Holes in a Quantum Spin Liquid - PowerPoint by 1Q9uOIA

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									        Quantum Phase Transition in
  Quasi-two-dimensional Frustrated Magnet
                         Collin Broholm
  Johns Hopkins University and NIST Center for Neutron Research
        M. A. Adams                        ISIS
        Y. Chen                            JHU
        D. V. Ferraris                     JHU
        N. Harrison                        LANL
        T. Lectka                          JHU
        D. H. Reich                        JHU
        J. Rittner                         JHU
        M. B. Stone                        JHU
        Guangyong Xu                       U. Chicago
        H. Yardimci                        JHU
        I. Zaliznyak                       BNL
* Work at JHU Supported by the National Science Foundation
                      Outline of Seminar
      A simple D=1 quantum magnet: Copper Nitrate

      A not so simple D=2 quantum magnet: PHCC

      Frustration in PHCC

      Field induced phase transition in PHCC

      Conclusions

            Some results published in M. Stone et al., PRB 64, 144405 (2001)
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   The beauty of magnetic dielectrics
     Well defined low energy Hamiltonian
         H   J ll 'S l  S l '   Exchange interaction
                     ll '

                 D S
                      l
                             
                             l
                              z 2
                                    Single ion anisotropy


                  B H   gl Sl   Dipole in magnetic field (Zeeman)
                             l

     Chemistry provides qualitatively different H
     Vary H with pressure, magnetic field
     Efficient experimental techniques
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                Magnetic Neutron Scattering
                           
                          kf              
                ki    2                 Q  ki  k f
                      
                      Q                  E i  E f

The scattering cross section is proportional to the
Fourier transformed dynamic spin correlation function
              1             1        
S (Q,  )       dt e it  eiQ( R  R ')  S (t ) S ' (0) 
                                                         
              2              
                             N RR '               R       R

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                       MACS spectrometer
                      now being built at NIST




108 n/cm2/s in dE=0.2 meV
21 detection channels                 Design by C. Brocker,
                                      C. Wrenn, and M. Murbach
Singlet Ground State in Cu-Nitrate




                          H = J1  S 2 n  S 2 n 1    S 2 n1  S 2 n  2 
                                      n
     Qualitative description of excited states
     A spin-1/2 pair with AFM exchange has a singlet - triplet gap:

                                            Stot  1
                                      J
                                            S tot  0
    Inter-dimer coupling allows coherent triplet propagation and
     produces well defined dispersion relation




    Triplets can also be produced in pairs with total Stot=1



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   Triplet waves in dimerized copper nitrate

                     k BT  J




Yale 11/29/01                      Xu et al PRL (2000)
                     Magnetizing a gapped quantum magnet
                               Copper Nitrate T=0.1 K
                     1.0
   (emu/mole Cu)




                     0.8
                                                            Field induced order
                     0.6

                     0.4

                     0.2

                       0
                     0.6 0         2     4      6       8

                     0.5                H (T)
                     0.4
       <S z >




                     0.3

                     0.2

                     0.1
                                                                Eckert et al (1980)
                       0
                           0       2     4      6       8

                                        H (T)
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                  Singlet Ground state in PHCC
                /max




                             J1=12.5 K
                             =0.6




                               T J1      Daoud et al., PRB (1986).
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   Structure is “consistent” with spin chains
                    PHCC = C4H12N2Cu2Cl6




                                      N           Cl
                c                 C           c
                                                  Cu

                       a                  b
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                 PHCC is quasi-two-dimensional
                Is PHCC quasi-one-dimensional?
           Dispersion  to “chains”
              No dispersion along b
            Dispersion along c axis


                Could be spin planes
                Not chains but chain




                                        (meV)




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2D dispersion relation




                          (meV)
                                                    1
                               0
                                    h
                                        1   0
                                                l
     Other means of destabilizing Neel order
    Weak connectivity: Order in one part of lattice does not
    constrain surrounding spins




    Magnetic Frustration: All spin pairs cannot simultaneously
    be in their lowest energy configuration


                                            Frustrated


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A Frustrated Route to Moment Free Magnetism?
  1. Assume Neel order, derive spin wave dispersion relation
  2. Calculate the reduction d S in staggered magnetization
     due to quantum fluctuations
  3. If d S  S then Neel order is an inconsistent assumption


        1 1             1 d Q g Q                3       
  dS 
       2S N
            R SR SR  2S  v  Q
                 

                             BZ

            d S diverges if  Q   0 on planes in Q-space

                Frustration can produce local soft modes
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                that destabilize Neel order
            Neutrons can reveal frustration
    The first -moment of scattering cross section equals
    “Fourier transform of bond energies”

                                                            S r  S r d  1  cos Q  d 
                          1 1
      d  S(Q,  )  
      2

                          3N
                                                 J
                                                  rd
                                                       d



                                            d4         d3
     H         1
                2   J S d   r    S r d
                    rd                                       d2
                                                 d1
    bond energies are small if J d and/or  S r  S r d  small
    Positive terms correspond to “frustrated bonds”
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                Measuring Bond Energies




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                Frustrated bonds in PHCC
                                                                    .
                                                     di    Jd<S0 Sd>
                                                     1           -1.4(3)
                                                     2            0.6(3)
                                                     3           -0.4(1)
                                                     4           -0.2(3)
                                                     5            0.1(3)
                                                     6          -0.95(5)
                                                     7            0.1(2)
                                                     8            0.6(2)
                 Green colored bonds increase ground state energy
                        The corresponding interactions are frustrated
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           Results in zero field
 Systems thought to be one dimensional may
 represent a richer class of quantum spin liquids.
 Neutron scattering required to classify these.
 Experimental realizations of spin liquids were
 sought, not found, in symmetric frustrated magnets.
 Hypothesis: Spin liquids may be more abundant in
 complex geometrically frustrated lattices.
      Zeeman splitting of cooperative triplet

                         PHCC T=60 mK




                          GS-level crossing for H8 T


                           Quantum phase transition
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                H-T phase diagram


                             PHCC




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                                      H=14.5 T   T=1.77 K
Field-induced AFM Order




                          Intensity
                                                 x300c



                                        Q  ( 1 ,0, l)
                                              2
      Frustrated bonds   parallel spins




                ˆ
                c
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                    a
Bragg Intensity  M2
                       Temperature Driven Criticality




                                                 T=0.44(2)




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                H-T phase diagram


                             PHCC




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                Reentrant low T transition?




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                Extracting the critical field

                                              2H
                                  H  HC 
                     I (H )  I0 
                                  H      
                                          
                                      C  
                                Fit range




                                                    T  1.635 K



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    Reentrant behavior close to critical point


                                                  gapless
                3 D long range order




                                       Spin gap

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   Reentrant behavior in other frustrated magnet




     P. Schiffer et al., PRL (1994).
     Y. K. Tsui et al., PRL (1999).


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   Magneto-elastic effects in frustrated magnets?

                ZnCr2O4 frustrated spinel AFM




                                                Lee et al., PRL (2000).
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    Critical exponent H versus temperature




                                 H
                                         Tmin




          No indications of change in critical properties at T*
          However, transition could be weakly first order
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                  Conclusions
 Quasi-two dimensional singlet ground state PHCC
 Neutron scattering reveals frustrated bonds that may be
  instrumental in suppressing Neel order
 Ordered state consistent with bond energies derived from
  inelastic scattering at H=0
 Phase diagram features a cross-over to quasi-two-
  dimensional gapless paramagnetic phase
 At low fields ordered phase drops below extrapolation of
  cross over line to gap-less phase
 Indications of low T reentrant behavior
 Anomalous low T phase boundary may result from
  magnetoelastic effects close to QC point

								
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