Orbital order in the spinel ZnV 2 O 4
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1 Orbital order in the spinel ZnV 2 O 4 Roser Valentí Institute of Theoretical Physics, J.W.Goethe-University of Frankfurt Collaborator: Tulika Maitra (Univ. Twente) Financial support: DFG (FOR 419, SFB/TRR 49) 1
2 Outline Frustrated spinel structure ZnV 2 O 4, spin=1 Orbital ordering? spin orbital lattice ab initio DFT + lattice models Maitra, Valentí PRL (2007) in press 2
3 Spinel structure AB 2 O 4 Cubic closed-packed array of O, cations A, B: AB 2 O 4, A atoms occupy tetrahedral sites A and B cations BO 6 octahedra B 4 tetrahedra GEOMETRIC FRUSTRATION! 3
4 Spinel structure AB 2 O 4 Space Group Fd 3m (227) O 7 h O h : 1, 1,9(2),9( 2),4(±3),4(± 3),3(±4),3(± 4) A: (8a) (1/8, 1/8, 1/8) B: (16d) (1/2, 1/2, 1/2) O: (32e) (u,u,u) Perfect Spinel u = 1/4 4
5 a 1g 5 Spinel structure AB 2 O 4 Crystal Field splitting B 3d ion perfect spinel O: (u,u,u), u = 1/4 eg d t2g Isolated Ion cubic Octahedral crystal field trigonally distorted octahedral crystal field: e π g u = 1/4 + δ δ > 0 trigonal expansion δ < 0 trigonal compression t 2g
6 Spinel ZnV 2 O 4 V 3+ : 3d 2 Experiment powder: T c =51K cubic tetragonal (Ueda et al. JPSP (1997), Fd 3m I4 1 /amd (c/a = 0.995) Reehuis et al. EPJB (2003)) eg d Isolated Ion t2g cubic dxz,dyz dxy orbital order? tetragonal c/a < 1 T N =40K Antiferromagnetic order 6
7 Antiferromagnetic order O Zn V z y x 7
8 Spinel ZnV 2 O 4 V 3+ : 3d 2 Experiment sensitive to sample preparation single crystal: spin glass, no phase transition (S.G. Ebbinghaus et al. Jour. All. a. Comp. ( 04)) single crystal, powder: T c =50K cubic tetragonal (S.H. Lee et al. PRL (2004) F 43m I 4m2 or I 4 (non-centrosymmetric) 8
9 Which is the driving mechanism of the two phase transitions? How is the magnetic ordering stabilized? Geometrical frustration huge degeneracy of the ground state. 3d 2 system, strong correlation effects spin and orbital degrees of freedom spin-orbit coupling (L=1, S=1) 9
10 Spinel ZnV 2 O 4 V 3+ : 3d 2 Theory interplay of lattice, orbital and spin degrees of freedom? Effective-model approach: (Y. Yamashita et al. PRL 00, H. Tsunetsugu et al. PRB 03, O. Tchernyshyov PRL 04, Di Matteo et al. PRB 05) 1) Jahn-Teller coupling 2) spin-orbital Kugel-Khomskii interaction (superexchange V-V interaction) 3) spin-orbit coupling (L=1, S=1) -λl S orbital order? 10
11 Spinel ZnV 2 O 4 V 3+ : 3d 2 Theory interplay of lattice, orbital and spin degrees of freedom? Effective-model approach: (Y. Yamashita et al. PRL 00, H. Tsunetsugu et al. PRB 03, O. Tchernyshyov PRL 04, Di Matteo et al. PRB 05) 1) Jahn-Teller coupling 2) spin-orbital Kugel-Khomskii interaction (superexchange V-V interaction) 3) spin-orbit coupling (L=1, S=1) eg d Isolated Ion t2g cubic dxz,dyz dxy tetragonal c/a < 1 11
12 Spinel ZnV 2 O 4 V 3+ : 3d 2 Theory interplay of lattice, orbital and spin degrees of freedom? Effective-model approach: (Y. Yamashita et al. PRL 00, H. Tsunetsugu et al. PRB 03, O. Tchernyshyov PRL 04,Di Matteo et al. PRB 05) 1) Jahn-Teller coupling 2) spin-orbital Kugel-Khomskii interaction (superexchange V-V interaction) 3) spin-orbit coupling (L=1, S=1) eg d Isolated Ion t2g cubic dxz,dyz dxy tetragonal c/a < 1 12
13 Spinel ZnV 2 O 4 V 3+ : 3d 2 Theory interplay of lattice, orbital and spin degrees of freedom? Effective-model approach: (Y. Yamashita et al. PRL 00, H. Tsunetsugu et al. PRB 03, O. Tchernyshyov PRL 04, Di Matteo et al. PRB 05) 1) Jahn-Teller coupling 2) spin-orbital Kugel-Khomskii interaction (superexchange V-V interaction) 3) spin-orbit coupling (L=1, S=1) eg d Isolated Ion t2g cubic dxz,dyz dxy tetragonal c/a < 1 13
14 Spinel ZnV 2 O 4 V 4+ : 3d 2 ab initio DFT calculations (T. Maitra, R. Valentí PRL 07) FPLAPW (WIEN2k) ZnV 2 O 4 in I4 1 /amd: tetragonal+trigonal distorsion LSDA-DOS 15 Zn VO 10 DOS (states/ev/atom) DOS (states/ev/atom) Energy (ev) dz2 dx2-y2 dxy dxz dyz Energy (ev) 14
15 Spinel ZnV 2 O 4 V 4+ : 3d 2 ab initio DFT calculations (T. Maitra, R. Valentí PRL 07) FPLAPW (WIEN2k) ZnV 2 O 4 in I4 1 /amd: tetragonal+trigonal distorsion LSDA-DOS LSDA+U-DOS U = 4-6 ev 15 Zn VO eg DOS (states/ev/atom) d Isolated Ion t2g cubic dxz,dyz dxy tetragonal c/a < 1 DOS (states/ev/atom) Energy (ev) dz2 dx2-y2 dxy dxz dyz DOS (states/ev/atom/spin) x Z dxy dxz dyz Energy (ev) Energy-E f (ev) 15
16 Spinel ZnV 2 O 4 electron density LSDA+U isovalue 0.6 e/å 3 c a b orbital order: A-type Antiferro-orbital along c and ferro-orbital in ab alternating d xz + d yz, d xz d yz DFT: d xz ± d yz Tsunetsugu, Motome PRB 03: d xz, d yz Jahn-Teller + Kugel-Khomskii 16
17 Spinel ZnV 2 O 4 inclusion spin-orbit coupling relativistic ab initio DFT calculation: LSDA+U+SO second variational method electron density: tetragonal cubic no A-type orbital order trigonal distortion d xz ± id yz (compare di Matteo et al., Tchernyshyov) l z =0.75 µ B, s=1.69 µ B j = 0.94 µ B compares to experimental j=0.63 µ B. 17
18 Spinel ZnV 2 O 4 LSDA+U Bandstructure LSDA+U+SO SO pushes unoccupied V d bands up in energy increase band gap decrease of bandwidth 18
19 Spinel ZnV 2 O 4 Possible AFM configurations: O Zn Zn V z O V y x z y x the experimental configuration (Rehuuis et al. EPJB 03, Lee et al. PRL 04) is energetically favorable (ab initio DFT) LSDA+U+SO 19
20 Magnetic excitations Perkins, Sikora to be published 07 spin-wave excitation spectrum above the magnetically ordered state LSWA MEM ω (k) [mev] LSWA - Linear spin wave theory MEM - Magnetic excitonic model 10 0 Γ M Y Γ M+ Y+ Γ Z orbital ordering with/without SO affects the spin-wave excitation spectrum decrease of bandwidth 20
21 Conclusions ZnV 2 O 4 orbital order is a subtle interplay: correlations effects spin-orbit coupling Jahn-Teller distortion relativistic ab initio DFT no A-type orbital order orbital distribution favors the observed AFM phase total magnetic moment agrees with experiment 21
22 ZnV 2 O 4 orbital order is a subtle interplay: correlations effects spin-orbit coupling Jahn-Teller distortion relativistic ab initio DFT no A-type orbital order orbital distribution favors the observed AFM phase total magnetic moment agrees with experiment need for experiments! 22
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