-neighbour Cu(II) ions and PTMTC
ligands within a 2-D layer. The minimum of χT corresponds to a short-range or-
276      8 Magnetic Nanoporous Molecular Materials




Fig. 8.11. (a) A honeycomb (6,3) layer showing the distribution of the copper ions (sphere)
and the central methyl carbon, which has the most spin density, of the PTMTC radicals (dark
sphere); (b) Value of χ T as a function of the temperature for as-synthesized (filled circle) and
evacuated (open circle) MOROF-1.


der state where the spins of adjacent magnetic centers are antiparallel, provided
that there is no net compensation due to the 3:2 stoichiometry of the Cu(II) ions
and PTMTC radical units. The huge increment in χT at lower temperatures indi-
cates an increase in the correlation length of antiferromagnetically coupled units of
Cu(II) and PTMTC as randomising thermal effects are reduced, either via in-plane
                                 8.3 Magnetic Nanoporous Coordination Polymers           277

long-range antiferromagnetic coupling and interplane dipolar–dipolar magnetic
interactions. The magnetization curve at 2 K exhibits a very rapid increase, as ex-
pected for a bulk magnet, although no significant hysteretic behavior was observed.
The magnetization value increases much more smoothly at higher fields up to a
saturation value of 1.2 µB , which is very close to that expected for an S = 1/2
magnetic ground state. Thus, this molecular material can be considered as a fer-
rimagnet with an overall magnetic ordering at low temperatures (∼2 K), which
shows the behavior of a soft magnet.
    A second remarkable feature is the reversible “shrinking–breathing” process ex-
perienced by MOROF-1 upon solvent uptake and release. Indeed, when MOROF-1
is removed from solution and exposed to air, the crystalline material loses ethanol
and water guest molecules very rapidly, even at room temperature within a few
seconds, becoming an amorphous material with a volume decrease of around 30%
(see Figure 8.12). Even more interesting, the evacuated sample of MOROF-1 ex-
periences a mechanical transformation, recovering its original crystallinity and up
to 90% of its original size after exposure to liquid or vapor EtOH solvent.




Fig. 8.12. Real images of a crystal of MOROF-1 followed with an optical microscope. The top
series represents the “shrinking” process, in which a crystal of MOROF-1 exposed to the air
exhibits a volume decrease of around 30%. In the down series, the same crystal exposed again
to ethanol liquid begins to swell. The scheme represents the structural changes of MOROF-1
in contact or not with ethanol or methanol solvent. (Reproduction with permission from [57].)
278     8 Magnetic Nanoporous Molecular Materials

   This chemical and structural reversibility is also accompanied by changes in the
magnetic properties that are macroscopically detected. Magnetic properties of an
evacuated amorphous sample of MOROF-1 show similar magnetic behavior to that
shown by the as-synthesized crystals of MOROF-1, with two main differences: (a)
the displacement of the χ T minima from 31 K for as-synthesized to 11 K for the
evacuated MOROF-1 samples and (b) the magnetic response of the filled MOROF-
1 sample at low temperature, where the long-range magnetic ordering is attained,
results in a much larger (up to one order of magnitude) magnetic response than
that of the evacuated MOROF-1 material. From these results it was inferred that
the effective strength of the magnetic interactions for the evacuated sample of
MOROF-1 was less than that observed for the as-synthesized crystals. Thus the
most striking feature exhibited by MOROF-1 is that the structural and chemical
evolution of the material in the process of solvent inclusion can be completely
monitored by the magnetic properties. When MOROF-1 is re-immersed in ethanol
solvent, a fast recovery up to 60% of the signal can be seen during the first minutes,
whereupon, the recovery of magnetic signal seems to be linear with the logarithm
of time (see Figure 8.13).



8.4 Summary and Perspectives

The use of organic ligands has been shown to be an efficient methodology for the
preparation of magnetic nanoporous materials due to the chemical versatility of
organic ligands, their capability to be good superexchange pathways for magnetic
coupling and the possibility of benefiting from crystal engineering techniques to
arrange transition metal ions within a wide variety of open-framework structures.
   The synergism of magnetic properties and nanoporous materials, together with
the molecular characteristics of coordination polymers, opens a new route to the de-
velopment of Multifunctional Molecular Materials. For instance, magnetic zeotype
structures offer excellent conditions to encapsulate different functional materials
with conducting, optical, chiral and NLO properties, among others. In consequence,
the resulting material combines the magnetic properties of the framework and the
inherent properties and applications of the protected functional molecules. Another
field of research where this type of material will have an enormous interest in the
near future is magnetic sensors. Throughout this chapter, different examples of
nanoporous materials whose magnetic properties can be modulated by the pres-
ence of guest molecules within the channels have been shown. From amongst them,
special mention of the complex MOROF-1 is deserved. The enhanced magnetic re-
sponse of a filled sample when compared to that exhibited by an evacuated sample
of MOROF-1, together with the reversible solvent-induced structural changes ex-
perienced by this sponge-like material, open the door to the possible development
8.4 Summary and Perspectives          279




Fig. 8.13. (a) Powder X-ray diffrac-
tograms (XRPD) of MOROF-1, show-
ing the steps of the transformation of the
amorphous, evacuated phase in contact
with ethanol vapor: a, amorphous phase;
b, 0; c, 4.5; d, 5; e, 6; f, 8; g, 10; h,
26; i, 28; j, 52 h. Inset, XRPD of the
as-synthesized MOROF-1. (b) and (c)
Reversible temperature-dependent χT
value behavior of the amorphous, evac-
uated phase in contact with ethanol liq-
uid at 1000 and 10,000 Oe, respectively.
(d) Reversible field-dependent magne-
tization of the amorphous, evacuated
phase in contact with ethanol liquid.
In (b), (c) and (d), amorphous phase
(open circle), amorphous phase in con-
tact with ethanol for 5 min ( ), 12 min
( ), 30 min ( ), 15 days ( ) and as-
synthesized MOROF-1 (filled circle).
280      8 Magnetic Nanoporous Molecular Materials

of magnetic sensors based on open-framework molecular magnets. Moreover, from
more than 15 different solvents so far used, including several alcohols, such re-
versible behavior has only been observed for EtOH and MeOH solvents; a fact that
enhances the selectivity of the sponge-like magnetic sensor. Also one can imagine
molecular (drug) delivering devices activated by external magnetic fields.
   But before all this potentiality becomes a reality, much work has to be done by
chemists in the near future to develop new synthetic methodologies that overcome
the inherent difficulties of this type of system: (1) the ultimate design is never
obvious; (2) the final products are often poorly crystallized and prevent one from
obtaining structural information; (3) the overall thermal stability is generally lim-
ited to the intrinsic thermal stability of the organic ligand and, therefore, is lower
than some inorganic-based porous materials like zeolites and (4) since “Nature
hates a vacuum”, many structures collapse in the absence of the guests.


Acknowledgments

We want to thank our collaborators in the development of magnetic nanoporous
molecular materials based on organic radicals, both in our institute (C. Rovira) and
abroad (K. Wurst from Innsbruck University and J. Tejada and N. Domingo from
UB).



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9 Magnetic Prussian Blue Analogs
     Michel Verdaguer and Gregory S. Girolami




9.1 Introduction

Magnetic solids have numerous and important technological applications: they
find wide use in information storage devices, microwave communications systems,
electric power transformers and dynamos, and high-fidelity speakers [1–3]. By far
the largest application of magnetic materials is in information storage media, and
the annual sales of computer diskettes, compact disks, optical disks, recording tape,
and related items exceed those of the celebrated semiconductor industry [3–5]. The
demand for higher bit-density information storage media and the emergence of new
technologies such as magneto-optic devices make it crucial to expand the search
for entirely new classes of magnetic materials [2, 3].
    In response to the increasing demands being placed on the performance of
magnetic solids, over the last decade or so there has been a surge of interest in
molecule-based magnets [6–20]. In such solids, discrete molecular building blocks
are assembled, with their structures intact, into 0-, 1-, 2-, or 3-dimensional arrays.
One of the attractive features of molecular magnets is that, by choosing appropriate
building blocks, the chemist can exert considerable control over the connectivity
and architecture as well as the resulting magnetic properties of the array. The local
exchange interactions, which can be specifically tailored through judicious choice
of appropriate molecular building blocks, dictate the bulk magnetic behavior of the
solid. By choosing molecular building blocks whose singly occupied molecular
orbitals (magnetic orbitals) are of specific symmetries, and by linking the building
blocks into arrays with favorable geometric relationships between the building
blocks, the synthetic chemist can exert powerful control over the properties of new
molecule-based magnetic materials.
    Although the high molecular weights and low bulk densities observed for essen-
tially all molecule-based magnets preclude their use as permanent magnets, they
are potentially useful as magnetic recording media [21] or quantum computing de-
vices [22]. More significantly, however, some molecule-based magnets exhibit bulk
properties quite unlike those of conventional magnetic solids. For example, some
are optically transparent, and others are non-magnetic in the dark but magnetic in
284     9 Magnetic Prussian Blue Analogs

the light. Until quite recently, the magnetic ordering temperatures of these unusual
solids were too low (<100 K) to make them of practical use. If room-temperature
molecule-based magnets could be discovered, however, they could serve as the
basis of entirely new magneto-optical technologies and be the keys to the develop-
ment of so-called “photonic” computers that use photons instead of electrons as the
information carriers [22–25]. The first room-temperature molecule-based magnet
was V(TCNE)2 ·xCH2 Cl2 an amorphous air-sensitive substance that decomposes
thermally at about 80 ◦ C [26]. The discovery of other room-temperature molecule-
based magnets with improved properties could lead to significant applications of
these unusual materials.
   In this context, Prussian Blues (PBs) and their analogs (which we will refer to
as PBAs) are an especially amazing and evergreen family of compounds. Recent
investigations of the chemistry and physical properties of PBs have stimulated an
astonishing rebirth of interest in the magnetism of complex solids, and a revival
of the chemistry of inorganic cyanide chemistry. Prussian Blues and their analogs
can easily be synthesized by the reaction of hexacyanometalates [B(CN)6 ]p− with
transition metal Lewis acids Aq+ in water to give neutral three-dimensional net-
works Ap [B(CN)6 ]q ·nH2 O. We shall see, however, that this apparent simplicity
can be misleading.
   After this introduction, we present in Section 2 a brief historical survey and
the general structure of PBs. In Section 3, we describe their magnetic properties
including theoretical models that allow one to predict and to understand the ex-
change interactions between adjacent spin centers in PB frameworks. In Section 4
we summarize some of our efforts and successes in synthesizing Magnetic Prussian
Blue (MPB) analogs with magnetic ordering temperatures (TC ) around or above
room temperature [27–39] and even above the boiling point of water [40, 41]. The
last part of this section describes possible applications of high TC PBs. Section 5
is devoted to new trends such as photomagnetic properties, tuning of the magneti-
sation, nanomagnetism and prospects in the context of a blossoming of cyanide
chemistry and molecular magnetism.



9.2 Prussian Blue Analogs (PBA), Brief History, Synthesis
    and Structure

In 1704 a Berlin draper named Diesbach discovered by chance a recipe to make
a new blue pigment useful for paints and fabrics. This discovery was reported
anonymously in 1710 [42] and the recipe itself was described in 1724 by Woodward
and Brown [43, 44]. This pigment, now called Prussian Blue (or Berlin Blue), was
the first synthetic coordination compound. The history of its discovery, and the
various theories about its nature and the origin of its bright colour, were reviewed
          9.2 Prussian Blue Analogs (PBA), Brief History, Synthesis and Structure            285

recently in the context of the development of chemical ideas in the 18th and 19th
centuries [45, 46]. A more complete history of this remarkable bright Blue pigment
is in preparation [47]. Information about its history is available in the very useful
book by Sharpe [48].


9.2.1    Formulation and Structure

The parent species Prussian Blue has the idealized formula FeII 4 [FeIII (CN)6 ]3 ·
14H2 O and a conventional unit cell shown in Figure 9.1a. Its stoichiometry is some-
times written as FeII [FeIII (CN)6 ]3/4 ·7/2H2 O. In fact, the formulae of Prussian Blue
and its analogs are often written in two different ways: as Mx A[B(CN)6 ]z ·nH2 O or
as M4x A4 [B(CN)6 ]4z 4(1−z) ·nH2 O, where M is an alkali metal cation [45, 46, 49,
50]. In the latter formulation (which is based on the conventional cell), the pres-
ence of the intrinsic vacancies and their amount per cell is easily seen; hereafter,
we will use both formulations, the choice depending on which feature we wish to
emphasize.
   For z = 1, the Prussian Blue solids adopt face-centered cubic (fcc) structures
(Figures 9.1b and c), as first proposed by Keggin and Miles [49], with unit cells
that comprise eight octants (the interiors of the octants are referred to as interstitial
or tetrahedral or cuboctahedral sites). There are two types of octahedral metal sites
in the fcc structure: strong ligand-field sites (C6 coordination environments) and
weak ligand-field sites (N6 coordination environments).
   For z < 1, and therefore for Prussian Blue itself, Keggin and Miles proposed that
the interstitial sites contained the “excess” A ions [49], but this suggestion was later
disproven by Ludi and coworkers [50–56], who proposed, from powder diffraction
data and density measurements, that the B sites are fractionally occupied, and that
the A centers surrounding the vacant sites have one (or more) water molecules in
their coordination spheres (Figure 9.1a). Zeolitic water molecules and/or charge




            (a)                                (b)                               (c)
Fig. 9.1. Three structures of cubic Prussian Blue analogs: (a) {A(II)}1 [B(III)(CN)6 ]2/3 ·nH2 O,
A1 B2/3 ; (b) A(III)[B(III)(CN)6 ], A1 B1 ; (c) Cs(I)A(II)[B(III)(CN)6 ], Cs1 A1 B1 .
286     9 Magnetic Prussian Blue Analogs

balancing cations generally occupy the interstitial sites; the hydrogen bond network
may help to stabilize the structure, as suggested by Beall et al. [57].
    The crystal structure of Prussian Blue FeIII [FeII (CN)6 ]3 ·14H2 O was determined
                                                4
by Buser, Ludi, and Güdel in 1972 from a single crystal obtained by slowly mix-
ing very dilute solutions of FeCl2 and K4 [Fe(CN)6 ] in concentrated hydrochloric
acid [55]. The most intense reflections suggest that the space group is F m3m, but
the actual space group (taking into account the weak reflections) is P m3m. Inter-
estingly, depending on the crystallization conditions, the [Fe(CN)6 ] vacancies are
either (i) disordered in the crystal, giving an apparent high-symmetry structure with
a fractional occupancy (3/4) of the [Fe(CN)6 ] sites or (ii) ordered, thereby lowering
the symmetry. An important structural point to keep in mind is that the presence of
vacancies is intrinsic to PBs whenever z < 1. It is not a “defect” structure as too
often claimed in the literature. Some important properties are determined by these
vacancies (see below).
    Ludi and Güdel summarized their findings in their beautiful review [50]. The
Prussian Blue structural framework is closely related to that of perovskites ABO3 ,
such as CaTiO3 , except that: (i) the octahedral metal centers are connected by
cyanide bridges instead of oxide ions to form the cubic framework, and (ii) the
[B(CN)6 ]p− units found in the solid are unchanged from the hexacyanometalate
reactant used in the synthesis. In other words, unlike the [TiIV O6 ]4− units in per-
ovskite, which are not stable in water, the [B(CN)6 ]p− units have an independent
existence in solution. Prussian Blue and its analogs can therefore be considered as
molecule-based materials, because they can be synthesized directly from prebuilt
molecular precursors.




                  (a)                                                  (b)
Fig. 9.2. Scheme of a [B(CN)6 ] vacancy in a Prussian Blue analog: (a) vacancy; (b) detail of
an octant with a vacancy and an alkali metal cation.
          9.2 Prussian Blue Analogs (PBA), Brief History, Synthesis and Structure        287

   In a “perfect” model of Prussian Blue, the A−N≡C−B unit is linear, and the
metal atoms in the A and B sites have perfect octahedral geometries. In fact, detailed
X-ray diffraction Rietveld analyses show that the [B(CN)6 ] units are often tilted,
as is often found for the [BO6 ] octahedra in the ABO3 perovskites. The tilting
results in A−N≡C angles that are less than 180◦ . Such distortions have important
consequences on the overlap of local wavefunctions and on the magnetic properties.




                       (a)                                                 (b)
Fig. 9.3. Schematic tilting of the octahedra in perovskites and Prussian Blue analogs.



   Prussian Blue is obtained by the addition of iron(III) salts to potassium hexa-
cyanoferrate(II); among the puzzling aspects of Prussian Blue was its relationship
to a similar substance known as Turnbull’s Blue, which was obtained by addition of
iron(II) salts to potassium hexacyanoferrate(III). The problem was solved by Möss-
bauer spectroscopy which revealed that the two compounds are actually identical:
very rapid electron-transfer between the iron(II) and the hexacyanoferrate(III) ions
gives rise to the same mixed-valence compound as before. The so-called “soluble
forms” of PB are actually colloïdal suspensions of Kx FeIII [FeII (CN)6 ]z ·nH2 O.
   Robin was the first to point out that the bright blue color of Prussian Blue is
due to an intervalence transition between the iron(II) and iron(III) centers [58].
Indeed, PB is a typical example of Robin and Day’s second class of mixed-valence
complexes: the valence is delocalized at high temperatures and localized at low
temperatures [59].
288      9 Magnetic Prussian Blue Analogs

9.2.2    Synthesis

The syntheses of compounds in the Prussian Blue family are simple, at first glance.
In one common recipe, an aqueous solution containing an [A(H2 O)]q+ cation is
added dropwise to an aqueous solution containing a [B(CN)6 ]p− anion. The stoi-
chiometry of the product will depend on the oxidation states of A and B and also on
the amount of charge-balancing alkali metal cations C+ that are incorporated into
the interstitial sites. If no alkali metal ions are incorporated, a neutral precipitate
is formed with stoichiometry A[B(CN)6 ]q/p ·nH2 O. For example, if an A2+ cation
is added to a potassium salt of a [BIII (CN)6 ]3− anion, one usually obtains a solid
of stoichiometry A[B(CN)6 ]2/3 ·4H2 O, which is often referred to as the 3:2 com-
pound A3 [B(CN)6 ]2 ·xH2 O where x ∼ 16. In contrast, if an A2+ cation is added
to a cesium salt of the [BIII (CN)6 ]3− anion, one usually obtains the 1:1 compound
CsA[B(CN)6 ]·xH2 O, where x ∼ 1. The different stoichiometries reflect the better
fit of the larger Cs+ cations in the interstitial sites of the fcc structure.
    Hexacyanometalate anions are known for many of the transition elements, and
thus Prussian Blue analogs can be prepared with a variety of metals in the B sites.
The paramagnetic derivatives of the first-row transition elements (i.e., excluding
the well-known derivatives of FeII and CoIII ) are as follows:
• [B(CN)6 ]4− is known for B = VII and MnII ;
• [B(CN)6 ]3− is known for B = TiIII , CrIII , MnIII , and FeIII
• [B(CN)6 ]2− is known only for B = MnIV
   The syntheses of some of these precursors have long been known, and others
were designed or improved for the purpose of obtaining magnetic Prussian Blues;
among the latter are [TiIII (CN)6 ] [33], [MnIV (CN)6 ] [34], and [CrIII (CN)6 ] [35],
[MoIII (CN)6 ]3− [199]. All of these species are low-spin owing to the large ligand
field splitting induced by the cyanide ligands, and the spins of these anions vary
from S = 1/2 for the TiIII , MnII , and FeIII derivatives, to S = 1 for the MnIII
derivative, to S = 3/2 for the VII , CrIII , and MnIV derivatives. It is advantageous
when these anions are kinetically inert (and indeed most of them are), so that the
cyanide ligands do not dissociate during the synthesis of the Prussian Blue phase.
The [B(CN)6 ]n− anions are Lewis bases. They may be treated with a large variety
of Lewis acids, particularly transition metal cations, to generate compounds in the
Prussian Blue family. Among the paramagnetic metallic ions that can be placed in
the A sites are VII , CrII , MnII , FeII , CoII , NiII , CuII , and FeIII . Generally, these ions
are added as aquated salts of weakly coordinating anions. When located in the A
sites, the paramagnetic ions generally remain high-spin because the N-coordinated
cyanide and water molecules are weak field ligands. Thus, the spins of the A ions
in Prussian Blue analogs range from S = 1/2 for CuII to S = 5/2 for MnII and
FeIII . Interestingly, in the case of CrII and CoII , low spin states can be adopted
when they are ligated by four or more N -bound cyanides [36]. In contrast to the
[B(CN)6 ] precursors, it is better for these A ions to be kinetically labile so that the
         9.2 Prussian Blue Analogs (PBA), Brief History, Synthesis and Structure    289

complexation with the nitrogen atoms of the [B(CN)6 ] anions is facilitated. Inert
ions such as CrIII are more difficult to incorporate into the A sites. Despite the
apparent simplicity of the syntheses, many complications can arise. For example,
some of the hexacyanometalate precursors are difficult to purify, and even when
pure salts are obtained, the [B(CN)6 ] anions may hydrolyze, oxidize, or dispropor-
tionate in solution before reacting with the A cation. Protecting the solutions from
air and keeping the solutions at 0 ◦ C sometimes helps to minimize these problems.
   The solid Prussian Blue analogs can also suffer from one or more of the following
problems:

1. The product may contain a variety of species in the interstitial sites. The Prussian
   Blue analogs behave like sponges and tend to fill the interstitial sites with solvent
   molecules or with the counterions used in the synthesis. Even the solvents used
   to wash the solid product can enter these sites. If these species are incorporated
   randomly into the interstitial sites, the resulting disruption of the regularity
   of the structure can lower the magnetic ordering temperature. It is sometimes
   helpful either to add an excess of an alkali metal cation so as to fill as many of
   the interstitial sites as possible with well-defined counterions, or to use starting
   materials with large counterions such as tetraalkylammonium cations and p-
   toluenesulfonate anions, so that water molecules are the only available species
   that are small enough to fit into the interstitial sites [40, 41].
2. The solid may be amorphous, poorly crystalline, or contain several phases.
   These problems relate to the kinetics and thermodynamics of the crystallization
   process. For example, in the series Mx Co[Fe(CN)6 ]z , where M is an alkali
   cation, the product consists of a single phase when M = Cs but two phases
   when M = Rb, K, or Na. The two phases in the latter salts differ in the chemical
   environments about the A sites, which lead to the cobalt atoms being high spin
   CoII in one phase, and low-spin CoIII in the other. The homogeneity of Prussian
   Blue analog powders must be carefully checked. The crystallinity and purity
   of the product can sometimes be improved by adding the reagents as slowly
   as possible, by changing the identity of the alkali metal cation, by diluting,
   by changing the reaction temperature, or by adjusting the pH. In some cases,
   carrying out the synthesis by slow diffusion in H tubes or in gels may be effective
   in improving the crystallinity of the solids, although hydrolysis of the [B(CN)6 ]
   anions may be a problem with slow-growth techniques. We have found that
   poorly crystalline materials are usually obtained from organic solvents, probably
   because the growth of the solid from solution is irreversible.
3. The water content may vary from sample to sample. The water content, espe-
   cially for compounds with a stoichiometry different from 1/1, is very dependent
   on the work-up and storage conditions. The amount of water can sometimes
   affect the magnetic properties.
4. The bridging cyanide ligands may undergo linkage isomerism [27, 36, 38]. This
   troublesome problem involves the two possible ways that cyanide can be linked
290     9 Magnetic Prussian Blue Analogs

   in a bimetallic or mixed valence compound: B−C≡N−A or B−N≡C−A. The
   extent of linkage isomerism depends strongly on the electronic structure of A and
   B, and is related to the change in ligand field stabilization energies that results.
   For example, linkage isomerism does not occur at all in CsMnII [CrIII (CN)6 ] but
   is easy in CsNiII [CrIII (CN)6 ]·2H2 O. The latter compound is pale gray when first
   prepared but turns yellow within days at room temperature due to the formation
   of square planar diamagnetic [NiII (CN)4 ]2− entities in the structure. Although
   in this case the linkage isomerism causes the nickel atoms to change from high-
   spin to low-spin, breaks up the 3D structure, and deeply changes the magnetic
   properties of the solid, in other cases linkage isomerism has only a small effect.
5. Intermetallic charge transfer and redox processes may occur. Prussian Blue itself
   is a good example of this phenomenon because it can be obtained either by treat-
   ment of [FeII (CN)6 ]4− with Fe3+ or by treatment of [FeIII (CN)6 ]3− with Fe2+ ; the
   latter reaction leads, after a very quick electron transfer, to the same compound,
   FeIII [FeII (CN)6 ]3 ·14H2 O. Ludi and Gudel observed that PB is also obtained in
      4
   air from [FeII (CN)6 ]4− and Fe2+ [55]. We observed that [FeIII (CN)6 ]3− is easily
   reduced and leads to solid state compounds contaning [FeII (CN)6 ]4− units. The
   photoinduced magnetism of some Prussian Blues also depends on an electron
   transfer process (see Section 9.4).

   We hope it is clear from the preceding discussion that Prussian Blue analogs
must be prepared very carefully to obtain pure samples with reproducible magnetic
properties.




9.3 Magnetic Prussian Blues (MPB)

Solids with the Prussian Blue structure are especially attractive as candidates for
new molecule-based magnets for several reasons: they can be prepared at room
temperature from well-characterized and chemically stable building blocks, the
metal centers are linked covalently into a 3D network, and a wide range of metals
with different spin states and oxidation states can be substituted into the structure.
Furthermore, the bridging cyanide ligands can promote strong magnetic exchange
couplings between paramagnetic centers. These features allow considerable con-
trol over the nature and magnitude of the local magnetic exchange interactions.
These features were recognized progressively in the past and we begin with a brief
historical survey.
                                            9.3 Magnetic Prussian Blues (MPB)        291

9.3.1   Brief Historical Survey of Magnetic Prussian Blues

The magnetic properties of Prussian Blue analogs were summarized in 1997 by
Dunbar et al. in a review on modern perspectives of the chemistry of metal cyanide
compounds [60]. We focus here on some complementary and critical aspects.
   In 1928, Davidson and Welo published the first magnetic investigation of the
parent species Prussian Blue; they measured the magnetic susceptibility at three
temperatures in the range 200–300 K [61]. This early work was followed by more
extensive studies of Prussian Blue and some analogs in 1940 [62], but it was not
until much later, in 1968, that Prussian Blue was shown to be a ferromagnet with
TC = 5.6 K [63]. The parallel alignment of the magnetic moments in Prussian Blue
was confirmed later by neutron diffraction [64] and polarized neutron diffraction
[65] recent accurate polarized neutrons experiments demonstrate weak but size-
able delocalization of the spin on the “diamagnetic” FeII centers (P. Day, work
in progress, May 2004). The rather low magnetic ordering temperature is a con-
sequence of the diamagnetism of half of the metal centers (the low-spin d6 FeII
centers, which occupy the strong ligand-field sites) so that the through-bond dis-
tance between high-spin d5 FeIII is 10.28 Å and the exchange coupling is very
weak. Mayoh and Day showed quantitatively that the ferromagnetism between the
high-spin Fe3+ ions is due to the admixture of the low-lying intervalence FeII -FeIII
excited state with the ground state [66].


               10.28Å
     Fe(III)-NC-Fe(II)-CN-Fe(III)
 Para S = 5/2   Dia       Para S = 5/2
                                         Fig. 9.4. FeIII –NC–FeII –CN–FeIII entities in
                                         Prussian Blue. Exchange interaction is very weak
                                         between two paramagnetic FeIII ions at more than
                                         10 Å.

   By preparing other metal-substituted analogs of Prussian Blue in which every
metal center is paramagnetic, however, the through-bond distance between nearest
spin centers is reduced from 10 Å to about 5 Å, and the exchange coupling should
be much stronger than it is in Prussian Blue itself. Such metal-substituted analogs
of Prussian Blue should have ordering temperatures much higher than 5.6 K, and
determining how high has been one of our goals.
   The first low temperature investigations of the magnetic properties of metal-
substituted analogs of Prussian Blue appeared in the 1950s. Bozorth et al. studied
a series of solids prepared by adding Mn2+ , Fe2+ , Fe3+ , Co2+ , Ni2+ , and Mn2+
to [FeIII (CN)6 ]3− ; selected reactions with [MnIII (CN)6 ]3− and [CrIII (CN)6 ]3− were
also performed [67]. Unfortunately, the solids prepared from the latter two anions
were not analyzed chemically, and the solids prepared from [FeIII (CN)6 ]3− were
shown to contain between 25 and 45% by weight of inert material (oxide, sulfate,
292                       9 Magnetic Prussian Blue Analogs

and potassium). Nevertheless, this paper is notable for the finding that some of
these solids had magnetic ordering temperatures between 3 and 50 K, the latter
being observed for a material prepared from Mn2+ and [MnIII (CN)6 ]3− . At about
the same time, Anderson et al. reported some similar (though less well documented)
findings [68], concluding that “certain of the complex cyanides of elements of the
3d transition group appear to be ferromagnetic at very low temperature”.
    In 1980, Trageser and Eysel oxidized Na3 [MnIII (CN)6 ] with perchloric acid
and obtained a brown–purple material formulated as MnII [MnIV (CN)6 ]·1.14H2 O
[69]. Magnetic studies carried out by Klenze and Kanellokopulos showed that the
compound is a ferrimagnet with an ordering temperature of 49 K. These work-
ers proposed a superexchange mechanism in which adjacent metal orbitals of π
symmetry communicated by means of both the filled π-orbitals and the empty π ∗
orbitals of the cyanide ligand. In the early 1980s, Babel investigated the magnetic
properties of a series of Prussian Blues analogs [70–74]. He obtained mainly para-
magnetic phases because either A or B in the CsA[B(CN)6 ]·nH2 O structure was
diamagnetic. In one case, however, Babel got a striking result: CsMnII [CrIII (CN)6 ]
was a ferrimagnet with a magnetic ordering temperature of 90 K (Figure 9.5).
    In a review paper [74], he reported on cyanocomplexes with different dimension-
alities and proposed that the exchange mechanism involved interactions through
the π and π ∗ orbitals of the cyanide ligand. By the late 1980s, no molecule-based
                      5                                                    200
                                                          CsNi[Co(CN)6]

                                                           CsZn[Cr(CN)6]
                      4
                                                                           150
Magnetisation / µ B




                                                          CsMn[Cr(CN)6]
                                                                                 χ M -1 / mol cm -3




                      3
                              CsMn[Cr(CN)6]                                100
                      2                                   CsCo[Co(CN)6]



                                                                           50
                      1                                   CsFe[Co(CN)6]
                                                          CsMn[Co(CN)6]


                      0                                                 0
                          0      50    100    150   200   250   300   350
                                               T/K
Fig. 9.5. Inverse of the molar susceptibility (right scale) vs. temperature in magnetic Prussian
Blues analogs CsI AII [BIII (CN)6 ], with A:B, 1:1 stoichiometry. A Curie law is observed when
only one of A and B is paramagnetic. A long-range magnetic order is observed at 90 K for
CsI MnII [CrIII (CN)6 ] whose magnetisation at low T is reported (left scale) (adapted from
Babel [66]).
                                               9.3 Magnetic Prussian Blues (MPB)          293

magnet of any kind had been reported with an ordering temperature higher than
90 K. At that time, our groups concluded that Prussian Blue magnets with signifi-
cantly higher ordering temperatures should be obtainable if a proper strategy could
be followed. We achieved the goal of obtaining Prussian Blues with high ordering
temperatures both by synthesizing many new members of this family and investi-
gating their low-temperature magnetic properties, and by better understanding the
factors that lead to larger magnetic couplings between adjacent spin centers. The
following sections summarize some of the exchange models used and the results
over the last twenty years. Our steps were very much inspired by the theoretical
model and the experimental results of the late Olivier Kahn.


9.3.2     Interplay between Models and Experiments

For any two interacting centers carrying spins S1 and S2 , the magnetic interaction
is described by the Hamiltonian H = −J S1 · S2 , where J is the strength of the
interaction. The spin of the ground state of the resulting coupled system will depend
on the magnitudes of S1 and S2 , and also on the sign of J . The possible spin
arrangements are shown in Figure 9.6.
   To obtain magnetic materials, we need to have a non-zero resultant spin. We
must avoid situation (a), in which two identical spins couple antiferromagnetically
(J < 0), giving a zero resulting spin. In case (b), a diamagnetic neighbor is present;
longer-ranged coupling between spin centers can occur (as in Prussian Blue itself),
but J and the ordering temperature will be small. In case (c), a ferromagnetic
interaction between nearest neighbors (J > 0) aligns the magnetic moments and
provides a long-range magnetic order. We shall see that ferromagnetic interactions
are rare in Prussian Blue analogs. Finally, case (d) represents a very appealing
situation, in which the usual antiferromagnetic interaction gives rise to a non-
zero resultant spin, if the two spins S1 and S2 are different in absolute value.
Unfortunately, the spin Hamiltonian does not provide insights into how to control
the sign or magnitude of J . For this, we needed to find the proper orbital strategy.


    JAF           JF                JF          JAF




  SA SB       SA SB = 0 SA       SA SB         SA SB
    (a)           (b)              (c)           (d)

Fig. 9.6. Spin arrangements in Prussian Blues: (a) antiferromagnetic interaction between iden-
tical neighboring spins; (b) ferromagnetic interaction through a diamagnetic neighbor (double
exchange in Prussian Blue); (c) ferromagnetic interaction between identical neighboring spins;
(d) antiferromagnetic interaction between different neighboring spins: ferrimagnetism.
294       9 Magnetic Prussian Blue Analogs

9.3.2.1     Mean Field, Ligand Field and Exchange Models
The most successful model for understanding the magnetic properties of insulating
magnetic solids is the “mean field model,” which was originally suggested by Weiss
and refined by Néel [76]. Here, we briefly give the basic elements of this model.
   Consider an insulating two-component magnetic solid AB in which A and B
are interpenetrating subnetworks, each of which consists of a set of identical spin
centers. The mean field model assumes that all the spins within each subnetwork are
oriented in the same direction. It further postulates that the interaction between the
two subnetworks A and B can be described by the molecular field coefficient W , and
that the interaction within each subnetwork can be described by the coefficients
WA and WB . The parameter W can be positive (for ferromagnetic interactions)
or negative (for antiferromagnetic interactions); the parameters WA , and WB are
always positive.
   The effective local magnetic fields HA and HB acting on the magnetic moments
of the sub-networks A and B are:

   HA = H0 + W MB + WA MA
   HB = H0 + W MA + WB MB                                                       (9.1)

where H0 is the applied field, and MA and MB are the mean magnetisations of
sub-networks A and B. At high temperatures, the magnetisations of subnetworks
A and B are proportional to the effective local field, so that:

   MA = [H0 + W MB + αW MA ] · CA /T
   MB = [H0 + W MA + βW MB ] · CB /T                                            (9.2)

where CA and CB are the Curie constants of the spins constituting sub-networks
A and B, respectively, and where α = WA /W and β = WB /W . Solving these
equations for MA and MB , and then calculating the magnetic susceptibility χ from
the definition χ = (MA + MB )/H0 gives the following expression:

            (T − θa )      γ
   1/χ =              −                                                         (9.3)
               C        (T − θ )
where the parameters C, θ , θa , and γ are functions of CA , CB , W , α, and β (see
Ref. 75 for the exact form of these functions).
   The mean field model has not been extensively used for ferromagnets, where
fluctuations in the mean field restrict the analysis to the high temperature range
and impede analysis of the data close to the magnetic ordering temperature, but
the model is well adapted for ferrimagnets (antiferromagnetic interactions between
the A and B subnetworks). For such solids, the mean field model predicts that the
plot of 1/χ vs. T at high temperatures should be hyperbolic, and this curve is often
referred to as a Néel hyperbola.
                                           9.3 Magnetic Prussian Blues (MPB)     295

  For a magnetic solid consisting of an array of identical S = 1/2 centers, the
magnetisation at low temperature is given by:
  M = Nµ tanh[µH /kT ]                                                         (9.4)
where N is Avogadro’s constant, µ is the magnetic moment, H is the local magnetic
field, and k is Boltzmann’s constant. More generally, for the case in which the solid
consists of two subnetworks A and B whose constituent spin centers have spins
SA and SB and g values gA and gB , respectively, the magnetisation within the A
subnetwork is (β, Bohr magneton):
  MA = NgA βSA BS [gA SA β(H + hA )/kT ]                                       (9.5)
where hA = W (εMB + αMA ), BS is the Brillouin function (with its argument in
square brackets), and ε equals 1 if W is positive and −1 if W is negative. To obtain
this expression, we have assumed that the applied field is negligible compared to the
mean field (so that the mean field dominates). We can obtain a similar expression
for MB ; the total magnetisation M is equal to (MA + εMB ).
   Solving the system of two equations for MA and MB (which is usually done
numerically rather than analytically) and finding the total magnetisation as a func-
tion of temperature gives magnetisation curves that depend on the details of the
exact system studied: the results depend on the nature of A and B, on the fraction
of occupied sites, on the parameters α and β, and, for ferrimagnetic systems, on
the parameters x = µA /µB and y = nA /nB , where µA and µB are the magnetic
moments on A and B, and nA and nB are the number of atoms A and B in the
unit considered. Depending on the values of x and y, Néel predicted very different
shapes for magnetisation curves M(T ) including some that change sign at a certain
temperature (called the “compensation temperature”) at which the magnetisations
of the sub-networks A and B are exactly equal and opposite in direction [75]. The
model was used in a predictive and clever way by Okhoshi et al. in their studies
of the compensation points in the magnetisation curves of polymetallic magnetic
Prussian Blues (see Section 9.5.2).
   The ideas developed by Néel in his 1948 paper [75] (see also Herpin [76] and
Goodenough [77]) within the frame of mean field theory to interpret the magnetism
of perovskite ferrimagnets ABO3 are fully valid for MPBs. In particular, the ex-
pression for the susceptibility close to the ordering temperature TC can be used to
extract the following very useful relation:
  kTC = Z|J | CA CB /NA g 2 β 2                                                (9.6)
where Z is the number of magnetic neighbors, |J | is the absolute value of the
exchange interaction between A and B, CA and CB are the Curie constants of A
and B, weighted by the stoichiometry, NA is Avogadro’s constant, g is a mean
Lande factor for A and B, and β is the Bohr magneton. Equation (6) clearly shows
that TC can be maximized by increasing the number of magnetic neighbors, by
increasing the magnitude of J , and by increasing CA and CB . For the Prussian
296     9 Magnetic Prussian Blue Analogs

Blues of stoichiometry Mx A[B(CN)6 ]z ·nH2 O, we can follow several strategies to
maximize TC :

• Maximize Z by controlling the Prussian Blue stoichiometry. The number of
  nearest neighbors Z is dictated by the value of z in the Prussian Blue formula.
  In Prussian Blues with a 1:1 A:B stoichiometry (i.e., lacking vacancies in the
  [B(CN)6 ] sites), the number of nearest neighbors Z adopts its maximum possible
  value of 6. In the frequently encountered 3:2 A:B systems (in which z = 2/3
  and one-third of the B sites are vacant), the number of nearest neighbors Z is
  only 4. As the number of vacancies in the MPB structure decreases, TC becomes
  larger. We shall use these conclusions later.
• Maximize |J | by changing the identities of the spin centers A and B in the two
  subnetworks. We develop this point in the following paragraph.
• Maximize the Curie constants CA and CB by proper choice of the metals A and
  B. This approach to maximize TC proves to be less useful than the other two, as
  we shall see.


Ligand field model
In Prussian Blue magnets, the exchange mechanisms that dictate the magnitude
of J involve the delocalization of spin from the metal centers onto the cyanide
bridges. The extent of spin delocalization is readily explicable in terms of ligand
field theory.
   In the idealized Prussian Blue structure of stoichiometry Mx A[B(CN)6 ]z ·H2 O,
each B atom is surrounded by the carbon atoms of six cyanide ligands and will
always experience a large ligand field (with very large octahedral splitting). As a
result, the B atoms will be low spin with unpaired electrons (if any) only in the t2g
orbitals (Figure 9.7a). It may be noted that the octahedral is sufficiently large (and
the antibonding orbitals e∗ so high in energy) that no [B(CN)6 ] complex exists with
                           g
more than six d-electrons: such complexes are not stable. In contrast, the A atom is
surrounded by the nitrogen atoms of six cyanide ligands (when the stoichiometry
is z = 1), or by four cyanides and two water molecules (when the stoichiometry
is z = 2/3). The A atoms thus experience weak ligand fields, and are usually
high-spin (Figure 9.7b and c), although in a few cases [CrII , MnIII , CoII , see below]
the A atoms can be low-spin.
   Because cyanide is a moderate σ -donor, a weak π-donor, and a moderate π-
acceptor, spin delocalization can occur by means of both σ and π mechanisms.
The nitrogen pz orbital mixes with the dz2 orbital of the A ion to which it is directly
attached (σ symmetry), and the nitrogen px and py orbitals mix with the dxz and
dyz orbitals of the A ion (π symmetry). The singly occupied orbitals (or magnetic
orbitals) on both metals are sketched in Figure 9.7: φ(t2g ) magnetic orbitals on the
B site, and either φ(t2g ) or φ ∗ (eg ) magnetic orbitals (or both) on the A site. The
dotted lines represent the nodal surface of the orbitals on the internuclear axis.
                                                9.3 Magnetic Prussian Blues (MPB)          297




Fig. 9.7. Local magnetic orbitals in an isolated (NC)5 –B–CN–A(NC)5 binuclear unit: (a) φ(t2g )
magnetic orbitals in B(CN)6 ; (b) φ(t2g ) magnetic orbitals in A(NC)6 ; (c) φ ∗ (eg ) magnetic
orbitals in A(NC)6 .

   Previous experimental studies of paramagnetic molecules containing C-bonded
cyanide ligands show that there is a small spin density on the carbon atom but
a larger spin density on the nitrogen atom. Figure 9.7a closely follows the spin
density maps obtained from polarized spin neutron diffraction [78] and solid state
paramagnetic NMR studies [79] of [BIII (CN)6 ] salts (B= Fe, Cr). From this simple
ligand field analysis, it is possible to draw an important conclusion about the
exchange: the empty π ∗ orbitals of the cyanide ligands play an important role in the
antiferromagnetic exchange interactions in Prussian Blue analogs. Consequently,
we predicted that substituting into the structure metals that have single electrons
in high-energy (and more radially expanded) t2g orbitals should afford Prussian
Blues with higher magnetic ordering temperatures. Higher-energy d-orbitals are
characteristic of the early transition metals in lower oxidation states, owing to the
lower effective nuclear charges of these elements. Accordingly, building blocks
such as aquated salts of VII and CrII , and hexacyanometalate derivatives of VII ,
CrII , and CrIII , should afford Prussian Blue compounds with much higher magnetic
ordering temperatures.

Orbital symmetry and the nature of the magnetic exchange coupling
The relationship between the symmetry of the singly-occupied orbitals on two
adjacent spin carriers and the nature of the resulting magnetic exchange interaction
is one of the most useful concepts available to the synthetic chemist interested in
designing molecule-based magnetic systems with specifically tailored magnetic
properties [6–8, 19, 80].
   To predict the value of |J |, two different approaches have been used: Kahn’s
model, in which the magnetic orbitals are non-orthogonalized, and Hoffmann’s ap-
proach, in which the magnetic orbitals are orthogonalized. Both models predict that
orthogonal orbitals give rise to ferromagnetism and that non-orthogonal orbitals
give rise to antiferromagnetism.
   Consider the case of two electrons residing in two identical orbitals a and b on
two adjacent sites. In Kahn’s model [7, 81–83], the singlet-triplet energy gap, J
298      9 Magnetic Prussian Blue Analogs

(= Esinglet − Etriplet ), is given by:
   J = 2k + 4βS                                                                  (9.7a)
where k is the two-electron exchange integral (positive) between the two non-
orthogonalized magnetic orbitals a and b; β is the corresponding monoelectronic
resonance or transfer integral (negative), and S is the monoelectronic overlap inte-
gral (positive) between a and b. In Hoffmann’s model [84], J is given by:
   J = 2Kab − (E1 − E2 )2 /(Jaa − Jab )                                          (9.7b)
where Kab is the two-electron exchange integral (positive) between two identical
orthogonalized magnetic orbitals a and b ; (E1 − E2 ) is the energy gap between
the molecular orbitals 1 and 2 built from a and b , Jaa is the bielectronic inter-
electronic repulsion on one centre, and Jab the equivalent on two centres. In both
Eqs. (9.7a) and (9.7b), the first term is positive and the second term is negative; thus
J can be represented as the sum of two components, a positive term JF that favors
a parallel alignment of the spins and ferromagnetism, and a negative term JAF that
favors an antiparallel alignment of the spins and short-range antiferromagnetism.
   J = JF + JAF                                                                  (9.7c)
When the two a and b orbitals are different, no rigorous analytical treatment is
available, but a semi-empirical relation was proposed by Kahn [85]:
   J = 2k + 2S(       2
                          − δ 2 )1/2                                              (9.8)
where δ is the energy gap between the (unmixed) a and b orbitals, and is the
energy gap between the molecular orbitals built from them.
   When several electrons are present on each centre, nA on one side, nB on the
other, J can be described as the sum of the different “orbital pathways” Jµν ,
weighted by the number of electrons [86]:

   J =          Jµν /nA nB                                                        (9.9)
           µν

where µ varies from 1 to nA and ν varies from 1 to nB .
   When only one electron is present per site, the situation is simple: a short-
range ferromagnetic interaction leads to a triplet ground state [86]; a short-range
antiferromagnetic interaction leads to a singlet ground state. When each site bears
a different number of electrons, the short-range ferromagnetic coupling leads to a
total spin ground state which is the sum of the spins: ST = SA + SB ; the short-range
antiferromagnetic coupling leads to a total spin ground state which is the difference
of the spins: ST = |SA − SB |. Figure 9.6 illustrates these situations. A key point is
that antiferromagnetism between two neighbors bearing different spins leads to a
non-zero spin in the ground state. For a bulk solid [75], this situation is known as
ferrimagnetism.
                                           9.3 Magnetic Prussian Blues (MPB)       299

9.3.2.2    Application to Magnetic Prussian Blue Analogs
The Prussian Blues are excellent “textbook” examples of the use of symmetry to
analyze the exchange interactions in magnetic solids, because their cubic structures
greatly simplify the analysis. Furthermore, magnetic exchange is a short-range
phenomenon, and thus we can neglect interactions with second nearest neighbors
(which are more than 10 Å away) and with more distant magnetic centers, and
consider only the interactions between adjacent metal atoms. The analysis thus
reduces to a consideration of the exchange interactions present between two metal
centers connected by a cyanide linkage: i.e., in a (CN)5 A−N≡C−B(CN)5 subunit
(Scheme 9.1).


           CN                     NC

                                                             x
                CN                    NC
NC         M'        C   N        M        NC                    z
      NC                     CN                          y

           CN                     NC                                 Scheme 9.1


    Suppose that the two adjacent metal centers each carries a single unpaired elec-
tron in a d-orbital (we will refer to such orbitals as “magnetic orbitals” after Kahn).
If the two magnetic orbitals are orthogonal, then the ground state of the system has
parallel electron spins. In contrast, if the two magnetic orbitals are not orthogonal,
then the ground state of the system generally has antiparallel electron spins. In
other words, orthogonal orbitals lead to local ferromagnetic interactions whereas
non-orthogonal orbitals favor local antiferromagnetic interactions. The behavior
is simply a two-site analog of Hund’s rule, and has the same quantum mechanical
origin.
    For systems in which the interacting magnetic centers each contain several
magnetic orbitals, or that consist of arrays of many spin centers, the symmetry
relationship between each magnetic orbital on one spin carrier must be considered
with respect to the various magnetic orbitals on the adjacent spin carriers. Mutu-
ally orthogonal magnetic orbitals will contribute to the ferromagnetic exchange
term, whereas non-orthogonal magnetic orbitals will contribute to the antiferro-
magnetic term. The net interaction is simply the sum of all the ferromagnetic and
antiferromagnetic contributions.
    In a Prussian Blue compound, the A and B centers are octahedral and connected
together by nearly linear A−N≡C−B cyanide bridges. (Even when this linkage is
somewhat non-linear, the basic conclusions remain unchanged.) The B atom, which
is surrounded by the carbon atoms of six cyanide ligands, is in a large ligand field.
As a result, all known [B(CN)6 ] units are invariably low spin and have electrons
300       9 Magnetic Prussian Blue Analogs

only in the t2g orbitals. In contrast, the A atom, which is surrounded by nitrogen
atoms of cyanide ligands or oxygen from water molecules, is in a weak ligand
field and is almost always high-spin. For the A atoms, it is possible for unpaired
electrons to be present only in the t2g orbitals (for d2 or d3 ions), only in the eg
orbitals (for d8 and d9 ions), or in both the t2g and eg orbitals (for d4 through d7
ions).
   For the Prussian Blues, therefore, three situations arise:
1. When only eg magnetic orbitals are present on A, all the exchange interactions
   with the t2g magnetic orbitals present on [B(CN)6 ] will be ferromagnetic. Thus,
   if a Prussian Blue is prepared by adding a d8 or d9 A cation such as NiII or CuII to a
   paramagnetic [B(CN)6 ] anion, a ferromagnet should result. The accuracy of this
   analysis was illustrated by the preparation in 1991 of NiII [FeIII (CN)6 ]3 ·xH2 O
                                                                  2
   and CuII 2[FeIII (CN)6 ]3 ·xH2 O, both of which are ferromagnetic as predicted
   [87].
2. When only t2g magnetic orbitals are present on A, all the exchange interactions
   with the t2g magnetic orbitals present on [B(CN)6 ] will be antiferromagnetic.
   In this case, if the Prussian Blue is prepared by adding a d2 or d3 cation to
   a paramagnetic [B(CN)6 ] anion, a ferrimagnet should result. The first such
   compounds were described in 1995 [29] and will be discussed below.
3. When both t2g and eg magnetic orbitals are simultaneously present on A, fer-
   romagnetic and antiferromagnetic interactions with the t2g magnetic orbitals
   on [B(CN)6 ] coexist and compete. Here, the overall nature of the interaction
   is not so simple to predict. Usually, the antiferromagnetic interactions dom-
   inate and the solid orders ferrimagnetically. For example, Babel’s compound
   CsMnII [CrIII (CN)6 ]·xH2 O falls into this class and is ferrimagnetic. But this may
   not always be the case, FeII [CrIII (CN)6 ]2 ·xH2 O and CoII [CrIII (CN)6 ]2 ·xH2 O are
                               3                               3
   ferromagnetic with low TC s and weak exchange interaction.


9.3.2.3     Molecular Orbital Analysis
Semi-empirical extended Hückel calculations have afforded detailed informa-
tion about the high energy molecular orbitals directly related to exchange in the
(CN)5 A−N≡C−B(CN)5 units. Typical molecular orbitals constructed from linear
combinations of the magnetic φ(t2g ) orbitals appear in Figure 9.8 (for clarity, our
graphical representation exaggerates the amount of A–B mixing):
  bonding:     ϕ1 = λ+ φt2g (B) + µ+ φt2g (A) (λ+               µ+ )             (9.10a)
  antibonding: ϕ2 = λ− φt2g (B) − µ− φt2g (A) (λ−               µ− )             (9.10b)
The precise contribution of each atomic orbital to these MOs depends on their
energies and radial extensions. Nevertheless, the importance of the participation of
the cyanide bridge in the exchange phenomenon is clearly apparent.
                                                  9.3 Magnetic Prussian Blues (MPB)           301

    Before mixing, the energy difference between the magnetic orbitals φ(t2g )(A)
and φ(t2g )(B) is δ; after mixing the energy gap between ϕ2 and ϕ1 is . The dotted
lines display the nodal surfaces in the orbitals along the internuclear axis: there is
one nodal surface in the bonding orbital, and two in the antibonding orbital.
    The situation in the case of orthogonal φ(t2g )(B) orbitals and φ(eg )(A) orbitals
is shown in Figure 9.9a. In the insert (Figure 9.9b), we emphasize the spin density
borne by the nitrogen in the two orthogonal py and pz orbitals. The overlap density
ρ, which is given by the expression:

   ρ = φ(t2g )(B) · φ(eg )(A)                                                              (9.11)

is strong on the nitrogen and, from this situation, we expect a strong ferromagnetic
interaction because the exchange integral k is proportional to ρ 2 [86]. In all the
cases, Figures 9.8 and 9.9 display the triplet electronic configuration.
    The conclusions from Figures 9.8 and 9.9 are straightforward: the t2g (B)–eg (A)
pathways lead to ferromagnetic (F) interactions, the magnitude of which is expected
to be significant, owing to the electronic structure of the cyanide bridge and the


               y
   E
                    z                                           ϕ2

            B C N
    t2g                      δ      ∆                      y

                                                                    z

    ϕ1
                                            CN     A
                                                                t2g

Fig. 9.8. Molecular orbitals ϕ1 and ϕ2 built from φ(t2g ) magnetic orbitals in the (NC)5 –B–
CN–A(NC)5 binuclear unit.


   E           y              (a)
                                                       y
                   z


                                                                        z
            B C N
    t2g                                     C N A
                             (b)
                                                               eg
                         C              N

Fig. 9.9. Orthogonal magnetic orbitals in the (NC)5 –B–CN–A(NC)5 binuclear unit: (a) Or-
thogonal φ(t2g ) (B) and φ(eg ) (A) orbitals left unchanged in the binuclear unit; (b) Insert: spin
density in two orthogonal p orbitals of nitrogen (py and pz ).
302       9 Magnetic Prussian Blue Analogs

special role of nitrogen; the t2g (B)–t2g (A) pathways lead to antiferromagnetic (AF)
interactions; as the ( − δ) gap becomes larger, so does |J |.


9.3.2.4     Experimental Answers
We can use this orbital analysis to predict the nature of the interaction be-
tween various paramagnetic cations with a representative hexacyanometalate ion,
[CrIII (CN)6 ], in which the octahedral CrIII center is spin 3/2 with a (t2g )3 electronic
configuration. The number and the nature of the exchange pathways are represented
in Figure 9.10 and summarized in Table 9.1 for known divalent cations AII of the
first period of the transition elements, from VII to CuII .


Table 9.1. Curie temperatures as a function of A in AII [CrIII (CN)6 ]2/3 ·xH2 O.

 AII ion                     V      Cr     Mn    Fe   Co    Ni    Cu
 Configuration dn            d3     d4     d5    d6   d7    d8    d9
 Nature of the transitiona   AF     AF     AF    F    F     F     F
 TC /K                       330    240    66    16   23    60    66
a AF = ferrimagnetic, F = ferromagnetic.



   A simple overlap model predicts that A ions with d3 through d7 configurations
should couple antiferromagnetically, and those with d8 and d9 configuations should
couple ferromagnetically. As Table 9.1 shows, this prediction holds true except for
A = Fe and Co; the reasons for these exceptions will be discussed below.
   If we now look at the results given in Figure 9.11 and Table 9.2 (including Ref.
[88–94]), we can check other aspects of the theoretical predictions given above.
   To begin, comparisons between two particular compounds are especially in-
teresting: Babel’s CsMnII [CrIII (CN)6 ]·H2 O is a ferrimagnet with TC = 90 K, and
Gadet’s compound CsNiII [CrIII (CN)6 ]·H2 O is a ferromagnet with the same order-
ing temperature. The TC values are relatively high for molecule-based magnets,
and this fact supports the conclusions of Figure 9.9 about the strength of ferro-
magnetic pathways. If the J values for the Ni and Mn derivatives are evaluated
from formulae (9.1) and (9.4), we find that, if everything is equal, JCrNi ≈ 2|JCrMn |
and that jF , the mean coupling of a single ferromagnetic orbital pathway, and jAF ,
the corresponding antiferromagnetic coupling, are roughly equal in absolute value.
Similar conclusions about the importance of ferromagnetic pathways can be drawn
from the study of discrete molecular analogs of Prussian Blues, for which J values
can be computed using analytical expressions [95].
   It is also interesting to compare the TC values of Babel’s and Gadet’s compounds
(which have six magnetic neighbors) with the ordering temperatures of related
A1 B2/3 systems with the same A and B pairs but with four magnetic neighbors.
                                                       9.3 Magnetic Prussian Blues (MPB)                 303

Table 9.2. Curie temperatures TC of Prussian Blue analogs.
 Compound                                      Ordering    TC /K     Ref.
 Cx A1 [B(CN)6 ]z ·nH2 Oa                      Nature
 K1 VII 1 [CrIII (CN)6 ]1                      Ferri       376       40
 VII 1 [CrIII (CN)6 ]0.86 ·2.8H2 O             Ferri       372       88
 K0.5 V1 [Cr(CN)6 ]0.95 ·1.7H2 O               Ferri       350       88
 Cs0.8 V1 [Cr(CN)6 ]0.94 ·1.7H2 O              Ferri       337       40
 VII 1 [CrIII (CN)6 ]2/3 ·3.5H2 O              Ferri       330       40
 V1 [CrIII (CN)6 ]0.86 ·2.8H2 O                Ferri       315       29
 CrII 1 [CrIII (CN)6 ]2/3 ·10/3H2 O            Ferri       240       28
 (Et4 N)0.4 MnII 1 [VII (CN)5 ]4/5 ·6.4 H2 O   Ferri       230       31
 Cs2/3 CrII 1 [Cr(CN)6 ]8/9 ·40/9H2 O          Ferri       190       28
 Cs2 MnII 1 [VII (CN)6 ]1                      Ferri       125       31
 (VIV O)1 [CrIII (CN)6 ]2/3 ·4.5H2 O           Ferri       115       89
 Cs1 MnII 1 [CrIII (CN)6 ]1                    Ferri       90        70
 Cs1 NiII 1 [CrIII (CN)6 ]1 ·2–4H2 O           Ferro       90        27
 MnII 1 [CrIII (CN)6 ]2/3 ·5–6H2 O             Ferri       66        36
 CuII 1 [CrIII (CN)6 ]2/3 ·5–6H2 O             Ferro       66        36
 NiII 1 [CrIII (CN)6 ]2/3 ·4H2 O               Ferro       53        27
 (NMe4 )MnII [CrIII (CN)6 ]                    Ferri       59        74
 MnII 1 [MnIV (CN)6 ]1                         Ferri       49        69
 CsNiII 1 [MnIII (CN)6 ]1 ·H2 O                Ferro       42        32
 K2 MnII 1 [MnII (CN)6 ]1 ·0.5H2 O             Ferri       41        30
 CoII 3 [CoII (CN)5 ]2 ·8H2 O                  Ferri       38        90
 MnII 1 [MnIII (CN)6 ]2/3 ·4H2 O               Ferri       37        30
 Cs1 MnII 1 [MnIII (CN)6 ]1 ·0.5H2 O           Ferri       31/27     30
 MnIII 1 [MnIII (CN)6 ]1                       Ferri       31        91
 NiII 1 [MnIII (CN)6 ]2/3 ·12H2 O              Ferro       30        32
 MnIII 1 [MnII (CN)6 ]2/3 ·solvent             Ferri       29        91
 (Me4 N)MnII [MnIII (CN)6 ]                    Ferri       28.5      70
 VIII 1 [MnIII (CN)6 ]1                        Ferri       28        91
 CoII 1 [CrIII (CN)6 ]2/3 ·4H2 O               Ferro       23        36
 NiII 1 [FeIII (CN)6 ]2/3 ·nH2 O               Ferro       23        92
 CrIII 1 [MnIII (CN)6 ]1                       Ferri       22        91
 CuII 1 [FeIII (CN)6 ]2/3 ·nH2 O               Ferro       20        87
 CoII 1 [CrIII (CN)6 ]2/3 ·nH2 O               Ferro       19        36
 FeII 1 [CrIII (CN)6 ]2/3 ·4H2 O               Ferro       16        36
 CoII 1 [FeIII (CN)6 ]2/3 ·nH2 O               Ferri       14        87
 CrII 1 [NiII 2 (CN)4 ]2/3 ·nH2 O              Ferri       12        93
 MnII 1 [FeIII (CN)6 ]2/3 ·nH2 O               Ferri       9         87
 FeIII 1 [FeII (CN)6 ]3/4 ·3.7H2 O             Ferro       5.6       94
a The formulae given were adapted from the literature to be related to one A cation – A [B(CN) ] ·nH O.
                                                                                       1      6 z   2
We did not include explicitly the vacancies A1 [BIII (CN)6 ]z 1−z ·nH2 O. In the references the same
compound is given different formulations. If we chose for example nickel(II) hexacyanoferrate(III),
one can find: NiII 3 [FeIII (CN)6 ]2 1 ·nH2 O, the simplest formula that indicates the neutral character
of the precipitate but is not related to a special structural entity; NiII 4 [FeIII (CN)6 ]8/3 4/3 ·4n/3H2 O,
which is related to the conventional cell, with 4 nickel(II), in line with the Ludi’s structural model;
NiII 1 [FeIII (CN)6 ]2/3 1/3 ·n/3H2 O, for one nickel(II), which is the one we adopted for simplicity;
NiII 3/2 [FeIII (CN)6 ]1 ·3n/8H2 O, related to one Fe; this one can be misleading since it suggests that there
are no vacancies of [FeIII (CN)6 ] and that part of the NiII are in the centre of the octant (Keggin model).
304       9 Magnetic Prussian Blue Analogs


                                         (t2g )3
                        9 AF               d3          •        •        •

                                                       [VII 3CrIII 2 ]
                                                            •
                               3F     (t2g )4(eg )2
                                                       •         •       •
                               9 AF        d4
                                                      [CrII 3CrIII 2 ]

                               6F     (t2g )4(eg )2        •         •
                   3-                                  •        •        •
  [Cr(CN)6]                    9 AF
                                           d5
                                                      [MnII 3CrIII 2 ]

      •   •   •                6F     (t2g )4(eg )2         •        •
                               6 AF          6         ••        •       •
                                           d
      (t2g )3 d3
                                                      [FeII 3CrIII 2 ]

                               6F     (t2g )5(eg )2         •        •
                               3 AF                     •• • •           •
                                           d7
                                                            II           III
                                                      [Co 3Cr                  2]


                         6F               (eg)2             •        •
                                                       •• •• • •
                                           d8
                                                      [NiII 3CrIII 2 ]

                         3F               (eg)1             ••       •
                                                        •• •• • •
                                            d9
                                                       [CuII 3CrIII 2 ]

Fig. 9.10. Nature and number of exchange pathways between chromium(III) and the divalent
transition metal ions of the first row of the periodic table.


The mean field theory predicts that the latter compounds should have ordering
temperatures 4/6 times 90 K, or 60 K. In fact, the prediction is quite accurate:
NiII 2 [CrIII (CN)6 ]3 ·xH2 O has TC = 53 K and MnII 2 [CrIII (CN)6 ]3 ·xH2 O has TC =
60 K.
   A more subtle prediction of the ligand field and exchange models is that early
transition metals should give higher exchange interactions thanks to a better inter-
action of their d orbitals with the π ∗ orbitals of the bridging cyanide. The example
of Cs2 MnII [VII (CN)6 ]·H2 O whose synthesis was published by Girolami in 1995 is
                                                9.3 Magnetic Prussian Blues (MPB)           305




Fig. 9.11. Variation of the experimental Curie temperatures of a series of MPBs {A1 [B(CN)6 ]z }
as a function of Z the atomic number, for different stoichiometries and electronic struc-
tures of the A and B transition metal elements: Series 1F: {A1 Fe(CN)6 ]2/3 }; Series 2F
and 2af: {A1 Cr(CN)6 ]2/3 }; Series 3af: {Mn1 [B(CN)6 ]1 }; Series 4af: {Mn1 [B(CN)6 ]2/3 };
Series 5F: {Ni1 [B(CN)6 ]2/3 }; Selected compounds: ×, Prussian Blue; §, KV[Cr(CN)6 ]; ∗,
CsMn[Cr(CN)6 ]; #, CsNi[Cr(CN)6 ]; elements A or B are shown by their atomic number Z
(bottom) and their symbol (top). (See Table 9.2 for numerical values.)


especially revealing [31]. This material is a ferrimagnet with a Néel temperature of
125 K. It can be compared with the two other isoelectronic Prussian Blue analogs,
CsMnII [CrIII (CN)6 ]·H2 O and MnII [MnIV (CN)6 ]·xH2 O. All three compounds have
high-spin d5 MnII centers in the weak ligand-field sites (N6 coordination envi-
ronments) and furthermore d3 metal centers in the strong ligand-field sites (C6
coordination environments). The main differences are the oxidation states of B,
which increase as the metal changes from VII to CrIII to MnIV , and the energies
and the expansion of the B t2g orbitals, which decrease in the same order. The
relative magnetic ordering temperatures of 125, 90, and 49 K for these three ma-
terials clearly show that incorporation of transition metals with higher-energy and
more diffuse t2g orbitals into the strong ligand field sites leads to higher magnetic
ordering temperatures. As the backbonding with the cyanide π ∗ orbitals becomes
more effective, the coupling between the adjacent spin centers increases, and so
does TC .
306       9 Magnetic Prussian Blue Analogs

9.3.3     Quantum Calculations

The above qualitative theoretical approach was based on simple symmetry or energy
considerations and did not rely on precise quantum calculations. The apparent sim-
plicity of the structure of Prussian Blues (especially the linearity of the A−N≡C−B
linkages and the octahedral environments of A and B), and the availability of a large
set of experimental data constitutes a favorable situation for theoreticians to com-
pute, reproduce, and predict the magnetic properties of Prussian Blue analogs,
including their magnetic ordering temperatures TC . It is therefore not surprising
that several theoretical methods at various level of sophistication have been applied
to magnetic Prussian Blues.
   In Volume II of this series, in a chapter entitled “Electronic Structure and Mag-
netic Behavior in Polynuclear Transition-metal Compounds”, Ruiz, Alvarez and
coworkers present different theoretical models of exchange interactions [96]. They
point out that the study of the electronic structure of coupled systems is more chal-
lenging than that of closed-shell molecules, in large part because the J values are
several orders of magnitude smaller than the total energy of the system. They point
out that “no single qualitative model [is] able to explain satisfactorily all features
of exchanged coupled systems and there are still a number of controversies about
the advantages and limits of the various approaches that have been devised.” Other
sources of valuable information about theoretical treatments of molecule-based
magnets are the books by Kahn [7] and Boca [97].
   In the following sections, we focus on some computational studies of Prussian
Blues. We start with semi-empirical calculations (extended Hückel), which allow
the considerations in the preceeding section to be evaluated semi-quantitatively.
Then we present some results obtained from density functional calculations based
on the broken symmetry approach [96]. Finally, a perturbative approach by Weihe
and Güdel is briefly presented.


9.3.3.1     Extended Hückel Calculations
The antiferromagnetic contribution JAF
We performed extended Hückel calculations on a series of bimetallic dinuclear
units [(CN)5 AII −N≡C−BIII (CN)5 ], where A = Ti, V, Cr, Mn, Fe, or Co and
B = Ti, V, Cr, Mn, or Fe [36, 98–100]. All of the B ions have (t2g )n electron
configurations; the A ions possess no more than seven d-electrons, so that in the
high-spin state they also have partly filled t2g orbitals. As a result, there is always
at least some antiferromagnetic contribution to the exchange between A and B. All
bond distances were kept fixed for all the combinations.
    As shown previously in Figure 9.8, key features of Prussian Blue analogs are
interactions (via the cyanide ligands) of a t2g orbital on one metal center with a t2g
orbital on an adjacent metal center. Although in a binuclear model system some of
                                             9.3 Magnetic Prussian Blues (MPB)        307

the pairwise t2g –t2g interactions are zero by symmetry, in a three-dimensional Prus-
sian Blue network every t2g orbital can find a related orbital on a neighboring metal
center with which it can interact strongly. Owing to the symmetry of the Prussian
Blue structure, it is sufficient to analyse the interaction for a single pair of orbitals
and to sum all the combinations presented by a three-dimensional network. Two of
the possible interactions between t2g and eg orbitals are also shown in Figure 9.9. In
this case the overlap is zero and the exchange interaction is strictly ferromagnetic.
Although a direct estimation of the strength of this ferromagnetic contribution is
not possible in the frame of semi-empirical methods, we will describe below how
qualitative estimates can be obtained. From Eq. (9.11), the antiferromagnetic con-
tribution to the coupling J is given approximately by the expression 2S( 2 −δ 2 )1/2 ,
where δ is the energy gap between the (unmixed) a and b orbitals, is the energy
gap between the molecular orbitals built from them, and S is the monoelectronic
overlap integral between a and b. For each pair of metals in the list above, the values
of and δ (Figure 9.8) have been calculated. Some features may be highlighted by
decomposing the antiferromagnetic term as ( 2 − δ 2 ) = ( − δ)( + δ). Indeed,
two effects contribute to the tendency of the electrons to pair: (i) a strong inter-
action between the two magnetic orbitals, which stabilises the bonding molecular
orbital (the strength of the interaction is gauged by the term − δ, and (ii) the
stabilization of charge transfer states in which an electron is transferred from one
magnetic orbital to the other (the importance of this phenomenon is gauged by the
term + δ. Therefore, to have a strong antiferromagnetic interaction, it is best if
both ( − δ) and ( + δ) are large. It should be noted that there is a non-trivial
dependence of on δ. The energy gap after mixing, δ, is equal to the energy gap
before mixing, , plus the energy change upon mixing, but the energy change is
enhanced when δ is small. Thus, ( − δ) becomes larger as δ becomes smaller,
whereas ( + δ) becomes larger as δ becomes larger.
    Our calculations show that both and δ have similar trends: their values are
maximized when metal atoms A and B possess d orbitals of very different energy,
and minimized when they are very similar. Such behaviour can be understood with
the help of Figure 9.7a and b (and Figure 5 in Ref. [99], not reproduced here). The
energies of the t2g orbitals on the A and B metals are affected by interactions with
both the low-energy filled CN π orbitals (a destabilizing interaction) and the high-
energy empty CN π ∗ orbitals (a stabilizing interaction involving back-donation).
As a general rule, the metal–carbon interaction is stronger than the metal–nitrogen
interaction, and both interactions are stronger for the early transition metals, which
possess higher energy and more diffuse d orbitals (low values of the ζ coefficient).
The final energy of the t2g orbitals also depends on the relative energies of the
(unmixed) d orbitals on the metallic ions with respect to the energy of the (unmixed)
cyanide π and π ∗ orbitals. Our calculations show that the stabilizing interaction
with the cyanide π ∗ orbitals dominates (thus lowering the t2g orbital energies)
when the A sites are occupied by TiII , VII , or CrII , but that the interactions with the
cyanide π and π ∗ orbitals cancel each other out (thus leaving the energies of the
308     9 Magnetic Prussian Blue Analogs




Fig. 9.12. Plot of the quantity ( 2 − δ 2 ) obtained from extended Hückel calculations for a
series of binuclear complexes [(CN)5 AII (µ-NC)BIII (CN)5 ] with A = Ti to Co and B = Ti to
Fe (see text).




t2g orbitals unchanged) when the A sites are occupied by MnII , FeII , or CoII . This
delicate balance affects the composition of the magnetic orbitals and the overlap
between them. In Figure 9.12 the corresponding ( 2 − δ 2 ) values are shown. The
higher ( 2 − δ 2 ) values are seen for the [(CN)5 TiII −N≡C−BIII (CN)5 ] dinuclear
units, and the highest value of all is found for the TiII FeIII couple. This result,
which at first seems counter-intuitive, is understandable once one recalls the effect
of the cyanide π and π ∗ orbitals on the energies of the d orbitals. Indeed, for such
a TiII FeIII system, the values ( + δ) and ( − δ) are both maximized: ( + δ) is
large because the t2g orbitals on Ti and Fe are so different in energy, and ( − δ)
is large because the diffuseness of the d orbital on Ti promotes efficient overlap
between the magnetic orbitals. The calculated surface suggests that Prussian Blue
compounds containing an early transition metal A cation should always possess
strong antiferromagnetic interactions, irrespective of the identity of the B metal
ion (this is one of the important qualitative arguments presented in a preceeding
section).
    As predicted by the Néel expression (Eq. (9.9), the TC values of MPB analogs
depend not only on the strength of JAF but also on the number of unpaired spins
nA and nB on both sites and the number of possible interactions N = nA nB be-
tween them. Taking this effect into account, we multiply ( 2 − δ 2 ) by the factor
       √
nA nB (nA + 2)(nB + 2)/nA nB to obtain the new surface shown in Figure 9.13.
                                                             9.3 Magnetic Prussian Blues (MPB)   309

8
             TC / a.u.
7

6

5

    4

    3

    2

    1
    0
        Ti
             V
                                                                            Fe(CN) 6
                 Cr
                                                                     Mn(CN) 6
                      Mn                                  Cr(CN) 6
                           Fe                   V(CN) 6
                                Co   Ti(CN) 6
                                               √
Fig. 9.13. Plot of the quantity ( 2 − δ 2 ) · N [(nA + 2)(nB + 2)/nA nB ] ∝ TC (arbitrary
units) (see text).

   The surface should mirror the TC values of MPB compounds made with A and
B metals from the first transition series. Indeed, these calculated trends agree well
with the experimental ones (see Table 9.2), both predicting that the maximum TC
value should be found for the VII CrIII pair.

The ferromagnetic contribution JF
Although the ferromagnetic contribution to J cannot be explicitly calculated, some
information about it can be obtained even from simple extended Hückel calcu-
lations. The exchange integral kab is directly proportional to the squared overlap
density defined in Eq. (9.11) ρab = |a |b . This contribution to the exchange in-
teraction is always present, and it becomes the only contribution when the overlap
Sab between the two orbitals is zero. This is the case for the t2g –eg interactions in
MPB analogs, where the overlap is zero by symmetry. The TC values of up to 90 K
found for those compounds that solely possess ferromagnetic pathways indicate
that the ferromagnetic interaction can be quite strong.
    To verify the presence of high ρt2g−eg overlap density zones, we began with the
results of the extended Hückel calculations described above for the dinuclear model
complexes [(NC)5 AII −N≡C−CrIII (NC)5 ], where A = Co, Ni, or Cu, and B = Cr.
The product ρt2g−eg could be visualised by plotting projections of the magnetic
orbital compositions taken directly from the extended Hückel output. Owing to their
influence on the density overlap, both the angular and radial normalisation constants
for all the single atomic wavefunctions were carefully checked. Figure 9.14 shows
310       9 Magnetic Prussian Blue Analogs




Fig. 9.14. Overlap density in the xz plane between the φ(t2g ) xz-type magnetic orbital centered
on Cr and the φ(eg ) z2 -type magnetic orbital centered on Ni.

the overlap density (in the xz plane) between the t2g xz-type magnetic orbital
centred on Cr and the eg z2 -type magnetic orbital centred on Ni. The overlap
density is symmetric with respect to the z axis.
    A similar result was obtained for the monoatomic µ-oxo bridge in a Cu–VO
complex [87]. Our result is counterintuitive for a diatomic bridge, where the spin
density for the atom farthest from the metallic centre is expected to be low. Indeed, it
is the strong delocalisation of the spin density on the nitrogen in the [B(CN)6 ] units
that allows the strong overlap density and the strong ferromagnetic interaction. In
contrast, for a µ-oxalato bridge, where the spin density is spread over the entire
molecule, the overlap density is weak and so is the coupling [210].

9.3.3.2     Density Functional Theory Calculations
Progress in computer speed and memory and in density functional theory (DFT)
techniques have now made it possible to carry out calculations on very complex
systems. Magnetic Prussian Blues are indeed complex systems to treat computa-
tionally. For example, the number of unpaired electrons per formula unit can be as
high as 8 (as in a CrIII −MnII system).
   DFT computations on magnetic Prussian Blues were performed on two model
systems, dinuclear complexes [(CN)5 A−N≡C−B(CN)5 ] and ideal face-centered-
cubic extended solids. For a system with identical two centres A and B and one
electron per centre, the method can be briefly summarized as follows.
   For two orthogonal orbitals φa and φb , the spin eigenfunctions of the system
are:
                 √
       S,0 = (1/ 2)(|φa αφb β| − |φa βφb α|)                               (9.12a)
                 √                                           √
       T,0 = (1/ 2)(|φa αφb β| + |φa βφb α|);     T,+1 = (1/ 2)(|φa αφb α|);
                 √
     T,−1  = (1/ 2)(|φa βφb β|)                                            (9.12b)
                                              9.3 Magnetic Prussian Blues (MPB)     311

Because the singlet state cannot be described by one single configuration, the
J value (J = ES − ET ) cannot be computed directly. Noodleman suggested a
broken-symmetry (BS) solution [see Ref. 96, 211–213]:
     BS   = |φa αφb β|   or   BS   = |φa βφb α|                                   (9.13)
which is a mixed state, combination of        S,0   and   T,0
             √
    BS = (1/ 2)[ S,0 + T,0 ]                                                      (9.14)
                                             √
The corresponding energy is EBS = (1/ 2)(ES + ET ) and the coupling is given
by:
  J = 2(EBS − ET )                                                                (9.15)
   In the context of DFT calculations, therefore, it is possible to compute J from
the energy of the broken symmetry state and the high spin state. Depending on the
kind of calculations (HF, UHF, DFT, . . . ) and the existence of “spin-projection”
processes [96], other expressions for J have been used, such as:
  J = 2(EBS − EHS )/SHS
                     2
                                                                                  (9.16)
The main conclusion is that J can be obtained in a reasonable computing time from
the difference of two energies. The calculation can be extended to systems with
more than one electron per metal centre.

Dinuclear models
The first DFT papers on dinuclear models of Prussian Blues were published by
Nishino, Yamaguchi et al. [101–103]. Their work continues a longstanding theo-
retical tradition of studying open-shell spin systems [81, 82, 84, 104, 105]. The
first two papers deal with very simple A−N≡C−B systems in which there is only
one bridge and no other ligands are attached to A and B [101, 102]. The third paper
deals with [(CN)5 A−N≡C−B(CN)5 ] units [103]. In all three papers, the symmetry
rules that we applied before are used to analyze the d–d orbital interactions. The
correct sign of the effective exchange integrals J is found. The authors carried out
ab initio unrestricted Hartree Fock (UHF) and DFT calculations to elucidate the
nature of the magnetic orbitals.
    For the unligated VII −N≡C−CrIII and NiII −N≡C−CrIII units, the magnitudes
of the calculated exchange integrals were much larger than the experimental val-
ues found for real dinuclear systems. We focus therefore on the last paper, which
deals with the more realistic situation in which the A and B centres have octa-
hedral coordination environments. Figure 9.15a shows the orbital interaction in
the A−N≡C−B entity. Figure 9.15b displays the molecular orbitals φA (HOMO)
and φS (LUMO) built from the t2g orbitals of the A and B metals and the π
and π ∗ MOs of the cyanide ligand; these molecular orbitals are, respectively,
(pseudo)antisymmetric and (pseudo)symmetric relative to a plane bisecting the
312     9 Magnetic Prussian Blue Analogs




Fig. 9.15. (a) Orbital interaction schemes in the BCNA entity; (b) symmetric (S) and antisym-
metric (A) natural MOs; h(c) magnetic orbitals obtained by mixing the S and A MOs (adapted
from Ref. [103]) (see text).

A–B axis. Figure 9.15c represents the magnetic orbitals φa and φb built from φA
and φS according to the relations within the UHF and DFT approximations:
   φa (spin up α) = cos θ φA + sin θ φS                                             (9.17a)
   φb (spin down β) = cos θ φA − sin θ φS                                           (9.17b)
(the authors use the Hamiltonian H = −2J SA SB ).
   Then the authors apply the Heisenberg model to describe the energy gaps be-
tween the ferromagnetic (HS) and antiferromagnetic (LS) states and, using the
approximate spin projection procedure (AP), find the following expression for the
effective exchange integrals Jab with various methods (X = UHF, DFT):
   JAP−X = (LS EX − HS EX )/[HS S 2      X   − LS S 2 X ]                             (9.18)
In addition to calculating J values, they also obtained an orbital picture of the ex-
change phenomenon and values for the atomic spin densities. Using the molecular
field approach (Langevin–Weiss–Néel), they also computed Curie temperatures
for the solid from the expression:
   TC =     ZA ZB |JAB | SA (SA + 1)SB (SB + 1)/3kB                                   (9.19)
where kB is Boltzmann’s constant, ZA and ZB are the numbers of magnetic neigh-
bors of A and B, respectively, and SA and SB the spins of A and B. Some of their
results are collected in Table 9.3.
                                                   9.3 Magnetic Prussian Blues (MPB)        313

Table 9.3. a Comparison of the computed J b and TC c values with experiment.

 System A–B      SB        SA    Jab /cm−1   TC /K (calc)    TC /K (exp)

 NiII –CrIII     3/2       1     +15.92      125             90
 NiII –CrIII
         2/3                                 102             53
 MnII –CrIII     3/2       5/2   −7.01       116             90
 MnII –CrIII
          2/3                                95              60
 VII –CrIII
        2/3      3/2       3/2   −75.56      815             (315)d
 VIII –CrIII     3/2       1     −31.24      246             (315)d
 MnII –VII       3/2       5/2   −14.49      239             125
a Adapted from Ref. [103] and Table 9.2. b J is computed in a [(NC) A−C≡N−B(NC) ]
                                                                    5          5
model. c From Eq. (9.19). d The sample contains both VII and VIII .


   The agreement between computation and experiment is not exact, but to obtain
a better fit the authors suggest the empirical law:

   TC (exp) = 1.2TC (calc) − 49.9 K                                                     (9.20)

This expression gives very good agreement between experimental and theoretical
values. The very large value for |J | in the VII –CrIII 2/3 system (which is ten times
larger than the value found for the MnII –CrIII system) can be related to the strong
participation of VII in the φb orbital (Figure 9.15) compared to the MnII , whose
orbitals are well localized (Figure 3 in Ref. [103], not shown here). Important

Table 9.4. a Atomic spin densities from methods UB2LYP in [(NC)5 A−C≡N−B(NC)5 ]

 System A–B            2S + 1b     Ac        Cc       Nc       Bc

 NiII –CrIII AF        2           −1.73     −0.12    0.07     3.06
 NiII –CrIII F         6           +1.73 d   –0.16    0.19     3.06
 MnII –CrIII AF        3           –4.75 d   –0.17    0.12     3.05
 MnII –CrIII F         9           +4.76     −0.09    0.11     3.06
 VIII –CrIII AF        2           –2.02 d   –0.17    0.15     3.06
 VIII –CrIII F         6           +2.02     −0.05    0.04     3.06
 VII –CrIII AF         1           –2.82 d   –0.23    0.19     3.03
 VII –CrIII F          7           +2.85     −0.04    0.05     3.06
 MnII –VII AF          3           –4.74 d   –0.14    0.14     2.63
 MnII –VII F           9           +4.76     −0.07    0.15     2.66
a Adapted from Ref. [103]. b Spin multiplicity for the computed states (AF = antiferromagnetic
coupling; F = ferromagnetic coupling). c Spin densities of A, C, N, and B; a positive sign means
that the magnetic moments are aligned along the field and a negative sign means the reverse. d
Spin multiplicities shown in bold italics correspond to the coupling observed experimentally.
314     9 Magnetic Prussian Blue Analogs

new information provided by these calculations is the atomic spin densities. Some
significant results are collected in Table 9.4.
   From Table 9.4, it can be concluded that (i) the chromium(III) centers bear the
spin density foreseen from its +3 valence; in contrast, the spin density of vana-
dium(II) is significantly decreased by delocalisation; (ii) the carbon atom always
bears a negative spin density, an observation that is consistent with Figgis’s spin
polarized neutron diffraction study of [CrIII (CN)6 ] salts [78]; this effect is due to
spin polarisation (SP) and is represented by the authors by the spin-flip excitation
from φS to φA orbitals shown in Figure 9.15; when the spin densities are decom-
posed into σ and π components, the SP effect is more significant for the π than for
the σ network; (iii) there is a significant positive spin density on nitrogen atoms of
the bridge; (iv) the spin density on the A ion is always less than expected from the
valence, thus suggesting that there is significant spin delocalisation.
   These calculations provide quantitative information about the mechanism of the
exchange interaction through the cyanide bridge. One striking observation of the
article is that, without the cyanide bridging ligand, at the same A–B distance, the
A–B interaction becomes negligibly small.
   DFT calculations have also been carried out for the homodinuclear complexes
Ln CuII −N≡C−CuII Ln and Ln NiII −N≡C−NiII Ln systems [106] based on the com-
putational procedures described in Ref. [108]. The results are relevant to dinuclear
complexes but not to Prussian Blues, and thus this work is outside the scope of the
present review.
   At present, additional computations on various dinuclear models of Prussian
Blues are in progress, including a study of the effect of incorporating metals of
different oxidation states or from the second row of the d-block, in order to deter-
mine whether larger J and TC values than those found in the vanadium–chromium
derivatives can be achieved. Indeed, larger |J | values are foreseen [108].


Three-dimensional models
At approximately the same time as the computations on the molecular dinuclear
models, three articles appeared on DFT calculations of three-dimensional net-
works, using computation packages adapted for solids [109–111]. These studies
afforded important insights into the band structure and density of states (DOS,
spin-polarized or not), the atomic spin density in the solid, and the crystal orbital
overlap populations (COOP), a concept introduced by Hoffmann [112].
   The first brief paper by Siberchicot was based on a local-spin-density approx-
imation using the augmented spherical wave (ASW) method and including spin–
orbit coupling [109]. Two species were studied: the ferromagnet CsNi[Cr(CN)6 ]
[27] and the ferrimagnet CsMn[Cr(CN)6 ] [70]. The calculated magnetic moments
(spin and total, spin+orbital) were in good agreement with the experimental values.
The spin polarized partial densities of states on the chromium and nickel clearly
showed semiconducting behavior with a rather large gap at the Fermi level EF , and
                                                      9.3 Magnetic Prussian Blues (MPB)   315

localized d bands near EF . The d band is split in energy by the octahedral ligand
field. For both solids, the empty (eg )0↓ levels derived from the CrIII orbitals are
above the Fermi level.
   In CsNi[Cr(CN)6 ], the filling of the d-bands is
   [NiII ]: [(t2g )3 (eg )2 ]↑ [(t2g )3 (eg )0 ]↓ ,
   [Cr III ]: [(t2g )3 (eg )0 ]↑ [(t2g )0 (eg )0 ]↓
The band structure is consistent with the observed ferromagnetic coupling between
NiII and CrIII . In comparison, for CsMn[Cr(CN)6 ] the filling is:
   [MnII ]: [(t2g )3 (eg )2 ]↑ [(t2g )0 (eg )0 ]↓ ,
   [Cr III ]: [(t2g )3 (eg )0 ]↓ [(t2g )0 (eg )0 ]↑
which agrees with the experimental antiferromagnetic coupling between MnII and
CrIII .
   The same two species were studied in more detail by Eyert and Siberchicot [110].
Again a local density approximation was employed, using augmented spherical
waves (ASW) in scalar-relativistic implementations, taking particular care in the
optimisation of empty spheres and the Brillouin zone sampling. A new feature
was the evaluation of the crystal orbital overlap populations, which permitted an
assessment of the chemical bonding in the solid [112, 113]. The electronic structure
was analysed by means of two sets of calculations, one non-magnetic and the
other magnetic, the first serving as a reference for the discussion of the magnetic
configurations.
   The density of states and COOP analyses suggested the following: in the two
compounds, the band structure reflects mainly the strong bonding within the
cyanide and the ligand field splitting. In contrast, near the Fermi level (from −1.2 eV
to 0.5 eV), the situation is completely changed: in the manganese derivative, the
bands mix and split in a way reminiscent to t2g –t2g overlaps in Figure 9.8, whereas
in the nickel compound, they do not (as in Figure 9.9, t2g –eg ). This difference has
dramatic consequences for the magnetic properties.
   The spin-polarized calculations demonstrate that the ground state is indeed fer-
rimagnetic in CsMn[Cr(CN)6 ] and ferromagnetic in CsNi[Cr(CN)6 ] (the ferrimag-
netic state of CsNi[Cr(CN)6 ] is computed to be 9.8 mRyd higher in energy than
the ferromagnetic state). The computed atomic moments are given in Table 9.5.
   The spin-polarized densities of states for CsMn[Cr(CN)6 ] are given in Fig-
ure 9.17 and beautifully illustrate the opposite polarisations of the metallic bands
[Cr(t2g )3 ]↑ (at −1.5 eV) and [Mn(t2g )3 (eg )2 ]↓ (at −2.0 and −0.5 eV). In addition,
the polarisations of the bridging carbon and nitrogen atoms in the same energy
range help to explain the mechanism of the polarisation. Indeed, a close examina-
tion of the spin polarized DOS in the Fermi level region level led the authors to
“point out that the overlap of magnetic orbitals already present in the non-magnetic
configuration completely fixes the antiferromagnetic coupling while disallowing a
ferromagnetic correlation”.
316     9 Magnetic Prussian Blue Analogs

a)




b)




                                                                  Fig. 9.16. Total and partial
                                                                  crystal orbital overlap
                                                                  populations (COOP): (a)
                                                                  in CsMn[Cr(CN)6 ]; (b)
                                                                  in CsNi[Cr(CN)6 ] (from
                                                                  Ref. [110]].

   An analogous demonstration results from the spin-polarized densities of states
for CsNi[Cr(CN)6 ], given in Figure 9.18, where now the orthogonality of the
[Cr(t2g )3 ]↑ and the [Ni(eg )2 ]↓ orbitals leads to identical polarisations of these bands.
The densities of states also show that the carbon and nitrogen atoms participate
significantly in the exchange mechanism.
   One important conclusion that can be drawn from this study is that the electronic
interactions present in three-dimensional Prussian Blue solids are very similar to
those seen in discrete molecular analogs. Furthermore, exchange models such as
that proposed by Kahn and Goodenough–Kanamori, involving t2g –t2g overlap and
                                               9.3 Magnetic Prussian Blues (MPB)         317

Table 9.5. Local magnetic moments in CsA[Cr(CN)6 ] (A = Mn, Ni).a

 Atom    µ/µB in CsMn[Cr(CN)6 ]      µ/µB in CsNi[Cr(CN)6 ]

 Cs                0.001                      0.001
 A                −4.200                      1.369
 Cr                2.658                      2.717
 C                −0.061                     −0.046
 N                 0.001                      0.129
 Cell             −2.000                      5.000
a Adapted from Ref. [110].




Fig. 9.17. n polarized partial densities of states of ferrimagnetic CsMn[Cr(CN)6 ] (from Ref.
[110]].


orthogonality of the t2g and eg orbitals as described in Figures 9.8 and 9.9, do in
fact constitute accurate descriptions of the electronic structures of Prussian Blues
in the solid state, particularly near the Fermi level. The DFT calculations, however,
afford much more quantitative information about the resulting magnetic properties.
318     9 Magnetic Prussian Blue Analogs




Fig. 9.18. Spin polarized partial densities of states of ferromagnetic CsNi[Cr(CN)6 ] (from
Ref. [110].


Periodic UHF – CRYSTAL calculations
Harrison et al. [111] carried out a study of several Prussian Blue compounds us-
ing the periodic unrestricted Hartree–Fock approximation as implemented in the
CRYSTAL package. The compounds studied were KA[Cr(CN)6 ] (A = V, Mn,
Ni) and Cr[Cr(CN)6 ]. Structural optimisation was performed, and the optimized
structures closely resemble those determined experimentally. To compare the ener-
gies of the various magnetically ordered states, they obtained self-consistent field
solutions, sometimes using a “spin-locking” procedure to constrain the initial total
spin. The authors calculated the magnetic ordering energies and the relative con-
tibutions of exchange, kinetic and Coulomb interactions according to Anderson’s
model [114], as shown in Table 9.6.
   The total energies clearly show the strong stabilisation of the ferrimagnetic state
in the CrIII and VII compounds (corresponding to high TC s) and of the ferromag-
netic state in the NiII derivative. From these results and an analysis of the Mulliken
spin populations, the authors conclude that “an ionic picture of the metal–ligand in-
teractions and a superexchange model of the magnetic coupling naturally emerges
from first principles calculations of the ordering energetics of bi-metallic cyanides.
                                                 9.3 Magnetic Prussian Blues (MPB)         319

Table 9.6. Magnetic ordering energies in CrIII [CrIII (CN)6 ] and KAII [CrIII (CN)6 ] models.a

 A        d configuration   Total b,c   Exchange b    Kinetic b   Coulomb b

 CrIII    (t2g )3            4.33        14.70        −12.57       2.20
 VII      (t2g )3            4.40        9.91         −2.78       −2.74
 MnII     (t2g )3 (eg )2     0.79        14.70         0.29       −0.75
 NiII     (t2g )6 (eg )2    −1.78       −7.49          5.60        0.11
a Adapted from Ref. [111]. b Values are in milliHartree. c Positive values favor ferrimagnetic
states; negative values favor ferromagnetic states.

. . . Ferromagnetic coupling [is favoured] for the A(eg )2 –Cr(t2g )3 arrangement as
the superexchange integral is dominant. . . Antiferromagnetic coupling is favoured
for the A(t2g )3 –Cr(t2g )3 arrangement where the effects of the orthogonality con-
straint on the metal d-orbitals is dominant. In the antiparallel configuration the
orthogonality constraint is relaxed through delocalisation of the metal d-orbitals
and concomitant polarisation of the orbitals of the CN group”.


9.3.3.3     Valence Bond Configuration Interaction (VBCI)
            and Perturbation Theory
Güdel and Weihe have recently applied their valence bond/configuration interaction
model to the A−N≡C−B units in materials related to Prussian Blues [115, 116].
They define the interactions between two d orbitals, a and b, and the π and π ∗ MOs
of the cyanide as shown in Figure 9.19; the integrals are defined by the following
one-electron Hamiltonian h:
     Va = a|h|π ; Vb = b|h|π ; Va∗ = a|h|π ∗ ; Vb∗ = b|h|π ∗                            (9.21)
As shown in Figure 9.20, the exchange splitting is obtained by mixing into the
ground configuration selected one-electron excited configurations: ligand-to-metal
charge transfer (LMCT) states, metal-to-metal charge transfer (MMCT) states,
and metal-to-ligand charge transfer (MLCT) states. The wavefunction for each
configuration is obtained and the interaction matrix elements with the ground state
are calculated as described in the appendices of Refs. [115] and [116]. The energies




                                                  Fig. 9.19. Interactions between p symmetry
                                                  orbitals in the A–NC–B entity (adapted from
                                                  Ref. [115]).
320     9 Magnetic Prussian Blue Analogs




Fig. 9.20. Ground and excited configurations in the A–NC–B entity (adapted from Ref. [116]):
Case I: interactions between singly occupied metallic a and b orbitals and π and π ∗ ; Case
II: interactions between singly occupied metallic a and b orbitals and π and π ∗ ; Case III:
interactions between singly occupied metallic a and b orbitals and π and π ∗ ; from top to
bottom: ground, LMCT, MMCT and MLCT configurations. For each configuration the possible
spin states and the relative energies are shown (adapted from Ref. [115]).
                                            9.3 Magnetic Prussian Blues (MPB)      321

           ∗    ∗
  A,   B,  A,   B , and Uab are defined in Figure 9.20. I2 is defined as a one-centre
two electron exchange integral.
   The authors suggest that one can choose a mean value for all the LMCT and
MLCT transition energies, a mean value V for all the interaction integrals and a
mean value I for the one-centre two-electron exchange integral. After making some
other approximations, they arrive at simple expressions for Jcalc that depend on the
number of unpaired electrons residing on A and B, Table 9.7.


Table 9.7. Calculated magnetic couplings for different A−N≡C−B linkages.a

 A/B Elect. Config.   Jcalc            Examples (A/B)

 d5 /d3               +32Q/15 b        MnII CrIII , MnII VII , MnII MnIV
 d8 /d3               −4Q + W/3 c      NiII CrIII
 d3 /d3               +32Q/9           CrIII CrIII , VII CrIII
 d3 /d1               +16Q/3 − 2W/3    CrIII VOIV
 d2 /d3               +8Q/3            CrII CrIII
a Adapted from Ref. [115]. b Q = V 4 / 2 U . c W = [1+{(2U +   )/U }+2(U + )/ ]I /U .


   The authors made the debatable assumption that the parameters Q and W were
constants (i.e., independent of the nature of A or B), and then carried out a least-
squares optimization, with Q and W as adjustable parameters, to fit Jcalc and Jexp .
Using an expression similar to Eq. (9.19), the authors calculated the magnetic or-
dering temperature, obtaining a reasonably linear correlation with experiment. This
approach, however, is intrinsically flawed: in the series of Prussian Blues in which
the AB pairs are MnII VII , MnII CrIII , and MnII MnIV , the model predicts that Jcalc
should be invariant, and TC should equal 280 K for all three compounds, because
the electronic configuration of all three species is d5 /d3 . In fact, the experimental
Curie temperatures decrease monotonically across this series, from 125 to 90 to
49 K. The authors recognize that in this case the transferability of the parameters
Q and W is not a good approximation, in line with the arguments presented earlier
that J is strongly dependent on the energies (and diffuseness) of the orbitals on the
metal centers, with early transition metals in low oxidation states giving rise to the
largest J values. The authors conclude that “according to our calculations ordering
temperatures much higher than those already achieved should not be expected for
Prussian Blue analogs containing 3d metals,” a conclusion similar to that obtained
from semi-empirical calculations. This pessimistic but realistic conclusion leaves
open the possibilities provided by the 4d and 5d transition metals. There is still
hope for further improvements in TC .
   We would like to conclude this theoretical survey by mentioning some recent
papers that use the Anderson model [114] and particularly the kinetic exchange
contributions to explain the ferromagnetism experimentally observed in systems
322     9 Magnetic Prussian Blue Analogs

where ferrimagnetism might be expected, at first glance. Examples of such systems
include certain Prussian Blues that contain the CrIII –FeII pair [117], which is one of
the exceptions we quoted before in discussing Table 9.1 and Figure 9.11, and certain
non-Prussian Blue solids (constructed from octacyanometalate building blocks)
that contain the MoV –MnII pair [118]. In this short review, we can only describe
the highlights of the theoretical work on Prussian Blues and related cyanide-bridged
model open-shell systems. The reader is referred to the articles cited for additional
references to such studies.




9.4 High TC Prussian Blues (the Experimental Race
    to High Curie Temperatures)

We are now in a position to use the theoretical models to guide experiment and
enhance the Curie temperature of Prussian Blue analogs. To set the stage, before
we began our work, the highest ordering temperature seen for any Prussian Blue
analog was TC = 90 K.
    Because we need interactions in the three directions of space, for the B centre,
a d3 , (t2g )3 electronic configuration, S = 3/2, is better adapted than an electronic
configuration with S < 3/2: VII , CrIII , MnIV > MnIII > FeIII . Because the ordering
temperature is proportional to Z, the number of magnetic neighbors, everything be-
ing equal, a MA1 [Cr(CN)6 ]1 stoichiometry with six neighbors should be preferred
to a A1 [Cr(CN)6 ]2/3 one with only four neighbors. Because the highest possible
ferromagnetic interactions allow one to reach only TC = 90 K [27], a ferrimag-
netic strategy must be looked for. Because the interaction between the metallic
d orbitals and the cyanide π ∗ MOs increases with earlier transition elements, it
should be better to work with chromium, vanadium or titanium, when the chem-
istry allows. In the Mx Mn1 [M(CN)6 ]1 series (see Section 4.2), starting from 49 K
for the Mn1 [MnIV (CN)6 ]1 derivative [69], 90 K is found for Cs1 Mn1 [Cr(CN)6 ]1 ,
[70] and 125 K for the Cs2 Mn1 [VII (CN)6 ]1 [31] and then 230 K when the sample is
optimized [31]. From the MnII derivative of Klenze in 1980 to the VII materials of
Girolami in 1995 took 15 years. Because the ferromagnetic exchange pathways are
non-negligible, if one wants to enhance the absolute value |J | of a ferrimagnetic
system, it is necessary to decrease the ferromagnetic contributions (see Eq. (9.2c)).
This means choosing an A ion that has as few eg electrons as possible. Figure 9.10
shows how this goal can be achieved: whereas MnII has two eg electrons, CrII has
only one (if high-spin), and VII has none. Furthermore, the use of the early tran-
sition ions CrII and VII will enhance the absolute value of the antiferromagnetic
interaction by backbonding more effectively with the cyanide π ∗ orbital.
 9.4 High TC Prussian Blues (the Experimental Race to High Curie Temperatures)      323

   Indeed these approaches have worked pretty well [119]! Whereas
MnII [CrIII (CN)6 ]2/3 ·xH2 O has TC = 60 K, CrII [CrIII (CN)6 ]2/3 ·xH2 O has TC =
240 K [28], and VII /CrIII Prussian Blues have TC s that range from 315 K [29]
to 376 K [40]. Nevertheless, from the MnII derivative of Babel in 1982 to the
amorphous VII analog of Ferlay in 1995 took 13 years. And four years more for
Girolami’s crystalline VII compound. The situation deserves some comment.


9.4.1    Chromium(II)–Chromium(III) Derivatives

In 1993, we described the synthesis of two Prussian Blue analogs prepared by
adding [Cr(H2 O)6 ]2+ to [CrIII (CN)6 ]3− [28]. In the absence of a source of ce-
sium cations, a light gray precipitate of stoichiometry CrII [CrIII (CN)6 ]2/3 ·10H2 O
is isolated. The material has a single C–N stretching band in the IR spectrum at
2194 cm−1 , and this frequency suggests that all of the cyanide ligands are C-bound
to CrIII . Magnetisation measurements show that the compound orders ferrimagnet-
ically at 240 K, although interestingly the saturation magnetisation suggests that
some CrII centers are low-spin. Relative to the previous record for highest TC for
a Prussian Blue, that of 90 K for Babel’s or Gadet’s compound, a TC of 240 K
represents a significant step towards room temperature.
    In an attempt to increase the number of magnetic neighbors by preparing a 1:1
compound, the same reaction was carried out in the presence of Cs+ . Under these
conditions a green compound of stoichiometry Cs0.67 CrII 1 [CrIII (CN)6 ]0.9 ·4.5H2 O
was isolated [28]. The infrared spectrum of this compound, however, features two
cyanide stretching bands, due either to linkage isomerism or to a partial conversion
of high-spin CrII centers (S = 2) to low-spin CrII centers (S = 1). The latter
hypothesis is supported by the fact that the magnetisation at saturation is well
below the expected value calculated assuming that all the CrII centers are high-
spin [28]. As a result, the magnetic ordering temperature of 190 K, while still high
for a Prussian Blue analog, is lower than that of the 3:2 compound. Because the
chemistry of the system did not allow further increase in TC by increasing the A:B
ratio to 1:1, we tried another approach: we hoped that compressing the solid under
pressure would decrease the distances, enhance the orbital overlaps, increase the
antiferromagnetic interaction, and thus increase the ordering temperature. Instead,
a disaster happened. Compressing the sample under a pressure of 4 kbar causes all
of the CrII centers to become low-spin, and the local antiferromagnetic coupling
causes the solid to become diamagnetic below its ordering temperature because the
spins of the low-spin CrII centers exactly cancel those of the CrIII centers [120]:
  MT = MCrIII − −MCrII                                                           (9.22a)
with Cr , d , S = 3/2 and high spin Cr , d , S = 2, one obtains:
        III   3                          II   4


  MT /µB = |MCrIII − MCrII HS | = |((2/3) × 3) − (1 × 4)| = 2                    (9.22b)
324     9 Magnetic Prussian Blue Analogs

Instead, with CrIII , d3 , S = 3/2 and low-spin CrII , d4 , S = 1, one obtains:
   MT /µB = |MCrIII − MCrII LS | = ((2/3) × 3) − (1 × 2) = 0!                     (9.22c)
This change was shown beautifully by the thermal variation of the magnetisation
under pressure. In chemistry, as in Roman history, the Tarpeian rock is close to the
Capitol. Three years later, with the same system, Sato, Hashimoto et al. used an elec-
trochemical method and succeeded in getting a derivative with TC = 270 K, which
was furthermore switchable from ferrimagnetic to paramagnetic electrochemically
[121]. Two years later, with the same electrochemically-synthesized chromium–
chromium system, Miller et al. were able to prepare thin layers of materials, either
amorphous or crystalline, with TC ranging from 135 to 260 K depending on the
oxidation states of the chromium. They observed a robust negative magnetisation
in low field that they assigned to single ion anisotropy of chromium(II) [122].


9.4.2   Manganese(II) –Vanadium(III) Derivatives

To check the hypothesis of an improved interaction using early transtion metals led
us to replace the [CrIII (CN)6 ]3− precursor by [VII (CN)6 ]4− [32]. We have already
commented on the higher TC presented by the ferrimagnet CsI 2 MnII [VII (CN)6 ]
(125 K) compared to its homologs CsMnII [CrIII (CN)6 ] (90 K) and MnII
[MnIV (CN)6 ] (49 K) (see Section 9.3.2.4). Cs2 MnII [VII (CN)6 ] is prepared in aque-
ous solution under argon from K4 [VII (CN)6 ] and MnII (OSO2 CF3 )2 (CH3 CN)2 in
the presence of Cs(OSO2 CF3 ). It is an air-sensitive green solid. It crystallizes
in a face-centered-cubic (fcc) lattice with a = 10.66 Å. Its magnetisation at
saturation is in line with an antiferromagnetic coupling between vanadium and
manganese. When (NEt4 )2 [VII (CN)6 ] is treated with MnII (OSO2 CF3 )2 (CH3 CN)2
in the absence of Cs(OSO2 CF3 ), the crystalline yellow solid obtained, formu-
lated as (NEt4 )0.5 MnII 1.25 [VII (CN)5 ]·2H2 O is a strongly coupled ferrimagnet with
TC = 230 K. The color of the two compounds, green and yellow, the absence of an
intervalence band in the near-infrared spectrum indicates that there is no electron
transfer between the metallic centres. X-ray powder diffraction shows that the sec-
ond compound is crystalline but does not adopt a fcc structure. The XRD pattern
and the unusual ratio of CN− to V suggest that the structure is more complex. Inter-
estingly, Babel has shown that attempts to substitute cations larger than Cs+ into the
Prussian Blue lattice usually gives rise instead to lower dimensional structures with
substantially decreased magnetic phase transition temperatures [74]. Even though
the large (NEt4 )+ cations prevent the adoption of the cubic structure, the high
value of TC suggests that the structure still consists of a 3D array of interacting spin
centers, with a very strong antiferromagnetic coupling constant. The magnetisation
data of the two compounds are revealing on this point. One of the characteristic fea-
tures of ferrimagnetic materials is the presence of a minimum in the thermal χM T
curve: the higher the temperature of the minimum, the higher the antiferromagnetic
 9.4 High TC Prussian Blues (the Experimental Race to High Curie Temperatures)       325

coupling constant J . CsI 2 MnII [VII (CN)6 ] presents such a minimum at about 210 K.
However, there is no visible minimum in the (NEt4 )0.5 MnII 1.25 [VII (CN)5 ]·2H2 O
data: because the saturation magnetisation allows one to rule out a ferromagnetic
coupling, it means that the minimum is displaced above the observed temperature
range and that |J | is strong. The hypothesis that the back-bonding with the cyanide
π ∗ orbitals become more effective with VII ions is fully confirmed. The conclusion
of Ref. [31] was: “These two V-based molecular magnets represent an important
step in the design of molecular magnets with high TN . Through judicious choice of
cations and metal centers, TN values above 300 K should be possible.” The stage
was set for another step.



9.4.3   The Vanadium(II) –Chromium(III) Derivatives

Our ultimate success in obtaining Prussian Blues with ordering temperatures above
room temperature resulted indeed from the idea to enhance J by maximizing the
backbonding of the d orbitals of the metal A with the π ∗ orbitals of cyanide and
returning to the idea that increases in TC can be achieved by reducing the number of
ferromagnetic pathways. The metal ion best able to accomplish both of these goals is
VII . Upon adding the Tutton salt (NH4 )2 V(SO4 )2 ·6H2 O to K3 Cr(CN)6 , a midnight-
blue solid that has a stoichiometry of V[CrIII (CN)6 ]0.86 ·2.8H2 O precipitates from
solution. The magnetic ordering temperature is 315 K.
   Prepared in this manner, using Schlenk techniques, the expected
VII [CrIII (CN)6 ]2/3 stoichiometry is in fact not obtained, and a non-stoichiometric,
amorphous, compound results instead, probably because it precipitates very




                                                          Fig. 9.21. “A midnight blue
                                                          solid precipitates from so-
                                                          lution . . . ”. Molecule-based
                                                          magnets can be prepared in
                                                          mild conditions. They are
                                                          transparent and low density.
326       9 Magnetic Prussian Blue Analogs

1.5                                                           700
                          H = 30G                             600
                                                              500




                                             χ T / cm mol K
  1
                                                              400
                                                                               Tmin = 240 K
                                                              300
0.5
                                                              200
                                                              100




                                                        M
  0                                                             0
      0   50   100 150 200 250 300 350                           50   100 150 200 250 300 350
                  T/K                                                       T/K
                    (a)                                                       (b)
Fig. 9.22. Role of the oxidation state in VCr derivatives: thermal variation of (a) the
magnetisation of VII α VIII (1−α) [CrIII (CN)6 ]0.86 ·2.8H2 O (α = 0.42); (b) product χM T of
VIV O[CrIII (CN)6 ]2/3 .


rapidly and the interstitial sites are occupied by a variety of species. The A
sites contain a mixture of VII and VIII , and the formula of the compound is
best represented as VII α VIII (1−α) [CrIII (CN)6 ]0.86 ·2.8 H2 O with α = 0.42. The
magnetisation at saturation is very weak (0.15 µB ) and fits perfectly with the above
formulation. The coercive field corresponds to a very soft magnet (25 Oe at 10 K).
The compound is very sensitive to dioxygen. In a comment accompanying the
publication [119], Kahn underlined that on the one hand “the synthesis of such a
material can be considered as a cornerstone in the field of molecular magnetism”
. . . and that V[Cr(CN)6 ]0.86 ·2.8H2 O was “an excellent example on which to learn
(or to teach) the basic concepts of molecular magnetism”. On the other hand, Kahn
pointed out that [VCr] “is not a molecular compound, but rather an amorphous
and non stoichiometric compound”, “the saturation magnetisation is limited to
0.15 µB . . . “, ”the coercive field is only 10 Oe . . . ”. This was the first Prussian
Blue system to present a Curie temperature above room temperature, but it is far
from perfect.


9.4.3.1        Improving the Magnetic Properties of VCr Room Temperature
               Molecule-based Magnets
Further improvements in the TC for the VII /CrIII Prussian Blue analogs have been
achieved by varying the synthetic conditions so that the solids obtained are crys-
talline and more nearly stoichiometric. New syntheses were undertaken by our
groups and some others, in particular Miller and Epstein, as recently reviewed
[17, 18, 123, 124], and Hashimoto and Ohkoshi [25]. It would take too long to
detail all the results. The reader is advised to consult the original papers. A set
 9.4 High TC Prussian Blues (the Experimental Race to High Curie Temperatures)           327

of non-stoichiometric Prussian Blue analogs MI y V[CrIII (CN)6 ]z ·nH2 O (M = al-
kali metal cation) arose with TC s varying up to 376 K. We give hereunder some
information on these new compounds. Many factors affect not only the success-
ful synthesis of the compounds in the VCr series but also the magnetic properties
of the resulting solids (Curie temperature, magnetisation at saturation, coercivity
. . . ). Particularly important is the crystallinity and/or the magnetic domain size
of the particles. The structure of Prussian Blues is rich in void spaces, channels,
and (often) vacancies that can accommodate guest species (anions, cations, sol-
vent . . . ). These guest species can either improve or compromise the structural
organisation of the material. To convince the reader that this chemistry is indeed
not easy, we shall give only three examples in which the role of the solvent and of
the starting materials (“innocent” counterions) was investigated: (i) The reaction
carried out in H2 O with [V(MeOH)6 ]I2 as the starting material, gives compound
{VII 0.58 VIII 0.42 [Cr(CN)6 ]0.77 (I− )0.2 (NBu4 + )0.1 }·5H2 O (TC = 330 K). (ii) The reac-
tion in H2 O as solvent and the Tutton salt K2 VII (SO4 )2 ·6H2 O as the starting mate-
rial, gives the compound {VII 0.78 VIII 0.22 [Cr(CN)6 ]0.56 (SO4 2− )0.28 (K+ )0.11 }·4H2 O
(TC = 295 K). (iii) When the reaction is performed in methanol as solvent and
with [V(MeOH)6 ]I2 as the starting material, {V[Cr(CN)6 ]0.69 (I− )0.03 }·1.5MeOH.
(TC = 200 K) is obtained. The magnetisation curves can be found in Refs. [99,
125]. The counteranions and the solvents have large effects on the Curie tempera-
tures and also on the magnetisation at saturation. Large size and weak coordinating
anions as I− , do not induce disorder in the structures and the magnetic properties are
improved. As for the solvent, it can be expected that, when the kinetics of solvent
exchange in [V(solvent)6 ]2+ is faster, the substitution of the solvent molecules by
cyanides around the V2+ ion is more effective, the structure is better organized, and
the number of interactions between Cr and V increases. Among many synthetic at-
tempts, four were successful in improving the situation: changing the VII /VIII ratio
to improve the magnetisation [126]; using large counterions and slow precipitation
by the sol–gel technique, to improve the regularity of the structure [40]; using alkali
metal cations to change the stoichiometry [41]; and using VIII as a catalyst in the
synthesis [127, 128].
     Changing the VII /VIII ratio to improve the magnetisation [126], relies on the
observation that, in a VCr Prussian Blue ferrimagnet, the antiparallel alignment of
the neighboring spins in the magnetically ordered phase leads to a resulting total
magnetisation MT which is the difference between the magnetisation arising from
the subset of chromium ions MCr and that from the subset of vanadium ions, MV :

   MT = |MCr − MV |                                                                   (9.23)

Two situations may arise, one when the larger magnetic moments are borne by the
chromium ions and are aligned parallel to an external applied field (MCr > MV );
the other when MV > MCr . In the later case, the sign of the quantity (MCr −
MV ) is reversed and the magnetic moments of the vanadium ions now lie parallel
328      9 Magnetic Prussian Blue Analogs

to the field. In between, the magnetisation is zero. For example, in the analogs
(CI y VII α VIII 1−α [CrIII (CN)6 ]z ·nH2 O, it is easy to find that
    MT = −(3z − α − 2)                                                                 (9.24)
The spin values (magnetisation) of the compounds can be represented in a three-
dimensional space, in which the value of α varies from 0 to 1 and z varies from 2/3
to 1. The spin values are described by the plane in Figure 9.23.
   The compound {VII 0.45 VIII 0.53 (VIV O)0.02 [Cr(CN)6 ]0.69 (SO4 )0.23 (K2 SO4 )0.02 }·
3H2 O synthesized in this context [126] has a saturation magnetisation MS =
0.36 NA β. The calculated MT value is positive (MT = +0.36 NA β). On the
other hand, {CsI 0.82 VII 0.66 (VIV O)0.34 [Cr(CN)6 ]0.92 (SO4 )0.20 }3.6H2 O, prepared in
the presence of Cs and containing vanadyl, presents MS = 0.42 NA β. The calcu-
lated MT value is negative (MT = −0.36 NA β). The absolute values are in good
agreement with the experimental ones. The crucial difference between the two com-
pounds is the sign of MT , which is influenced by the balance between the values of z
(CrIII /V ratio) and the ratio VII /V. Conventional magnetisation measurements give
the absolute value of the macroscopic magnetisation but not the local magnetisation.
Instead, X-ray magnetic circular dichroism (XMCD), a new X-ray spectroscopy
developed with synchrotron radiation, is an element- and orbital-selective magnetic
local probe. Direct information is obtained about the local magnetic properties of
the photon absorber (direction and magnitude of the local magnetic moment). The
signal appears whatever the shape of the sample (crystals, powders . . . ). A chapter
of Volume I of this series by Sainctavit, Cartier dit Moulin, and Arrio is devoted

                                       VIIICrIII
S
             z                                                          S=0



         α
                                              +                              CIVIICrIII




 A-IVIIICrIII2/3                              -
                                   1

                                                         VIICrIII2/3

Fig. 9.23. Variation of the total spin (or magnetisation MT ) in the series CI y
VII α VIII 1−α [CrIII (CN)6 ]z ·nH2 O as a function of the vanadium fraction α and of the sto-
chiometry z (MT = −(3z − α − 2). The sign of the magnetisation changes above and below
the line S = 0 (see text).
 9.4 High TC Prussian Blues (the Experimental Race to High Curie Temperatures)         329

to this technique [129]: “Magnetic Measurements at the Atomic Scale in Molec-
ular Magnetic and Paramagnetic Compounds”. Figure 8, p. 146 therein, gives the
XMCD spectra at the chromium and vanadium edges and demonstrates: (i) The an-
tiferromagnetic coupling between vanadium and chromium ions (inversion of the
dichroic signal at the vanadium and the chromium K edges, for each compound).
(ii) The opposite local magnetisation of both chromium and vanadium: for a given
edge, the general shape of the dichroïc signal of the first compound is the opposite
of that found in the second. Further useful applications of X-ray absorption (EX-
AFS, XANES at the K and L2,3 edges and XMCD) in the study of Prussian Blues,
in particular CsNi[Cr(CN)6 ] and CsMn[Cr(CN)6 ] can be found in Refs. [130–133]
For the present discussion, the conclusion is that it is absolutely necessary to con-
trol the stoichiometry and the vanadium oxidation states to avoid generating an
antiferromagnet or, with complete oxidation of vanadium to vanadyl, the loss of
the high TC properties as in the (VIV O)[Cr(CN)6 ]2/3 derivative (TC = 115 K) [89]
(Figure 9.22b).
    Second, we found that precursors with large counterions afford a material
that closely resembles the preceding VCr material but whose structure is more
regular [40]. Combining aqueous solutions of the triflate salt V(O3 SCF3 )2 with
the tetraethylammonium salt [NEt4 ]3 [Cr(CN)6 ] under anaerobic conditions af-
fords a dark blue gel after about 10 min. The gel forms only if the reactant
concentrations are above a certain threshold (in our experiments the concen-
trations were 0.02–0.06 mol l−1 ). After 2 h, the gel becomes less viscous and
takes the appearance of a suspension. The suspended solids are collected by cen-
trifugation and washed with water to afford a dark dlue solid of stoichiometry
VII 1 [CrIII (CN)6 ]2/3 ·3.5H2 O·0.1[NEt4 ][O3 SCF3 ]. Unlike the material prepared in
the presence of K+ , NH4 + and SO4 2− counterions, this material is crystalline, with
a fcc cell parameter of a = 10.54 Å. Presumably because it is more highly crys-
talline, it has a slightly higher magnetic ordering temperature of 330 K. When the
sample is heated to 350 K, a change occurs and the ordering temperature is lowered
slightly to 320 K. Although the nature of this change is still under investigation, one
possibility is that the material simply dehydrates upon heating. Another possibility
is that a slight rearrangement (rotation) of the [CrIII (CN)6 ] octahedra leads to a
smaller J value (see Scheme 2 below).
    The next step was clear: change the stoichiometry to 1:1 by adding al-
kali metal cations [see Figure 9.24, derived from Eq. (9.19)]. If the synthe-
sis is conducted in the presence of 4.5 equivalents of CsO3 SCF3 , the ce-
sium salt Cs0.82 VII 1 [CrIII (CN)6 ]0.92 ·3H2 O·0.1[NEt4 ][O3 SCF3 ] (or Cs0.8 VCr0.9 ) is
obtained. A similar reaction with the potassium salt K3 [Cr(CN)6 ] leads to
K1 VII 1 [CrIII (CN)6 ]1 ·2H2 O·0.1KO3 SCF3 (or KVCr). Table 9.8 gathers important
characteristics of the three compounds. Figure 9.25 gives the X-ray powder diffrac-
togram of KVCr, Figure 9.26 presents the thermal variation of the magnetisation
and Figure 9.27 is devoted to the magnetisation vs. applied magnetic field at 5 K.
The low value of the magnetisation of KVCr is perfectly understood by looking
330       9 Magnetic Prussian Blue Analogs

Table 9.8. Properties of the three crystalline high-TC VCr compounds of Ref. [40]. a

                                      VII 1 CrIII 2/3   CsI 0.82 VII CrIII 0.94       KI 1 VII 1 CrIII

 a/Å                                  10.54             10.65                         10.55
 TC /K                                330               337                           376
 TC /K After treatment                320               337                           365
 Msaturation /kG cm3 mol−1            3.5               2.2                           0.7
 Msat expected /kG cm3 mol−1          5.7               1.0                           0.0
 Hcoercive /G                         10                15                            165
 Mremnant /G cm3 mol−1                570               750                           220
 TClosing hysteresis loop /K          350               350                           380
a Adapted from Ref. [40].


at Figure 9.23: KVCr, with α and z = 1 should have a zero magnetisation (line
S = 0). The observed low magnetisation at saturation is indeed the result of a
very small departure of stoichiometry z from 1 or of the oxidation state of vana-
dium from +2. Further data, experimental details, and comments can be found in
Ref. [40].
   The fourth and last issue we would like to address deals with the role of kinetics
in the formation of such compounds. The sol–gel technique above was a first
step in this direction. Furthermore, we discovered during our studies that: (i) in
a perfect anaerobic atmosphere (glove box, 3 ppm O2 ), the slowly precipitating


TC / a.u. 5.5

         4.5


          3.5


          2.5


          1.5

                                                                                    1.0
          0.5
                                                                                 0.8
                0.6                                                           0.6
                       0.7                                              0.4       α
                                0.8
                                                                  0.2
                                            0.9
                                 z                      1.0 0.0

Fig. 9.24. Variation of the Curie temperature (u.a.) in the series CI y VII α VIII 1−α [CrIII (CN)6 ]z ·
nH2 O as a function of the vanadium(II) fraction α and of the stoichiometry z.
 9.4 High TC Prussian Blues (the Experimental Race to High Curie Temperatures)   331




Fig. 9.25. X-ray powder diffraction of KVCr (from Ref. [40]).




Fig. 9.26. Thermal variation of the magnetisation of KVCr (from Ref. [40]).


solid is no longer a room temperature magnet (compound 1 in Figure 9.28), in
strong contrast with the results obtained by the Schlenck technique which lead
to room-temperature magnets (with uncontrolled amount of oxidized vanadium in
solution). (ii) Some oxidation of the vanadium ion during the synthesis is necessary
to reach a Curie temperature above ambient (compound 2 in Figure 9.28). Both
observations prompted us to look more closely at the role of vanadium(III) in the
synthetic process. The results are reported in Ref. [127].
   We found that small amounts of VIII during the synthesis (1% < VIII < 4%)
(Figure 9.29) led to derivatives which display a stoichiometry close to the V1 Cr2/3
ideal one. The solids are free from VIII . Their structure, obtained from EXAFS,
comprised of [CrIII CN)6 ] units linked to octahedral vanadium(II) ions by bent
C−N−V units (α = 168◦ ) as shown in Scheme 9.2. In contrast, without VIII , the
332                     9 Magnetic Prussian Blue Analogs




Fig. 9.27. Field dependence of the magnetisation of the VCr derivatives in Table 9.8.

                 6000

                              Compound 2

                 5000



                 4000
-1
 M / cm .G.mol
3




                 3000



                 2000
                                Compound 1

                 1000



                   0
                        0      50     100    150    200    250   300   350
                                               T/K
Fig. 9.28. Thermal dependence of the magnetisation of two compounds prepared with catalytic
amounts of V(III) (2, — —) and without (1, —◦—).

structures are disordered with a distribution of α angles and tilts of the [Cr(CN]6 ]
octahedra.
   The observed magnetisation fits well the V1 Cr2/3 stoichiometry (Figure 9.30).
The Curie temperatures obtained in this way are not the highest obtained so far but
 9.4 High TC Prussian Blues (the Experimental Race to High Curie Temperatures)         333


                          OH2

                               OH2   N    C Cr

                 Cr C     N
                                V
                      N
                                N

Scheme 9.2 Tilted configuration of [CrIII CN)6 ] and V(NC)4 (H2 O)2 octahedra.

       340


       320
                                                 T = 310 K

       300
                                                             a

       280                                                   b
T /K
 C




       260


       240


       220


       200
             0     10     20         30     40        50         60
                                % V(III)
Fig. 9.29. Curie temperatures vs. percentage of VIII in solution during the synthesis under
various conditions (see Ref. [127] for details).

they are reproducible and remain constant after heating the samples above TC . The
tilted configuration of the [CrIII CN)6 ] octahedra, reminiscent of the situation in
distorted perovskites, is therefore a thermodynamically stable one. The structural
model with α = 168◦ given in Scheme 9.2 allows a straightforward explanation of
the higher TC s of the metastable samples: they adopt a (metastable) structure with α
angles closer to 180◦ (corresponding to a smaller tilt of the [Cr(CN)6 ] octahedron)
and therefore larger orbital overlaps, |J |, and TC s. Heating the sample and cycling
the temperature brings the system to the stable structure with α angles closer to
168◦ and lower TC s. It is particularly significant that the stable TC = 310 K value,
reached here directly, is close to that of VII 1 CrIII 2/3 in Table 9.8, synthesized by
the sol–gel approach by Girolami after cycling the temperature around TC . The
334           9 Magnetic Prussian Blue Analogs

         1
                                  Compound 2




        0,5
   Β




                                  Compound 1
Μ/Ν µ
   Α




         0




    -0,5




         -1
                4             4              4               4      4      4
          -6 10       -4 10          -2 10         0      2 10   4 10   6 10
                                                 H / Oe
Fig. 9.30. Field dependence at 5 K of the magnetisation of two compounds prepared with
catalytic amounts of V(III) (2, — —) and without (1, —◦—).

key role of VIII can also be demonstrated in the synthesis of VCr Prussian Blue
analogs in which the stoichiometry is varied by inserting alkali metal cations (K,
Rb, Cs); these materials have stable TC s between 340 and 360 K and magnetisations
in agreement with the V1 Cr5/6 stoichiometry [128].


9.4.4          Prospects in High-TC Magnetic Prussian Blues

We list below some directions of research which are currently being explored by the
magnetic Prussian Blue community. Among others: magnetic devices, thin layers
and magneto-optical properties, dynamic magnetic properties etc.


9.4.4.1             Devices Built from [VCr] Room-temperature Magnets
Once room temperature is reached, it becomes possible to think about applications,
and the design of demonstrators and devices. Molecule-based magnets, such as the
[VCr] systems, are a useful tool to illustrate easily, near room temperature, what is
a Curie temperature. Figures 9.31 to 9.33 show several devices and demonstrators.
   Figure 9.31 displays a very simple demonstration, in which a disk of [VCr],
embedded in a polymer to protect it from air-oxidation, is attracted by a powerful
 9.4 High TC Prussian Blues (the Experimental Race to High Curie Temperatures)     335

             1                   2                    3                4


          Water               Water                Water
                                                                    Permanent
        T - 80 ºC            T - 80 ºC         T - 80 ºC             Magnet


RT
Magnet
          Holder             Holder                Holder            Holder
Fig. 9.31. Principle of a “flying” magnet.


permanent magnet located just above (2). The permanent magnet is located at the
bottom of a beaker filled with hot water: in contact with the hot bath, the temperature
of the [VCr] disk increases (3). When the temperature reaches TC , the disk falls
(4). Then, on cooling, it is ready to “fly” again when its temperature drops below
TC (1). One can dream of a machine built along the same lines, pumping water by
solar energy (free) and an atmospheric temperature bath (free).
   Figure 9.32 describes an oscillating magnet. The [VCr] compound is sealed in a
glass vessel under argon and suspended at the bottom of a pendulum [equilibrium,
position (2) in the absence of a permanent magnet]. It is then cycled between its
two magnetic states: the 3D-ordered ferrimagnetic state, when T < TC , and the
paramagnetic state, when T > TC . The three steps are: (i) the room temperature

                                                     Image




                                                          (1) (2)
             RT
           Magnet                                    Screen
                 (3)            (1)
                       (2)            Permanent
      Holder                          Magnet


                 Len
       Light Source, Sun …
Fig. 9.32. Principle of an “oscillating” magnet.
336     9 Magnetic Prussian Blue Analogs

magnet ([VCr]) is cold (T < TC , ferrimagnetic state). It is attracted (→) by the
permanent magnet and deviates from the vertical direction towards position (1).
The light beam is focused at this position (1), just above the permanent magnet and
heats the sample, the temperature of which increases; (ii) when T > TC , the hot
[VCr] magnet is in the paramagnetic state. It is no longer attracted and moves away
from the magnet (←) under the influence of its own weight. It is then air-cooled and
its temperature decreases; (iii) when T < TC , the cold [VCr] magnet is attracted
again by the permanent magnet (→) and returns to position (1). The system is ready
for a new oscillation. The demonstrator works well, and millions of cycles have
been accomplished without any fatigue. It is an example of a thermodynamical
machine working between two energy baths with close temperatures (sun and
shadow) allowing the conversion of light into mechanical energy. Figure 9.33a
shows a photograph of the demonstrator in use in our laboratory. Figure 9.33b
shows another demonstrator that could be used as a magnetic switch or thermal
probe: the [VCr] magnet located at the end of a diamagnetic bar, can take two




(a)




                                                         Fig. 9.33. Two demonstrators
                                                         (a) oscillating magnet trans-
                                                         forming light to mechanical
                                                         energy; (b) magnetic switch
(b)                                                      and thermal probe (see text).
 9.4 High TC Prussian Blues (the Experimental Race to High Curie Temperatures)         337

positions: when T < TC , it is in contact with the permanent magnet, the temperature
of which is tunable; when T > TC it is repelled by a mechanical couple installed
on the rotation axis, hence opening or closing an electric circuit [134].


9.4.4.2   Thin Layers, Electrochromism, Magneto-optical Effects
Magnetic Prussian Blue analogs display bright colors and transparency, among
other interesting properties. To exploit these optical properties, it is useful to pre-
pare thin films: a 1 µm thick film of a vanadium–chromium magnet is indeed quite
transparent. The best way to prepare thin films of these materials is by electro-
chemical synthesis or ion-exchange on Nafion membranes. Various films have
been prepared from hexacyanoferrates or chromates [135]. To obtain [VCr] thin
films, the experimental conditions must be adapted. One actually wants to produce
and to stabilise the highly oxidisable VII ion. Thus, strongly negative potentials are
applied at the working transparent semiconducting electrode. The deposition of the
[VCr] film is realised from aqueous solutions of [CrIII (CN)6 ]3− , and aqueous VIII or
VIV O solutions either at fixed potential or by cycling the potential. An interesting
property of [VCr] thin films is the exhibition of electrochromism during cycling.
The way is open for the preparation of electrochromic room temperature magnets
(see Refs. [99, 136–138] for illustrations and details).
   The magnetisation of a transparent magnetic film, protected by a transparent
glass cover, can then be probed by measuring the Faraday effect. Spectroscopic
measurements in the ultraviolet–visible range bring information about the mag-
netisation of the sample and its electronic structure. Observing the Faraday effect at
room temperature in these compounds is a first step towards demonstrating that the
materials can be used in magneto-optical information storage. Hashimoto [136] and
Desplanches [99, 137, 138] succeeded in obtaining from [VCr] room-temperature
magnets a magneto-optical signal at room temperature through a transparent semi-
conducting electrode. The thin films of VCr and CrCr materials presenting high
TC s are protected by a patent [139]. Faraday effects are also observed in low-Tc
Prussian Blues [140]. Electrochemically prepared films of trimetallic Prussian Blue
analogs exhibit second harmonic generation effects [141]. Even if further studies
are needed to control the purity and the homogeneity of the air-sensitive layers and
to correlate the magneto-optical effects with the local magnetisation of vanadium
and chromium, a very promising area is open.
   To conclude this section, we can state that, of all the Prussian Blue analogs
prepared to date, the highest TC s are seen for solids isolated by adding V2+ to
[CrIII (CN)6 ]3− , and that the KI 1 VII 1 CrIII material is the current record-holder. New
precursors, new bimetallic pairs, are coming, involving metal ions of the second
and third period of the transition metal ions, which may change the situation.
338     9 Magnetic Prussian Blue Analogs

9.5 Prospects and New Trends

Space is lacking in this review to develop further aspects of the chemistry and
physics of other magnetic Prussian Blues. Fortunately, many aspects have been
reviewed recently and the interested reader will find valuable information in the
references quoted below. We would like nevertheless to quote some promising
areas of development. They show that besides the problem of high TC much more
can be learned from, and done with, Magnetic Prussian Blues.


9.5.1   Photomagnetism: Light-induced Magnetisation

A new field was opened in the magnetic Prussian Blues story and in molecular
magnetism when Hashimoto and his team reported the existence of an exciting pho-
tomagnetic effect in a Prussian Blue analog formulated K0.4 Co1.3 [Fe(CN)6 ]1 ·5H2 O
(or K0.3 Co1 [Fe(CN)6 ]0.77 ·3.8H2 O, close to Co1 Fe2/3 ), that has been known for
a long time (Table 9.2) [142]. Starting from aqueous solutions of co(II) and
hexacyanoferrate(III), Hashimoto obtained a powder, containing potassium ions,
which exhibited photo-induced enhancement of the magnetisation at low temper-
ature and an increase in the Curie temperature: photoexcitation at the molecular
level, in the Co−NC−Fe unit, gives rise to a modification of the macroscopic
properties of the material, an important feature [143]. The authors suggested the
presence of isolated diamagnetic pairs CoIII −FeII in a compound otherwise built
from −CoII −NC−FeIII − units and a photo-induced electron transfer from FeII to
CoIII through the cyanide bridge. The enhancement of the magnetisation and the
increase in the Curie temperature simply follows from the increase in the number
of magnetic pairs in the photo-induced state. The publication of this first result
gave rise to a an impressive series of findings by several groups. Theoretical studies
were carried out by Yamaguchi [144], Kawamoto [145] including a patent for an
optical storage element [146] and experimental studies were performed by Bleuzen
[147, 148, 214], Gütlich [149], Hashimoto [25, 150–152], Miller [153] and Varret
[154, 155], who defined the conditions of appearance of the phenomenon, pointing
out the role of the ligand field around the cobalt, the role of the vacancies, the very
specific role of the alkali metal cations, the presence of several phases, etc. There
is not room here to give an exhaustive survey. Among many beautiful results, the
first evidence of a photo-induced diamagnetic–ferrimagnetic transition [25, 147]
and magnetic pole inversion [25, 150–152] can be underlined. Epstein and Miller
studied the dynamics of the magnetisation and proposed a model of a glass cluster
in the ground and photoexcited states, with an increase in spin concentration
in the photo-induced phase [153]. Although the Co–Fe systems are still being
actively studied [156–159], they are now joined by other systems constructed from
octacyanometalates, developed by Hashimoto [25, 160], Mathonière [161, 162],
                                                  9.5 Prospects and New Trends      339

Marvaud [163] etc. The field has been reviewed by several authors, emphasizing
the importance of optically switchable molecular solids. Varret, Nogues and
Goujon in the Chapter entitled “Photomagnetic Properties of Some Inorganic
Solids” in Volume I of this series [164], Hashimoto and Okhoshi [25], and more
recently Sato [165, 166], cite many references to work in this illuminating field.


9.5.2   Fine Tuning of the Magnetisation

The flexibility of the Prussian Blues, especially the ability to adjust at will
the composition, was used to play with the magnetisation of the systems, us-
ing the mean field model as a predictive tool (see Section 9.3.2.1). Okhoshi,
Hashimoto and coworkers produced an impressive series of new results begin-
ning with the coexistence of ferromagnetic and antiferromagnetic interactions in
a Nix Mn(1−x) [Cr(CN)6 ]2/3 a trimetallic Prussian Blue [167–169]. With the same
theoretical model, they looked at the compensation temperature and other phe-
nomena predicted by Néel [75]. They used competing ferromagnetic interactions
to tune the compensation temperatures in the magnetisation of ferrimagnets and
they were able to design systems with two compensation temperatures [170, 171].
They also describe an inverted hysteresis loop combining a spin–flop transition and
uniaxial magnetic anisotropy. Finally, they combined their efforts and experience in
photomagnetism and magnetisation to characterize photo-induced magnetic pole
inversion [172]. The results are reviewed in Refs. [25, 173]. The same authors
review the very peculiar magnetic properties of RbMn[Fe(CN)6 ] in Ref. [174].


9.5.3   Dynamics in Magnetic and Photomagnetic Prussian Blues

The AC susceptibility was not systematically exploited in earlier studies of MPBs.
Epstein and Miller opened this field. When measuring the alternative susceptibility
of different molecule-based magnets, they discovered unexpected new behavior,
often assigned to spin–glass behavior, as described before in the photomagnetic
CoFe PB analog [153, 175–178]. They found similar behavior in first-row transition
metal hexacyanomanganates [179]. Other authors suggested similar conclusions
in vanadium hexacyanochromates [180] and gadolinium hexacyanoferrates [181].
It appears that the synthetic conditions, the chemical stability, the crystallinity, the
homogeneity and the purity are important issues to control in order to understand
the dynamics.


9.5.4   Nanomagnetism

This field is still in its infancy but several papers have recently appeared, show-
ing the interest and the potential of magnetic Prussian Blues for the preparation
340     9 Magnetic Prussian Blue Analogs

of magnetic nanosized systems. In the trend to ever higher magnetic informa-
tion storage densities, obtaining nanosize magnetized particles is an important
issue, both for theory and applications. Prussian Blues allow top-down (breaking
three-dimensional PB solids) or bottom-up (controlling crystalline growth from
molecules in solution) approaches. The chemical flexibility of the PB analogs can
be a great advantage in tuning the final properties. In 2000, Gao et al. announced
that they were able to get obtain VCr derivatives with TC = 340 K, fcc lattice,
a = 11.78 Å, stable in air for days, with an average particle size of 5 nm, present-
ing long range ferrimagnetic behavior and spin–glass behavior [182]. In 2001 Mann
et al. prepared good quality inverse opals of Kx Co4 [Fe(CN)6 ]z from polystyrene or
silica colloïdal crystal templates [183]. Then, they used water-in-oil emulsions to
synthesize crystalline cobalt hexacyanoferrate, cobalt pentacyanonitrosylferrate,
and chromium hexacyanochromate in the form of 12–22 nm particles organized in
100 particle superlattices [184]. They expected that the preparation method would
be readily applicable toward the synthesis of other nano-sized molecule-based mag-
nets. It was successful with nickel hexacyanochromate in the hands of Catala et al.
who obtained 3 nm sized particles(with a wide distribution) [185]. Zhou adopted an
electrodeposition technique in the nanocavities of aluminum oxide films to fabricate
highly ordered Prussian Blue nanowire arrays 50 nm in diameter and 4 µm in length
[186]. Stiegman used the sol–gel technique competing with arrested precipitation
to obtain superparamagnetic nanocomposites: transparent nickel hexacyanochro-
mate and photomagnetic cobalt hexacyanoferrate [159]. Langmuir–Blodgett films,
which are known to incorporate Prussian Blue itself [187, 188] are also able to trap
MPB nanocubes in a thin film, as shown by Delhaes et al. [189]. The field will
most probably expand quickly if the difficult problem of characterisation of the
new phases can be solved.




9.5.5   Blossoming of Cyanide Coordination Chemistry

The cyanide ligand has a long history in coordination chemistry and organometallic
chemistry. It is known as a very dangerous, but also friendly, ligand. The reviews
by Fritz and Fehlhammer [190] in 1993 and by Dunbar and Heintz in 1997 [60]
pointed out the revival of cyanide chemistry. Molecular magnetism and MPBs
have contributed to the blossoming of cyanide coordination and organometallic
chemistry with new ideas, new concepts, new precursors (tetra-, penta-, hexa-,
hepta-, octa-cyanometalates), new architectures etc. Work by Ceulemans [191],
Decurtins [192, 193], Dunbar [194, 195], Hashimoto [196], Kahn [197], Julve
[198], Long [199, 200]], Mallah [201, 202], Marvaud [97], Murray [203], Okawa,
Ohba and Inoue [204], Ouahab [205], Rey [206], Ribas [207], Sieklucka [208].
and many others, shows that there is considerable interest in this area.
                                                   9.5 Prospects and New Trends        341

9.6 Conclusion: a 300 Years Old “Inorganic Evergreen”

These new directions of development are clear indications that the field of magnetic
Prussian Blues is very active, with various lines of development in addition to the
problem of reaching high critical temperatures, which was the main subject of the
present chapter. The deep color of Prussian Blue was, and remains, a fascination
for drapers, artists, and chemists. Magnetic and multifunctional Prussian Blues add
a new facet to this attraction, from fundamental quantum mechanics to appealing
applications, via solid state chemistry and physics. Ludi [209] was right when he
pointed out that Prussian Blue is indeed an “inorganic evergreen”. The statement
is especially specially appropriate for its 300th anniversary, celebrated this year.

Acknowledgments

The authors dedicate this chapter to the memory of their colleague and friend O.
Kahn, whose ideas inspired much of the work presented here. MV wishes to thank
Drs. S. Alvarez, E. Ruiz, M. Julve, F. Lloret, B. Siberchicot and V. Eyert for illumi-
nating discussions and suggestions about the theory of the systems. The authors are
grateful to their coworkers, without whom these magnetic Prussian Blues studies
could not have been done; their names appear in the cited articles. Funding from
the Pierre et Marie Curie University at Paris, the Department of Energy through
the Frederick Seitz Materials Research Laboratory at the University of Illinois at
Urbana-Champaign, CNRS, the European Community (TMR and Marie Curie Pro-
grammes), I.C.R.E.A. Barcelona and the European Science Foundation (Molecular
Magnets Programme) is sincerely acknowledged.



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10 Scaling Theory Applied to Low Dimensional
   Magnetic Systems
       Jean Souletie, Pierre Rabu, and Marc Drillon




10.1 Introduction

Since the 1960s, much work has been devoted to phase transitions and the study of
critical phenomena in the vicinity of the ordering temperature TC [1]. These studies
reveal the existence of striking similarities in the behavior of very different physical
systems. Most of the experimental results show that, superconductors apart [2], the
behavior of the order parameter is very different from that predicted by Landau
theory [3–5], indicating the key role played by fluctuations close to TC .
   A phase transition is characterized by pre-transitional processes with a variable
local order (short-range order) where the system fluctuates between states of close
energy. Approaching TC , ordered domains are formed whose mean size is the cor-
relation length ξ . The divergence of ξ and, accordingly, of the related susceptibility,
increases when T approaches TC . This description of the phase transition leads to
important results. Thus, in the vicinity of TC , the variation of the thermodynamical
functions is described by power laws (T − TC )γ where γ is the critical exponent
[6]. It is worth noticing that the critical exponents depend only on the spatial ex-
tent of the system, d, and on the number of components of the order parameter,
n, thus defining classes of universality. This induces two key ideas in the critical
phenomena theory, namely the concept of scaling invariance and the concept of
universality, as pointed out by Kadanoff [7], and checked by the calculations of
critical point behavior by Wilson and Wegner [8].
   In that area, magnetic phase transitions have likely been the most investigated,
because of the wide variety of compounds exhibiting different spins (Ising, planar
or Heisenberg) and lattice dimensionalities [9–12].
   In the present chapter, we develop a model of “hierarchical superparamag-
netism” which generalizes the idea of scaling by taking advantage of the non-
singular solutions that are introduced, together with the singular ones, when the
hypotheses of “critical scaling” are formulated. These non-singular solutions, al-
though they have the same legitimacy, have simply been set aside when the goal
was to describe the singularities of phase transitions. They happen to be very useful
348     10 Scaling Theory Applied to Low Dimensional Magnetic Systems

when correlations exist, but are not sufficient to trigger a long-range order at a finite
TC , either because frustration is strong, near e.g. an antiferromagnetic (AF) order,
or because we sit at, or below, a lower critical dimensionality. Model systems, such
as the 1D or 2D-Heisenberg systems of spin S = 1/2, 1, . . . ∞ display such behav-
ior. For this reason, much effort has been devoted to performing exact calculations
on such finite systems of increasing size, and in trying to infer which type of limit
is reached when the size diverges. On the other hand, the progress of chemistry
has made it possible to design organometallic clusters, chains or planes, of axial,
planar or isotropic spins, which closely approximate the abovementioned systems,
and are very appropriate to investigate the properties of interest. We will show with
a few examples, some based on the experimental behavior of real compounds and
others on theoretical data derived for finite Heisenberg chains, that the model of
hierarchical superparamagnetism provides the right framework to approach these
problems and suggest a strategy adapted to each case.



10.2 Non-critical-scaling:
     the Other Solutions of the Scaling Model

Let χ T = Nµ2 /3, where µ = [S(S + 1)]1/2 and χT is normalized to g 2 µ2 /k,   B
be the Curie constant of N independent spins, and ξ0 the typical size at the atomic
scale. In the presence of interaction, we assume that these spins are correlated in
space, and the correlation length ξ(T ) defines the size of the new objects. Their
volume is ξ d in space dimension d, and their number N = N0 (ξ/ξ0 )−d . Following
Néel in his description of fine magnetic particles, we similarly assume that the
moment of each object increases as a power d of ξ , where the dimensionality d
characterizes the magnetic order which sets in [13].
   Depending on the relation between d and d, we may then characterize different
situations: thus, if d = d, we describe a ferromagnet whose moment increases as
the volume of the units. By contrast, the moment in an antiferromagnet is accurately
compensated within the volume of the units but not, presumably, at the surface,
and d = d − 1 or (d − 1)/2 in the presence of disorder at the surface. In the
absence of any correlation between the magnetic ordering and the structure, the
uncompensated moment increases as ξ d/2 , a situation which occurs in spin glasses.
Then, the expression of the χ T product is given by:
   χ T ∝ ξ(T )−(d−2d )                                                            (10.1)
We now write that ξ increases when T decreases, and that it is possible, in the
spirit of Kadanov’s renormalization scheme, to connect by a “hierarchical recipe”
the successive steps of the cascade which relates ξ and ξ0 . Assuming, for example,
that ξ is multiplied by b when (J /TC − J /T ) is multiplied by a, then, if n steps
              10.2 Non-critical-scaling: the Other Solutions of the Scaling Model     349

are needed to relate Tn , where the correlation is ξn , with J , where it reduces to ξ0
[13], one obtains:
   J /TC − J /Tn = a × (J /TC − J /Tn−1 )
                 = a × a × a × . . . × (J /TC − 1) = a n × (J /TC − 1) (10.2a)
              ξn = b × ξn−1 = b × b × b × . . . × ξ0 = bn × ξ0         (10.2b)
By eliminating n between Eqs. (10.2a) and (10.2b), one derives the standard relation
of static scaling:
   ξ/ξ0 = (1 − TC /T )−ν = (1 − TC /T )−      /TC
                                                                                    (10.3)
with = νTC > 0 in order to ensure that log(ξ/ξ0 ) = 1 + /T + TC /2T 2 +
  TC /3T 3 + . . . is an increasing function of 1/T .
    2

   For > 0, the sign of TC fixes the curvature in such a way that the Arrhenius
law ξ/ξ0 = exp( /T ), corresponding to the TC /T = 0 limit, separates solutions
of positive curvature, ξ/ξ0 = (1−TC /T )− /TC , from those whose curvature is neg-
ative, ξ/ξ0 = (1 + TK /T ) /TK where TC = −TK , which have the same legitimacy
(see Figure 10.1).
   The “static scaling assumption” has measurable consequences. In particular,
using Eq. (10.1) and permitting TC to be positive, zero or negative, we find:
   χ T = C × (1 − TC /T )−(2d −d)ν = C × (1 − TC /T )−γ   for TC > 0 (10.4a)
   χ T = C × exp((2d − d) /T ) = C × exp(−W/T )           for TC = 0 (10.4b)
   χ T = C × (1 + TK /T )(2d −d) /TK = C × (1 + TK /T )−γ for TC = −TK (10.4c)




                                           Fig. 10.1. (a) log(ξ/ξ0 ) vs. 1/T and corre-
                                           sponding (b) ∂ log(T )/∂ log(χT ) vs. T diagram
                                           showing the typical variations expected for TC
                                           positive, zero or negative in the framework of
                                           the proposed model.
350     10 Scaling Theory Applied to Low Dimensional Magnetic Systems

The solutions (10.4a) are the familiar power laws appropriate to describe the usual
phase transitions, with γ being the critical exponent related to the spin and lattice
dimensionalities. Note that because we were careful by using J /T , which cancels
when T diverges, rather than T /J to construct the scaling variable (J /TC − J /T ),
all Eqs. (10.4) that we obtain have a sensible high temperature expansion. Thus,
the Curie–Weiss law χ = C/(T − W ) is recovered, with C = S(S + 1) being the
Curie constant (in Ng 2 µ2 /3k units), and W = (2d − d) the Weiss temperature.
                           B
    Let us now focus upon other aspects of the system of Eqs. (10.4) that have,
in general, been left aside. First, we observe that the solutions of type (10.4b) or
(10.4c) have the same legitimacy as the solutions of type (10.4a) and that they are
not forbidden by any thermodynamic rule. They are therefore natural candidates to
describe systems, sitting at or below a “lower critical dimensionality”, where spin
correlations are significant but no long-range order sets in at any finite tempera-
ture. Second, we observe that, for a given positive = νTC , the model provides,
depending on the sign of 2d −d, both ferromagnetic solutions where χT increases
upon cooling and AF solutions where χ T decreases. We will use hereafter the latter
to describe the magnetization of real AF systems, breaking with a tradition whereby
it is argued that the usual susceptibility does not contain valuable information, and
that the “staggered” magnetization should be considered instead.
    In order to check these ideas and to decide which expression is more appropri-
ate to describe experiments, we propose to differentiate Eq. (10.4) to obtain the
equivalent expression:

   ∂ log(T )/∂ log(χ T ) = −(T − TC )/γ TC                                     (10.5)

It appears that ∂ log(T )/∂ log(χ T ) is a linear function of T , in the temperature
window where the scaling argument is valid, and that γ −1 and TC are simultaneously
deduced from the intersection of the straight line with the axes (see Figure 10.1). In
the TC = 0 limit, where χ T is described by Eq. (10.4b), the straight line intersects
the axes at their origin.
   In previous works, we have reported examples where ∂ log(T )/∂ log(χT ) ob-
tained by differentiating the experimental data shows a unique linear regime, giving
a TC value that is positive, zero or negative [14, 15]. In some cases, we observe an
abrupt crossover, from one regime to the other (e.g. from solutions of type (10.4b)
to solutions of type (10.4a)) occurring at a given crossover temperature where the
effective space dimensionality changes (e.g. because correlations which are negli-
gible at the scale of atomic distances may become important on large segments).
   We will hereafter consider yet another situation where two different criticalities
seem to coexist in the same temperature range, i.e. where two solutions of type
(10.4b) are superimposed in a common temperature window.
                       10.3 Universality Classes and Lower Critical Dimensionality            351

10.3 Universality Classes and Lower Critical Dimensionality

As ξ(T ) diverges, it is argued that the physics should not depend on the local defects
or the details of the structure. Rather, it reflects the main anisotropies, such as the
dimensionality d of space and the dimensionality n of the order parameter, or spin
space symmetry, which persist and are dominant at long range. As a consequence,
the value of the critical exponent is expected to depend closely on these dimensional
features. We have reported in Table 10.1 the values of the critical exponent of χT
at the ferromagnetic transition, according to the dimensions of d and n, where
n = 1, 2, 3, for Ising, planar and Heisenberg spins, respectively and n = ∞ for the
spherical model. A finite number of interesting cases is observed, including two
exact solutions, the Ising chain model (n = 1, d = 1) and the Onsager’s solution
for the 2D-Ising model (n = 1, d = 2).


Table 10.1. Critical exponent of the χT = f (T ) dependence, according to the spin space (n)
and lattice (d) dimensionalities. The exponent conserves the mean field value γ = 1 for all
n at d ≥ 4. We suggest that γ diverges, for each n, at a lower critical dimensionality, dc (n),
which is 1 for the Ising case and is a frontier between the solutions of Eqs. (10.4a) and (10.4c).
Our finding for the 1D-Heisenberg case is also included.

               n = 1 (Ising)    n = 2 (XY)      n = 3 (Hbg)     n = ∞ (sph.)

  d=1                ∞                            −1.23S
  d=2               1.75            KT              ∞
  d=3               1.25            1.32           1.387               2
  d=4                 1               1              1                 1
 Mean field           1               1              1                 1



    Table 10.1 reflects results that bypass, to a large extent, the ferromagnetic tran-
sition itself. In particular, it is noticed that:

• A ferromagnetic transition occurs in mean field, the solution of which, γ = 1,
  corresponds to the limit of infinite dimensionality of space.
• The mean field solution is available down to an “upper critical dimensionality”,
  which is d = 4 in the ferromagnetic case.
• The long-range order is destroyed if the space dimension is decreased below a
  “lower critical dimensionality”, dc (n), characterized by a divergence of γ .
• In the space dimension between dc (n) and 4, there is still a ferromagnetic tran-
  sition but γ differs from the mean field value.

   As a result, we propose that solutions of Eqs. (10.4b) and (10.4c) well describe
the situations at and below dc (n), respectively, making possible the determination
352     10 Scaling Theory Applied to Low Dimensional Magnetic Systems

of γ to complete Table 10.1, either by analysing the theoretical results or by an
accurate analysis of the experimental data.
   There are difficulties that we propose to discover in typical examples, together
with a strategy inspired by our model of hierarchical superparamagnetism.


10.4 Phase Transition in Layered Compounds

Considerable attention has recently been focused on the design and synthesis of
ferro- or ferrimagnetic molecular materials [16]. Basically, the exchange interaction
in these materials usually has a low-dimensional character, and so they may be
considered as good candidates for studying isolated chains or layers.
    Layered systems with isotropic in-plane interactions are known to show long-
range order at T = 0, only. TC becomes finite only if any type of anisotropy
(exchange or dipolar-like, magnetocrystalline . . . ) is introduced, as demonstrated
for the weak in-plane anisotropy of dipolar origin which induces a 2D ordering [17,
18]. Recently, we have shown that a 3D long-range order might occur at a sizeable
temperature in layered compounds made of ferromagnetic layers up to 40 Å apart
[19]. Similar results have been observed for chain systems [20, 21] and therefore
the combination of in-plane (or in-chain) quantum exchange and inter-plane (or
inter-chain) dipolar interaction has been considered.
    Basically, the strength of the dipolar interaction is weak as far as single ions
are concerned and, for a pure dipole system, critical temperatures of a few K,
at most, can be expected. However, as the dipolar energy depends on the square
of the effective moment, the interaction between high spin correlated units, as for
instance temperature dependent domains in low dimensional ferro- or ferrimagnets,
can become efficient [22, 23].
    The series of hydroxide-based compounds M2 (OH)4−x Ax ·zH2 O (M = Co, Cu
and A = n-alkyl carboxylate anion) provides suitable examples of quantum mag-
netic layers coupled by dipolar interactions. The distance between metal hydroxide
layers is controlled in the range 9–40 Å by the length of the organic anions which
play the role of spacers (Figure 10.2) [24–26].
    The magnetic properties are shown to depend closely on the nature of the metal
ions and organic spacers. Thus, the compounds Cu2 (OH)3 (n-Cm H2m+1 CO2 )·zH2 O
have a ferrimagnetic character, while the cobalt(II) analogs order generally ferro-
magnetically with critical temperatures being 10–58 K for m ranging from 1 to 12
[24–26].
    From a structural point of view, the above hydroxy carboxylates consist of 2D
triangular arrays of CuII ions octahedrally surrounded by oxygen atoms belonging
to either hydroxide or long-chain carboxylate anions. The distance between layers
varies linearly with the length of the n-alkyl chain (m), according to the relation
d(Å) = d0 + 2.54m cos θ available for double organic layers, where θ is the tilt
                                      10.4 Phase Transition in Layered Compounds            353




                                                     Fig. 10.2. Layered structure of the
                                                     hydroxy carboxylate-based compounds
                                                     showing the metal-hydroxide layers well
                                                     separated in the space by organic chains.
                                                     The tilt angle (θ) of the chains depends on
                                                     the metal ion.


angle of the chains [19, 26]. For m = 10 and 12, d is found to be 35.9 Å and 40.7 Å,
respectively [19].
   The magnetic susceptibility χ (T ) is shown in Figure 10.3 for m = 9, which is
representative of the series. M/H recorded by cooling the sample in 1 T increases
strongly with decreasing temperature, and exhibits a transition at about TC = 21 K,
where ferromagnetic order sets in. The existence of a magnetically ordered state
is confirmed by the hysteretic effect observed at very low temperature. In the
following, we focus on the high-temperature region, where the correction due
to the demagnetizing field is small and can be neglected. Several features point




Fig. 10.3. Variation of χ (T ) and χT (T ) for Cu2 (OH)3 (n-C9 H19 CO2 ). The raw data (circles)
are well fitted by a model allowing for the competition of two exponential contributions of the
type of Eq. (10.4b).
354     10 Scaling Theory Applied to Low Dimensional Magnetic Systems

towards a ferrimagnetic or a non-collinear spin configuration within the copper(II)
layers, such as the presence of a well-marked minimum in the χT vs. T plot well
above TC (Figure 10.3).
    To discuss the results, we have plotted in Figure 10.4 ∂ log(T )/∂ log(χT ) vs.
T , as obtained from powder sample measurements in a conventional SQUID mag-
netometer.
    First, we observe, that ∂ log(T )/∂ log(χ T ) diverges at two extrema of the χT (T )
dependence. The maximum of χ T , near 20 K, is associated with the ferromagnetic
transition, while the minimum, at about 65 K, separates a high temperature win-
dow where ∂ log(T )/∂ log(χ T ) is positive, and the system is AF, from a lower
temperature regime where ferromagnetic correlations dominate. Trial values of
TC , which can be inferred from the regimes away from the singularity, are zero or
small enough to be neglected in the temperature range of interest. This leads us to
search for a fit above 40 K, by superimposing two exponentials of the type (10.4b),
one AF dominant at high temperature and the other, ferromagnetic, which prevails
at low temperatures when the former collapses. Note that the latter is fully justified
for a 2D Heisenberg ferromagnet, whose low-temperature behavior is given by




Fig. 10.4. Plots of ∂ log(T )/∂ log(χT ) and ∂ log(T )/∂ log(χT )ferro vs. T in Cu2 (OH)3 (n-
C9 H19 CO2 ). χ Tferro has been obtained by subtracting from the bulk χT data the AF compo-
nent which dominates the high temperature regime.
                                   10.4 Phase Transition in Layered Compounds       355

χ T = exp(4π J S 2 /T ), J being the in-plane exchange interaction [16]. We found
indeed an excellent fit (see Figure 10.3) over the whole range, with the expression:
   χ T = C1 exp(αJ /T ) + C2 exp(βJ /T )                                         (10.6)
where C1 = 0.619, αJ = −99.2 K, C2 = 0.037, βJ = +99.2 K.
    The driving interaction, responsible for the initial high temperature decay of
χ T , is antiferromagnetic (negative αJ ). It concerns most of the moments and
is attributed to the dominant in-plane interaction. In turn, the low-temperature
increase of χ T is dominated by the second term that is ferromagnetic-like.
    In order to know more about this ferromagnetic contribution, we have corrected
the bulk susceptibility from the AF component, determined above 50 K, to obtain
χ Tferro = χ T − C2 exp(W2 /T ). We thought that our knowledge of the AF compo-
nent, obtained in a domain where it is dominant, was sufficiently good to be extrap-
olated below 40 K and subtracted from the signal, in order to improve our knowl-
edge of the ferromagnetic component. The comparison of ∂ log(T )/∂ log(χT )ferro
with its bulk counterpart, in Figure 10.4, stresses the permanence of the ferro-
magnetic contribution. It is confirmed that, down to about 30 K, the ferromag-
netic component is well described by an exponential solution of the type (10.4b)
since ∂ log(T )/∂ log(χ T )ferro is proportional to T . We can, on the basis of this
observation, identify the space dimension d = 2 as a lower critical dimension for
ferromagnetic Heisenberg systems.
    The remarkable feature in Figure 10.4 is the abrupt crossover, that occurs at about
29 K, to a distinct regime where ∂ log(T )/∂ log(χT )ferro is still a linear function of
T , but aims towards a finite TC with a typical 3D exponent. A direct fit of the data
with Eq. (10.4a) in the temperature window 22–30 K, as suggested by Figure 10.5,
yields TC = 21.4 K and γ = 1.31, which is close to the theoretical 3D-Heisenberg
value. Note that the same analysis for m = 10 gives TC = 21.05 and γ = 1.36.
The crossover, once it has been spotted, can be made visible in the data themselves.
For example, in the Arrhenius plot of χ T vs. T (Figure 10.6), we notice a change
from a high temperature linear variation to a regime of strong positive curvature.
The fit with Eq. (10.4), is excellent in either case, and can be made better if we
take into account, near TC , the effect of the demagnetizing field, which limits
the divergence of the susceptibility. It is possible, by doing so, to minimize and
eventually to suppress the rounding the maximum on the ∂ log(T )/∂ log(χT ) vs. T
variation.
    The crossover is not surprising. As the temperature decreases, the 2D correlation
length increases leading to larger correlated domains. The interactions between
domains of the same plane increase with their perimeter, while the interactions
between domains of different planes increase with their surface area, so that suffi-
ciently large plates, even when far apart, will get coupled below some temperature;
accordingly, the transition which is observed ultimately is a 3D transition.
    The existence of a crossover can very seldom be made as visible as it is in
Figure 10.5. This alternative representation of the experimental evidence allows
356     10 Scaling Theory Applied to Low Dimensional Magnetic Systems




Fig. 10.5. The plot is an enlargement of Figure 10.4 where the crossover at T = 29 K in the
m = 9 system (CuC9), from a 2D regime where TC is zero and γ is infinite to a 3D regime
where TC = 21.4 K and γ = 1.31, appears magnified. The same graph shows the behavior of
Co2 (OH)3.5 (IMB)0.5 ·2H2 O (Corad1), that undergoes a similar crossover between the same
two classes of universality, although the physics involved is different.




Fig. 10.6. Arrhenius representation of log(χT ) and of log(χT )ferro vs. 1/T , for the m = 9
system. At high temperature the ferromagnetic component, (χT )ferro obeys Eq. (10.4b) and
is described by a straight line in this plot.
                                  10.4 Phase Transition in Layered Compounds         357

one, at a glance, to decide the reality of a scaling process, with regard to range and
parameters. It is then possible, coming back to the original data, to determine, in
this range, the best values of the parameters [15].
   The study of the metal-radical compound, Co2 (OH)3.5 (IMB)0.5 ·2H2 O, obtained
by aion-exchange reaction in Co2 (OH)3 NO3 with meta-iminonitroxidebenzoate
anion [26, 27], is another good illustration of what can be deduced from this par-
ticular reading of the experimental data. The structure consists of the stacking of
Ising-like Co(II) hydroxide layers and isotropic IMB radicals. Cobalt(II) ions oc-
cupy both octehadral and tetrahedral sites, while the basal spacing is found to be
22.8 Å.
   The χ T product shown in Figure 10.7a is not a monotonic function of tem-
perature, due to the influence of spin–orbit coupling competing with magnetic
interactions. The plot of ∂ log(T )/∂ log(χ T ) vs. T is shown in Figure 10.7b, and
compared to that of the copper(II) analog in Figure 10.5. Very similar situations




                                                        Fig. 10.7. Magnetic behavior
                                                        of Co2 (OH)3.5 (IMB)0.5 ·2H2 O:
                                                        (a) temperature dependence
                                                        of the χT product, (b) plot
                                                        of ∂ log T /∂ log(χT ) vs. T for
                                                        raw data (squares) and those cor-
                                                        rected for the high temperature
                                                        contribution, namely χTcorr =
                                                        χTmeas − 3.16 exp(−6.87/T )
                                                        (circles).
358     10 Scaling Theory Applied to Low Dimensional Magnetic Systems

are noticed from the universality class point of view, despite both systems being
extremely different from a microscopic point of view.
    Two singularities are observed at 8 K and 65 K, defining three temperature
ranges. These divergences point to extrema of χT = f (T ) occurring when there
is a balance between two regimes, as defined in the system of equations (10.4).
Thus, the minimum of χ T at 65 K separates a high temperature range where
∂ log(T )/∂ log(χ T ) is positive, with TC small or zero, from a low temperature
regime where ferromagnetic correlations dominate and where TC is also small.
The fit over the temperature range 15–300 K by using two exponentials gives
χ T = 3.16 exp(−68.7/T ) + 2.92 exp(20.46/T ).
    It is worth noticing that the χ T variation above 65 K does not correspond to AF
behavior, but actually to the effect of spin–orbit coupling for octahedral Co(II) ions.
There is no real explanation as to why the fit turns out to be so good with a plain
superimposition of the two exponential contributions, but it adequately describes
the spin–orbit coupling, which stabilizes discrete levels, and the low-temperature
divergence of the susceptibility of a 2D ferromagnetic system.
    In the critical regime, the apparent susceptibility χ must be corrected for the
demagnetizing field, which limits the effect of the external field. At the ferromag-
netic transition, χ = M/H saturates to a value 1/α, where α is the demagnetizing
coefficient.
    This determination of α allows one to deduce the intrinsic magnetic susceptibil-
ity χi = M/(H − αM), and to obtain the actual temperature dependence of χT ,
illustrated in the Arrhenius plot of Figure 10.8. The best agreement is obtained
for χ T ∝ (1 − 7.6/T )−1.40 which is consistent with the value expected for a 3D
Heisenberg ferromagnet. It is to be noted that the crossover from a 2D to a 3D
regime occurs at about 13 K (see Figure 10.7).




Fig. 10.8. Variation of χ T vs. 1/T for Co2 (OH)3.5 (IMB)0.5 ·2H2 O. The data corrected for
the demagnetizing effect are shown as χTcorr and compared to the power law variation (full
and dotted lines).
                                     10.4 Phase Transition in Layered Compounds           359

   The compound [Co(CO2 (CH2 )OC6 H5 )2 (H2 O)2 ] also exhibits changes of regime
at low temperature, due to the spin–orbit coupling effect and to the magnetic di-
mensionality [28].
   This system can be described as a layered cobalt(II)-diaqua-bis-µ-η1,η1-
phenoxyacetate polymer, as displayed in Figure 10.9. Each CoII atom is coordinated
by six oxygen atoms forming slightly elongated octahedra. The cobalt atoms are
interconnected within the layers via carboxylato bridges in a syn-anti conforma-
tion, thus forming square planar magnetic arrays separated by a double layer of
phenoxy acetate anions (Figure 10.9a). The latter are quasi-perpendicular to the
cobalt layers, which are 16.57 Å apart (Figure 10.9b).
   The temperature dependence of the χ T product shown in Figure 10.10 exhibits
a regular decrease from 300 K to 10 K, in agreement with the behavior of a non-
symmetrical ion submitted to spin–orbit coupling [29, 30] It is to be noticed that
for isolated octahedral Co(II) ions, a minimum value of χT ≈ 1.8 emu K mol−1
is expected, corresponding to a pseudo-spin S = 1/2 and g ≈ 4.4. Below 10 K,
χ T increases abruptly up to 2.81 emu K mol−1 at 2 K, according to the influence of
significant ferromagnetic correlations. As deduced from magnetization measure-
ments, no long-range order takes place at this temperature. The saturation moment,
Ms = 2.25 µB mol−1 , agrees with the expected value for octahedral high spin Co(II)
ions.
   Ac magnetic measurements were performed on a small platelet-shaped crystal
in an ac field of approximately 1 G (frequency 2.1 Hz), parallel to the Co(II) lay-




              (a)                                       (b)
Fig. 10.9. Structure of Co(CO2 (CH2 )OC6 H5 )2 (H2 O): (a) Perspective view showing the square
planar arrangement of the cobalt(II) atoms at the center of oxygen octahedra which are inter-
connected through carboxylato bridges (the H atoms are omitted for clarity); (b) View of two
neighboring CoII layers separated by phenoxy acetate moieties arranged in a double layer.
360      10 Scaling Theory Applied to Low Dimensional Magnetic Systems




Fig. 10.10. Variation of the χT product as a function of temperature for
Co(CO2 (CH2 )OC6 H5 )2 (H2 O). The magnetization vs. field curve measured at 2 K is
plotted in the inset.




Fig. 10.11. Low temperature magnetic susceptibility measured in an ac field of approximately
1 Oe at 2.1 Hz. A sharp peak in the real part of the susceptibility χ is seen just below 0.6 K
together with an abrupt increase of the out-of-phase susceptibility χ . The inverse suscepti-
bility 1/χ vs. T shows a positive Curie–Weiss temperature, characteristic of ferromagnetic
interactions.


ers (Figure 10.11). The real and imaginary parts of the susceptibility exhibit the
characteristic features of long-range ferromagnetic order at 0.57 K, and the plot of
the inverse susceptibility vs. T (see inset) confirms that ferromagnetic interactions
dominate.
                                     10.4 Phase Transition in Layered Compounds           361

   The field dependent magnetization measured at 90 mK, with the field parallel
or perpendicular to the surface of the crystal, agrees with an out-of-plane hard axis
of magnetization.
   The exchange coupling involving a bridging carboxylate ligand in syn-anti con-
formation is known to favor weak AF interactions between neighboring Co(II) ions
[31, 32] contrary to the observed behavior below 10 K. In fact, the structure shows
that two well distinct directions of local anisotropy are to be considered between
magnetic centers linked through dicarboxylato bridges. As a result, a competition
between the local anisotropy field and the exchange coupling likely promotes a
non-collinear spin ground-state [33–35].
   In order to discuss the magnetic behavior in the critical regime, we have corrected
the susceptibility from the influence of the demagnetizing field. From the maximum
value χa = 0.39 emu cm−3 at TC , we found the demagnetising factor α = 2.55,
which is a reasonable value for a flat disk-shaped sample with the field parallel to
the planes. We then deduced the actual temperature dependence of χT , illustrated
in the Arrhenius plot of Figure 10.12, and compared it to solution (10.4a) of the
static scaling model. The best fit is obtained for [14]:
   χ T ∝ (1 − 0.57/T )−1.39                                                            (10.7)
which confirms the 3D character of the transition (TC = 0.57 K), and agrees with
the value of 1.387 predicted for a Heisenberg system.




Fig. 10.12. Low temperature variation of the χT product vs. 1/T , where χ is the intrinsic
susceptibility corrected for demagnetization effects. The solid line is a fit of the nonlinear
scaling function χ T = C(1 − TC /T )−γ to the data, giving TC = 0.57 and γ = 1.39.
362     10 Scaling Theory Applied to Low Dimensional Magnetic Systems




                             Fig. 10.13. Structure of the terephthalate-based compound
                             Co2 (OH)2 (C8 H4 O4 ).


   Similarly to the above systems, the actual dimensionality of the terephthalate-
based compound Co2 (OH)2 (tp) (with tp = C8 H4 O4 ), was a matter of debate, due
to the strong anisotropy of the magnetic carriers.
   The structure, determined by an ab initio XRPD method, is illustrated in Fig-
ure 10.13 [34]. The terephthalates are pillared and coordinated to the cobalt hydrox-
ide layers, thus forming a three-dimensional network. The basal spacing is 9.92 Å.
Two crystallographically independent Co(II) ions are found: one (Co1) bound by
four hydroxyls and two carboxylic oxygen atoms, the other (Co2) bearing two
hydroxyls and four tp oxygen atoms.
   The temperature dependent magnetic susceptibility of Co2 (OH)2 (tp) agrees with
the presence of high-spin Co2+ ion. The χT product exhibits, upon cooling, a
smooth minimum at about 100 K, then a strong increase up to a sharp maximum
at 47.8 K and a decrease to zero (Figure 10.14a). From ac magnetic susceptibility
measurements and neutron diffraction [35], it has been emphasized that this maxi-
mum corresponds to a long-range AF order, and that a net moment associated with
a canted AF structure is stabilized below 44 K.
   The plot of ∂ log T /∂ log(χ T ) vs. T (Figure 10.14b) gives a very good agreement
between theory and experiment for the parameters TC = 48 K and γ = 1.28. The
exponent γ is very close to typical 3D values (γ = 1.32 for the planar form and
1.25 for the Ising model), showing the bulk character of the magnetic transition.
This result points to a driving contribution of π electrons in the bridging unit to
promote the 3D order, even though dipolar coupling between layers may also be
invoked.
                          10.5 Description of Ferromagnetic Heisenberg Chains        363




                                                          Fig. 10.14. Magnetic be-
                                                          havior of Co2 (OH)2 (tp): (a)
                                                          temperature dependence of
                                                          the χT product; (b) variation
                                                          of d log(T )/d log(χT ) vs. T .



   From these experimental examples, it appears that worthwhile information, such
as the spin space and lattice dimensionalities, and further exchange interaction
energy, may quite readily be obtained by using the scaling approach.




10.5 Description of Ferromagnetic Heisenberg Chains

In this section, we focus on the magnetic susceptibility of finite ferromagnetic rings
of n Heisenberg spins (S = 1/2, 1, 3/2, etc), obtained by the direct diagonalization
method, and we show, by using the scaling arguments developed above, that there
exists a unique closed form expression describing their magnetic behavior.
364      10 Scaling Theory Applied to Low Dimensional Magnetic Systems

   We have been guided by our confidence that:

1. Superparamagnetic scaling should describe the infinite one-dimensional sys-
   tems.
2. The use of finite rings is allowed if the correlation length is much smaller than
   the size of the rings.

   It follows that superparamagnetic hierarchical scaling should be obeyed down
to the lowest temperatures for very large rings.
   The behavior of ferromagnetic quantum Heisenberg chains has been analyzed
from the thermodynamical data obtained by exact diagonalization of the spin-
hamiltonian H = −J Si Si+1 , for S = 1/2, 1 and 3/2, and rings of maximum size
n = 14, 10 and 8, respectively.
   The results are given in Figure 10.15 as ∂ log(T )/∂ log(χT ) vs. T /J S(S +1) for
some finite quantum chains together with that of the classical spin chain (S = ∞)
which has analytical solution [36]. For a given S, ∂ log(T )/∂ log(χT ) is a linear
function of T , which is aiming towards a negative TC = −TK , down to a threshold
value TS (n). We observe that this linear plot intercepts the axes at TK and γ −1 , which




Fig. 10.15. Plot of the ∂ log(T )/∂ log(χT ) function vs. T /J S(S + 1) as determined from the
theoretical susceptibility of finite ferromagnetic rings of n Heisenberg spins for the spin values
S = 1/2 and 3/2.
                              10.5 Description of Ferromagnetic Heisenberg Chains             365

stay much the same for different n values. However, the linearity, and accordingly
the fit of data by Eq. (10.4c), is better for larger rings, suggesting that the following
expression is available for the infinite chain:
   χ T = C[1 +        J S(S + 1)/T ]−γ        for T > TS (∞)                              (10.8)
    Table 10.2 gives the best values of C, and γ , obtained for S = 1/2, 1 3/2, by
fitting the susceptibility data above TS (n), for n = 14 (S = 1/2), 10 (S = 1) and
n = 8 (S = 3/2). We observe, in all cases, that the Curie constant is within 1% of
the theoretical value S(S + 1). Similarly, we find that −γ = 0.75 within 1%. It
can be noted that the data for finite rings depart from the 1D-Heisenberg model at
a temperature TS (n) which becomes smaller as the rings become larger.


Table 10.2. Best values of the pertinent parameters for 1D-Heisenberg ferromagnetic chains
of spins S = 1/2, 1, 3/2. C is the Curie constant in Ng 2 µ2 /3k units, T is the negative critical
                                                           B
temperature (in S(S + 1) units), and γ the (negative) exponent characterizing systems in a
space dimension below a lower critical dimensionality.

        S           1/2       1       3/2

 C/(S(S + 1))      0.991    0.989   0.989
    −γ             0.742    0.735   0.731
    −γ /S          1.222    1.232   1.164



   The data display a negative curvature which signals, in Arrhenius coordinates,
a hierarchical scaling described by Eq. (10.4c), and that our model associates with
systems below a lower critical dimensionality. Finally, we find, although with less
accuracy (within 5%), that γ = −1.23S. This enables us to propose the following
expression for χ T by using the reduced temperature t = T /S(S + 1):
   χ t = [1 + 0.61J /St]1.23S        t > tS                                               (10.9)
which is clearly more tractable than the polynomial expressions reported for quan-
tum spins S in the literature [30, 37]. From this approach, we can deduce the
very low temperature behavior of a ferromagnetic chain, which is illustrated in
Figure 10.16 for S = 1/2.
   In the classical limit (S = ∞), the above expression becomes:
   χ t = exp(0.75J /t) t > tS=∞                                                          (10.10)
which indeed fits very well the theoretical expression of the magnetic susceptibility
for T > J [36].
   According to our definition, therefore, d = 1 would be a lower critical dimen-
sionality for classical Heisenberg spins but not for quantum Heisenberg ones, at
least for T > J . The latter would belong to the space dimension below dc , since
366      10 Scaling Theory Applied to Low Dimensional Magnetic Systems




Fig. 10.16. Plot in Arrhenius coordinates of χT vs. J S(S +1)/T for finite ferromagnetic rings
of n Heisenberg spins S = 1/2. The infinite 1D-Heisenberg chain is described by a power law
(see Eq. (10.9)).

their magnetic susceptibility is described by a finite power law, χ ∼ T −(1.23S+1) ,
over a very large temperature range.


10.5.1     Application to Ferromagnetic S = 1 Chains

This model has been used to describe the magnetic behavior of
Ni2 (O2 CC12 H8 CO2 )2 (H2 O)8 , in which the Ni(II) metal ions are located in
slightly distorted octahedral sites and form helical chains (Figure 10.17a) [38].
These ions are connected through a biphenyl-dicarboxylate ligand, the shortest
Ni–Ni distance along the chain being 4.94 Å. The chains are moreover connected
by inter-chain hydrogen bonds to form planes quasi-perpendicular to the [10-1]
direction.
   The magnetic behavior illustrated in Figure 10.17b agrees with the Curie–Weiss
law for T > 100 K, with C = 2.289 emu K mol−1 (two NiII ions per mole),
and θ = +1.08 K, pointing to a weak ferromagnetic interaction. Accordingly,
the χ T product is nearly constant from room temperature down to ∼150 K, then
shows a slight increase to a maximum of 2.49 emu K mol−1 at 16 K and a drop to
                               10.5 Description of Ferromagnetic Heisenberg Chains            367




                                  (a)




Fig. 10.17. (a) View of neighboring Ni(II) helical chains. Intra-chain and inter-chain hydrogen
bonds are illustrated as dashed lines (labeled B, C and D respectively); (b) χ(T ) and χT (T )
variation for Ni2 (O2 CC12 H8 CO2 )2 (H2 O)8 . The full line shows the best fit for a ferromagnetic
spin-1 chain model.
368     10 Scaling Theory Applied to Low Dimensional Magnetic Systems

1.69 emu K mol−1 at 2 K. The observed behavior is characteristic of the occurrence
of ferromagnetic correlations within the chains, while the drop to zero below 16 K
is reminiscent of either AF interchain interactions or a zero-field splitting effect.
The magnetisation versus field measurement exhibits a paramagnetic-like behav-
ior with a saturation value of 2µB per nickel. Neither a metamagnetic or spin–flop
transition is observed, suggesting that no long range 3D AF order is achieved at
this temperature.
    In order to evaluate the exchange interaction between neighboring nickel(II)
ions, the magnetic susceptibility has been fitted in the high temperature region by
considering a model of Heisenberg S = 1 ferromagnetic chain and the approach
developed in the framework of the scaling theory.
    It is shown that the analytical expression
  χ t = 3/8g 2 (1 + 0.61J /St)1.23S                                          (10.11)
fits the experimental data very well (Figure 10.17), giving g = 2.13 and J =
+1.06 K, in agreement with the θ value deduced above.
    So, from the proposed model and close examination of the crystal structure,
we merely deduce the ferromagnetic interaction between magnetic centers that is
shown to involve, in the present compound, biphenyl-dicarboxylate ligands and
hydrogen bonds.



10.6 Application to the Spin-1 Haldane Chain

The AF chain of Heisenberg spins with integer S values is still an object of in-
terest many years after Haldane conjectured that an energy gap separates the
singlet ground-state from the first excited state, while half integer spin chains are
gapless. After the pioneering work of Botet et al. [39] who solved numerically
the spin Hamiltonian for finite rings of n spins S = 1 with n = 6 to 12, further
calculations have been performed by means of the quantum Monte Carlo [40] and
the density-matrix renormalization group (DMRG) techniques [41] to determine
more precisely the energy gap as n diverges. The extrapolated value for the infinite
chain was estimated to be ≈ 0.41J [42] where J (> 0 for an AF coupling) is
the nearest neighbor exchange interaction.
   This system displays other fascinating features, for example the ground-state of
open chains is characterized by an effective spin S = 1/2 at each end of the chain
and the correlation length at T = 0 reaches a finite value ξq = 2J S/ , which
results directly from spin fluctuation effects.
   We derive here a simple phenomenological expression for the magnetic sus-
ceptibility of AF rings made of an even number n of Heisenberg spins S = 1
which, extrapolated to the thermodynamic limit, captures the main features of the
                                  10.6 Application to the Spin-1 Haldane Chain     369

Haldane chain. The method is based upon scaling arguments [13, 14] developed in
Section 10.2, which are applied to the theoretical data deduced for finite quantum
rings of size n. The whole procedure provides a new insight into the gap and the
finite correlation length at T = 0, and results in a closed expression available
for fitting experimental data, as demonstrated for two Haldane chain compounds
Y2 BaNiO5 and Ni(C2 H8 N2 )2 NO2 ClO4 .
    We use here the thermodynamic data of the finite AF rings of n spins S = 1
obtained by exact diagonalization of the spin Hamiltonian H = J Si Si+1 for
n up to 10, and by the density-matrix renormalization group (DMRG) technique
for n = 16 and 20. Periodic boundary conditions have been imposed to minimize
finite size effects, while only even n values have been considered to avoid frustration
effects.
    A standard DMRG procedure was used to construct the spin Hamiltonian ma-
trices in the DMRG basis [43]. It might appear surprising that the DMRG method,
in which usually the ground-state and one or two excited states are targeted in each
iteration, can provide accurate thermodynamic properties. In fact, it is well known
that, at each iteration, the DMRG space, which contains the lowest energy state,
has substantial projections from low-lying excited states, so that these can be well
described in the chosen DMRG basis. A description of the method is given in Refs.
[44, 45].
    Figure 10.18 shows ∂ log(T )/∂ log(χ T ) vs. T obtained from the data computed
for AF rings of n spins-1, with n = 6 to 20. In both the high and the low-temperature
regimes, the data are positive and approach a straight line which intersects the axes
near the origin at T = 0. This indicates that an AF exponential solution of the
type (10.4b) is relevant in either range. The high temperature solution χT =
CHn exp(−WHn /T ) is much the same for all n values, and valid for T > TM where
∂ log(T )/∂ log(χ T ) = 1 (this is where the magnetic susceptibility χ is maximum).
The low temperature solution χ T = CLn exp(−WLn /T ) is available for T < Tm
where ∂ log(T )/∂ log(χ T ) = 0.5 (this is where χ/T is maximum). The high and
low temperature regimes are described by different straight lines for T > TM and
T < Tm in the Arrhenius plot of Figure 10.19. The same data are also shown in
Figure 10.20 in a more traditional representation of χ vs. T /J . The corresponding
Cs and W s are listed in Table 10.3, and their dependence on 1/n is displayed in
Figure 10.21.
    The Curie constant in the high temperature regime is CH ∝ 0.673, within 1% of
the expected S(S + 1)/3 value. The associated activation energy, namely the actual
Weiss temperature, approaches WH = 1.44 J for all n, which is close enough to the
value 4J/3 deduced analytically for a ring of 4 spins. In the low temperature regime,
CLn = 2/n, which is the expected value for a singlet–triplet spin configuration
well separated from the high-energy states. The associated WLn is precisely the
singlet–triplet gap, (n), that is directly deduced by computation for finite chains
(see Table 10.3). It decreases as n increases, and its dependence on n is well
approximated by the power law 0.421 + 6.5n−1.74 (in J unit). In the n → ∞
370      10 Scaling Theory Applied to Low Dimensional Magnetic Systems




Fig. 10.18. ∂ log(T )/∂ log(χT ) vs. T /J deduced from exact calculations of the susceptibility
of AF Heisenberg rings of n spins S = 1 for n = 6, 16 and 20. Asymptotic behaviors are
observed in the high and low temperature regimes, namely above TM and below Tm .




Fig. 10.19. Variation of χT (T ) for finite AF Heisenberg rings of spins S = 1, shown as
log(χT ) vs. J /T , for n equal to 6, 8, 10, 16 and 20. At high temperature, we observe a unique
Arrhenius regime, whose activation energy is WH ≈ 1.44 J. Below Tm , distinct Arrhenius
laws are deduced, whose Curie constant is CL = 2/n and the activation energy WL reflects
the Haldane gap.
                                      10.6 Application to the Spin-1 Haldane Chain         371




Fig. 10.20. Plot of χJ /Ng 2 µ2 vs. T /J for n equal to 6, 8, 10, 16 and 20. The best values of
                              B
the coefficients C1n , W1n and C2n , W2n characterizing the low and high-temperature regimes
are given in Table 10.3.

Table 10.3. Best parameters characterizing the fits of the magnetic susceptibility of AF rings
of n Heisenberg spins S = 1.

 n     1/n        /J     CLn    WLn /J    CHn     WHn /J     C1n    W1n /J     C2n    W2n /J

  4   0.2500    1.000   0.486    0.999    0.680    1.495    0.204    0.769    0.506    2.087
  6   0.1666    0.721   0.329    0.720    0.674    1.444    0.178    0.605    0.544    2.090
  8   0.1250    0.594   0.248    0.593    0.673    1.438    0.145    0.512    0.558    1.916
 10   0.1000    0.525   0.193    0.524    0.673    1.439    0.132    0.475    0.561    1.844
 12   0.0833    0.502
 14   0.0714    0.486
 16   0.0625    0.478   0.162    0.483    0.673    1.437    0.132    0.475    0.561    1.844
 18   0.0555    0.469
 20   0.0500    0.457   0.191    0.523    0.673    1.438    0.128    0.463    0.561    1.819

 ∞ 0.0000       0.421                                       0.125    0.451    0.564    1.793


limit, it tends towards a finite value that may be compared to the Haldane gap,
  /J ∝ 0.41.
   We have also checked whether two superimposed exponentials could describe
the susceptibility at all temperatures (Figure 10.22). The optimization has been
achieved with χ (T ) rather than χ T (T ), because more weight is given to the data
in the range of the susceptibility maximum where both exponentials contribute a
sizeable amount. The best values of the different parameters are given in Table 10.3.
372      10 Scaling Theory Applied to Low Dimensional Magnetic Systems




Fig. 10.21. Variation of the parameters CLn , WLn , CHn and WHn (in J unit) characterizing
the asymptotic low and high-temperature Arrhenius regimes of the χT (T ) product.




Fig. 10.22. Best values of the coefficients C1n , C2n , W1n and W2n (in J unit) characterizing
the overall temperature dependence of the susceptibility of AF rings of n Heisenberg spins
S = 1 in a fit with two exponentials.
                                    10.6 Application to the Spin-1 Haldane Chain      373

    Clearly, the C coefficients need to be related by CHn ≈ C1n +C2n and CHn WHn ≈
C1n W1n + C2n W2n to reproduce the main features in the high temperature limit.
Similarly, we need CLn ≈ C1n and WLn ≈ W1n in the low temperature regime.
These constraints are pretty well realized, as noted in Table 10.3. The resulting fit
is very good (Figure 10.20), and even becomes excellent on increasing the number
of spins. For all these rings, we propose the following expression of the χT product
(normalized to Ng 2 µ2 /k)
                        B

   χ T = C1n exp(−W1n /T ) + C2n exp(−W2n /T ) for T /J > 0.1                      (10.12)

For the Haldane chain (n → ∞) limit, the best-fit parameters are C1 = 0.125,
W1 = 0.451 J, C2 = 0.564 and W2 = 1.793 J.1 In Ref. 46, the authors have
used the above equation to analyze the magnetic data of Y2 BaNiO5 , a typical AF
S = 1 chain system. The best fit parameters agree with our prediction, provided
that J = 300 K which matches with previous findings (J = 285–322 K) [47].
    Note that defects are expected to have very different effects in gapless 1D sys-
tems and Haldane chains [48]. In the former, they reduce the correlation length,
and the magnetism obeys the Curie-like contribution of the finite segments with an
odd number of spins. In turn, for the Haldane spin-1 chain, characterized by a finite
correlation length at low temperature, the valence-bond-solid (VBS) model sug-
gests a free spin-1/2 at each end of the segments, giving a staggered susceptibility,
but there is no significant change in the gap value.
    We have extended this analysis to the magnetic behavior of
Ni(C2 H8 N2 )2 NO2 ClO4 (denoted NENP) which is the archetype of the Hal-
dane gap systems [49]. A small temperature independent contribution χ0 , which
is observed to depend on axial symmetry, has been introduced. The agreement
between theory and experiment is excellent for the three crystal axes, as may be
observed in Figure 10.23 [50]. We need in this case J = 43 K along both axes to
match the paramagnetic Curie–Weiss temperature which is much the same along
all axes. The effect of the known anisotropy of this system is that the Haldane gap
which we deduce from the fit ranges from 0.53J along the a axis to 0.40J along
the b axis when we expect 0.451J for the isotropic crystal.
    To our knowledge, Eq. (10.12) is the only expression available to describe the
behavior of the Haldane chain over the whole temperature range. At high tem-
perature, everything behaves initially as in any system sitting at a lower critical
dimensionality: an exponential solution of the type (10.4b) is found, as in the case
of the classical Ising chain with nearest neighbor interactions.
    Note that, in the low temperature regime, gapped AF chains are usually described
by the expression χ = AT −1/2 exp(− /T ) [51]. The T −1/2 factor which follows
from field-theory mapping [52] is essentially related to the relativistic magnetic

 1 In the thermodynamic limit, the coefficients have been deduced by extrapolating the 1/n
  dependence of the Cs and W s, using third order polynomials.
374     10 Scaling Theory Applied to Low Dimensional Magnetic Systems




Fig. 10.23. Fit of the magnetic susceptibility of NENP along two crystallographic axes using
Eq. (10.12). From the Weiss constant WH = 1.793J , we deduce J = 43 K.


properties in the nanometric scale magnon dispersion [53], and has further been
quantitatively confirmed by Monte-Carlo calculations [54]. Actually, it can be
pointed out that this expression, which is dominated by the exponential, does not
differ significantly from the proposed approach, even for T /J ranging from 0.2 to
0.05, giving       = 0.409 J. Further, it becomes irrelevant at higher temperatures,
since little can be inferred from the magnitude of the prefactor, A.
   In the proposed model, we observe at low temperature the terminal stages of the
ordering of a different Ising-like chain, where the Curie constant bas been divided
by a factor five and the activation energy by a factor three.
   Such behavior could be explained by assuming that the n individual moments
of the initial chain are not permitted to order completely in a single process where
χ (T ) would grow from 0 to ∞ as is described in Section 10.2. The initial chain
of n spins, rather, is rearranged as a new chain of N/5 AF segments of five spins
each, with an uncompensated spin S = 1, due to the unbalance of the up and
down moments in the correlated state of each segment. The Haldane gap would
correspond to the renormalized interaction from segment to segment.
   This implies that some sort of dichotomy occurs, at an early stage, whereby a
finite length of five atomic distances is selected for each segment and the ordering is
made in two stages: the former accounts for the short range ordering 0 < ξ(T ) < ξq
which is responsible for the cohesion of each segment; the latter, ξq < ξ(T ), with
the Curie constant divided by five, describes the divergence of the correlation
between the newly defined segments. The expression (10.12) displays two simul-
taneous contributions accordingly. The segmentation length ξq = 5, which comes
                                                                 10.7 Conclusion       375

from the ratio of the Curie constants, turns out to be of the same magnitude as
the finite correlation length ξq = 2J S/ predicted for the Haldane chain in the
T = 0 limit [42]. Maybe, it is not much of a surprise, after all, if the susceptibility
does not vary very much once we reach rings of n > 10 spins, large enough to
contain several segments of size ξq . Interestingly, such rings already contain all the
elements which are required for describing the physics of the system.




10.7 Conclusion

We have illustrated in this chapter the pertinence of a strategy that extends to
the description of correlated systems, in general, the powerful ideas of scaling
previously reserved for single phase transitions. Of particular interest, for this
purpose, is the plot of ∂ log(T )/∂ log(χ T ) vs. T . This alternative representation
of the experimental evidence allows one, in one single process, to establish the
existence of a given scaling and to fix the extent of its validity range. It is then
possible to comment on the physical justifications of these limits and to determine,
within these limits, the pertinent parameters characterizing the particular scaling
that is requested. On the basis of the sign and magnitude of these parameters, it
seems possible to proceed with the classification sketched in Figure 10.1, and to
extend the notion of “universality class” to these systems that stand at or below a
lower critical dimension.




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Index




a                                            2,3-Dicyano-1,4-naphthoquinones 236–
Alternating chain model 123, 203–206              238, 243
Anthracenetetrone 240                        2,5-Dichloro-3,6-dihydroxy-1,4-
Azido 200, 203–205, 217–218                       benzoquinone 248–249
                                             2,3-Dihalo-5,6-dicyanoquinone 235, 243
b                                            2,5-Dimethyl-N,N -dicyanoquinodiimines
Bis(dithiolato)metallates 131, 143–146,           239–240, 242
      240–241, 243, 244–246                  Dipolar-dipolar interactions 277, 352, 362
Bis(dithiolato)metallates, see also Metal-   Dzyaloshinsky-Moriya interaction 42
      locenium bis(dithiolato)metallates
Bis(heptamethylindeny)iron(II) 250           e
                                             Electrochromism 337
c                                            Exchange between localized moments and
Canted antiferromagnetism 79–81                    conduction electrons, see RKKY
Chiral magnets 41–68                               model
[Co(C5 Me5 )2 ][TCNE] 232                    Exchange models 294–300, 306–322
Cobalt hydroxide carboxylates 263, 354,
      356–361                                f
Cobalt imidazolates 272, 273                 Faraday effect 44, 62–63
CoHMPA-B bis(2-hydroxy-2-                    Fe clusters 209, 219–220
      methylpropanimido)benzene              [Fe(C5 Me5 )2 ][TCNE] 225, 226–227,
      247                                          230–233, 242, 249, 250
Conductivity 105–155                           Hysteresis 231
Copper hydroxide layers 266–269,               Mössbauer 251–252
      352–355                                  Specific Heat 230, 253–254
[Cr(C5 Me5 )2 ][TCNE] 232, 242                 Structure 227, 251–256
Cr(NCS)4 126–130, 131                        [Fe(C5 Me5 )2 ][TCNQ] 225, 228–229,
Critical constants 77, 82, 347–375                 238–239, 242, 247, 250
Cu Phthalocyanine 110–111                      Structure 228–229
                                             Ferrimagnetic 19
d                                            Ferromagnetic 6, 8, 23, 27, 76
Dawson-Wells ions, see Polyoxometallates     Ferromagnetism and superconductivity
Decaethylferrocene 249                             107, 153
Dicyanamide, see M[N(CN)2]2                  Fisher chain 194, 200, 202, 209–211
Dicyanofumarate salts 233–235, 242           Fisher model 115
Dicyanomethylene 248
380     Index

g                                             Magnets, chiral, see Nitroxide chiral
Gd(III) and a nitronyl nitroxide radical            magnets,
      165–169, 170–173, 174–177, 180–184      Manganese formate 269–271
Gd(III) 161, 164–169                          McConnell model 3, 20, 25, 232–239,
Gd(III)-Cu(II) 164–165, 170                         250, 254–255
                                              Mean field approximation 201
h                                             Mechanism for magnetic ordering 81, 82
Haldane chain 368–375                         Metallocene 1–38
Heisenberg Model 78, 196, 197, 200, 253,        magnetic properties 4–37
     348, 351, 358, 361, 363, 366, 368, 370     structure 4–37
Hexacyanobutadiene 242, 247–248                 magnets 223–227
Hexacyanometallates 53–68, 105,               Metallocenium bis(dithiolato)metallates
     124–125, 127                                   1–38
Hexacyanometallates, see also Prussian blue   Metamagnetic 7, 8, 10, 11, 13, 14, 20, 30,
Hexahalohalometallates 122–124                      34, 35, 228–229, 236, 238, 241, 242,
Hexathiocyanatometallates 124–128                   243, 244
                                              [Mn(C5 Me5 )2 ][TCNE] 232–242
i                                             [Mn(C5 Me5 )2 ][TCNQ] 227, 242
                                              Mn(hfac)2 49–53
Ising model     189, 196, 253, 351
                                              Molecular orbital analysis 300–302,
                                                    310–319
k
                                              Monte Carlo Simulation of Magnetic
Kagomé lattice 72, 267, 268, 269
                                                    Properties 189–220, 374
Keggin ions, see Polyoxometallates
                                              Mössbauer spectroscopy 251–252
                                              Muon spin relaxation 251
l                                             [MX4 ]2− see Tetrahalometallates
Ladder-type structure 178                     [MX6 ]3− see Hexahalohalometallates
Lanthanides 161–185
Light-induced magnetization     338–339       n
                                              N− see Azido
                                                3
m                                             Nanoparticles 339–340
M(CN)6 ]n− see Hexacyanometallates and        Nanoporous magnetic materials 261–280
      Prussian blue                           Neutron diffraction 78, 94
M(NCS)6 ]3− see Hexathiocyanatometallates     Ni(C2 H8 N2 )2 NO2 CIO4 369, 373–374
M(ox)3 ]3− see Tris(oxalato)metallate         Nickel carboxylate 263, 265, 366–369
M[C(CN)3 ]2 , 71–73, 76, 85, 86               NiCp*2 ][TCNE] 232, 242
M[N(CN)2 ]2 , 71–100                          Nitroxide 357–358
  magnetic behavior 76–82, 84, 94–98             chiral magnets 49–53, 67
  structure 73–76, 79, 82–84, 87–93, 96,
      99                                      o
Magnetic semiconductor 121, 122               Octamethylferrocene    249–250
Magneto-chiral optical effects 48–49          Optical effects 337
Magneto-optical effects 43–48
Magnetostriction 153                          p
Magnets and conductivity 105–155              Pentamethylferrocene 249
Magnets, chiral, see Chiral magnets,          Perylene 112, 115, 143–146
                                                                       Index        381

Polychlorinated triphenylmethyl 273–278    Superconductivity and magnetism
Polyoxometallates (POM) 133–143                 107–108
POM see Polyoxometallates                  Superexchange 82, 170–173, 180–184
Porous materials see Nanoporous            Superparamagnetic scaling 364
Prussian blue 43, 53, 60–68, 161,
      238–341, 263,264                     t
  critical temperatures 302–305            TCNE see Tetracyanoethylene
  magnets 291–337                          TCNQ see 7,7,8,8-Tetracyano-p-
  structure 385–387                              quinodimethane (TCNQ)
  synthesis 384–385, 388–390               Tetracyanoethylene 169
                                           7,7,8,8-Tetracyano-p-quinodimethane
                                                 (TCNQ) 169, 238, 242
r
                                           Tetrahalometallates 111–122
Relativistic magnetic properties 373–384
                                           Thin layers 337
RKKY Model 107, 108–111, 120
                                           Tricyanomethanide see M[C(CN)3 ]2
Room temperature magnets 322
                                           Tris(oxalato)metallates 67, 105, 131, 146,
                                                 154, 202, 214–215
s                                          TTF–based electron donors 105–106,
Scaling see Critical constants                   111–143
Semiquinone 169, 178–180,
Specific heat 230                          v
Spin coupling mechanism 254–255            Valance bond configuration interaction
Spin crossover 72, 98–99, 271–272               319–322
Spin density 20, 26, 27, 253               Vanadium carboxylates 269
Spin flop 80
Spin fluctuations 78                       x
Spin frustration 72, 73                    XY Model     351

				
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