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Rare-earth nitrides an LSDA+U study

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					  Rare-earth nitrides: an LSDA+U
               study



Funding from NSF


                      Paul Larson
   Walter R. L. Lambrecht     &     Mark van Schilfgaarde
   Case Western Reserve University Arizona State University
                 APS March Meeting Z23.00004
                        March 17, 2006
                    http://pablo.case.edu
    Special thanks to Anathosios Chantis (Arizona State
                          University)
       Reasons to Study Rare-Earth Nitrides

●Several unanswered questions about fundamental and
 applied aspects of rare-earth nitrides

●Fundamental: Unclear about position of the 4f orbitals and
 the lowest energy state
●What is the right way to treat the 4f orbitals? What
 properties determine the lowest energy configuration?

●Applied: GdN (like EuO) is a magnetic semiconductor with
 Tc ~ 58K (spintronics)
●What are the magnetic properties of GdN? How do the
 magnetic properties vary for the other rare-earth
 nitrides?
0.99
Pr     6.3     Electronic Structure Method
0.94
                   Electronic structure calculations were done
Nd       6.6
                    using FP-LMTO – LSDA+U
0.99
                   LSDA+U adds Hubbard U correction on
Pm     6.9
                    localized orbitals within LSDA formalism1
1.0
                   Slater Fk integrals – atomic Hartree-Fock
Sm     7.1          calculations2
1.1                    Uf = F0 scaled to fit to photoemission data
Eu       7.4            Jf = (286F2 + 195F4 + 250F6)/6435
1.1                 unscreened
Gd       8.0       Additional Ud of 3.4 eV used to fix band gap
1.2
Tb       8.2
1.3
Dy       8.1
1.2
Ho       8.3
1.3               ● 1V.I. Anisimov, J. Zaanen, and O.K. Andersen Phys. Rev. B 44, 943 (1991).
Er     8.6          2 Joseph B Mann, Atomic Structure Calculations (Los Alamos internal report,
3 Steps for Band Structure of Rare-Earth
                Nitrides
Step 1: Add Hubbard Uf and Jf to 4f states
                         LSDA calculations place the
                         4f states too close to the
                         Fermi level

                         While occupied states move
                         down and unoccupied states
                         move up, the shift is often
                         not symmetric

                         Choosing values of Uf and Jf
                         is difficult, but shift of 4f
                         states not highly sensitive to
                         these values.

                     ● GdN       Uf = 8.0 eV, Jf = 1.2
3 Steps for Band Structure of Rare-Earth
                Nitrides
Step 2: LSDA Gap – Hubbard Ud and Jd on
                    LSDA
                5d states underestimates the band
                     gaps – not fixed by Uf and Jf
                     Band gap correction - push up
                     empty Gd 5d states using Ud
                     and Jd
                     Values chosen to fit optical
                     absorption data at X point
                     above Tc– average spin-
                     majority and spin minority
                     gaps– same values of Ud and Jd
                     used for other rare-earth
                     nitrides

                    ● GdN Ud = 3.4 eV Jd = 0.0 eV
                     (< Tc) Gap at X 0.00 eV ->
                     0.57 eV
3 Steps for Band Structure of Rare-Earth
                 Nitrides
  Step 3: Allow for Symmetry Breaking
                   For rare-earth nitrides, cubic
                   symmetry splits the 4f level
                   into a nondegenerate a2u and
                   triply degenerate t1u and t2u
                   Hund's rules requires the
                   largest orbital momentum – not
                   allowed in cubic symmetry
                   Partially filled t1u or t2u
                   become pinned at the Fermi
                   level
                   GdN is spherically symmetric,
                   but partially filled states
                   maximize L
                  ● PrN 4f states move down by
                   5.0 eV
LSDA+U Results for Rare-Earth Nitrides




                     L is opposite S for elements
                   lighter than GdN and parallel
                   for heavier than GdN
                   Most rare-earth nitrides
                   have highest L with large
                   energy gains
                   Larger values of Uf push the
                   4f bands lower in energy
   Magnetic Properties of Rare-Earth Nitrides
 Heisenberg  Hamiltonian used to obtain information about
  magnetic properties of rare-earth nitrides using total
  energies
 Three orientations chosen for calculating total energy in 4x
  supercell. FM and two AFM orientations along {001}
●AFMI                AFMIII

                        H = – i>j Jij Si . Sj
                        EFM = E0 – 6J1 – 3J2
                        EAFMI = E0 + 2J1– 3J2
                        EAFMIII= E0 + 2J1 – J2

                        Calculate to 2nd-nearest neighbor coupling
                         |J1| > |J2| > |J3|
  Rare-Earth Nitrides for Spintronic Applications




 Positive J corresponds to ferromagnetic state – most rare-
  earth nitrides
 Largest values for J1 and J2 are for GdN which is half filled
 Using the correct symmetry changes the values of J1 and J2
 Preliminary calculations in max-L symmetry show changes in
                       Conclusions
   The electronic structure of rare-earth nitrides requires
    three steps
    1. Shift rare-earth 4f states away from Fermi energy
    using Uf and Jf
    2. Shift rare-earth 5d states up to fix LSDA gap with Ud
    and Jd
    3. Allow for breaking of cubic crystal symmetry for 4f
    states

   Large spin splitting in GdN between spin-majority and
    spin-minority bands – red shift in band gap going
    through Tc (metal/insulator transition?)
   Ground state for most rare-earth nitrides explained by
    Hund's rules which maximize S and L for atomic-like 4f
    orbitals

   Magnetic properties predict that GdN has the strongest
       Rare-Earth Nitrides Band Gaps
             Direct at X                  -X
       Exp (eV)        Theor (eV)   < Tc (eV)     > Tc
(eV)
LaN    0.82        0.55             0.00        0.00
CeN    *           0.0                 0.00        0.00
PrN    1.03        0.60             0.00        0.14
NdN    0.8            0.92             0.37        0.74
PmN    *           0.74             0.00        0.38
SmN    0.7            0.89             0.00        0.49
EuN    0.76        1.24             0.60        1.35
GdN    0.98        0.98             0.12        0.68
TbN    0.8            1.13             0.31        0.88
DyN    0.91        1.20             0.23        0.47
HoN    1.05        1.23             0.40        0.67
ErN    1.2            1.21             0.34        0.52
TmN    1.1            1.39             0.57        0.68
YbN    1.03        2.32             0.60        0.83
LuN    1.55        1.67             0.93        0.93
Spin Splitting in Rare-Earth Nitrides

				
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