Evolution of Spin-Orbital-Lattice Coupling in RVO3 Perovskites

1. Evolution of Spin-Orbital-Lattice Coupling in RVO3 Perovskites Peter Horsch (MPI-FKF Stuttgart) Lou-Fe Feiner (Utrecht&Eindhoven) Giniyat Khaliullin (Stuttgart) Andrzej M. Oles (Cracow) Entanglement in Spin & Orbital Systems Cracow, Poland, June 18-22, 2008

2. Outline • Introduction: • Spin and orbital model for cubic vanadates • High anisotropy of magnetic and optical properties: • Orbital-Peierls dimerization in YVO3 • Phase diagram of RVO3 : Interplay of superexchange & orbital-lattice I.

3. Manganites & Vanadates: eg vs. t2g systems: robust vs. soft orbital order Manganites: • Eg-orbitals point to intermediate O-ions leading to strong Jahn-Teller orbital lattice coupling. LaMnO3 • Significant hole-doping is required to destroy orbital order. • In t2g systems soft orbital order ist expected in the undoped Mott insulator.

4. Cubic vanadates RVO3 : t2g-system Expectation: Jahn-Teller couplings & crystal fields much smaller than in manganites Hence Orbital fluctuations not completely quenched

5. Temperature-induced magnetization reversal in YVO3 crystals - C-type Antiferromagnet below TN =116 K - G-type below structural transition Ts = 77 K - Magnetization reversal near 100 K upon heating (cooling) in a weak magnetic field ! - Magnetization due to canting - Memory effect when switching on and off a strong magnetic field ! Y. Ren et al., Nature 396, 441 (1998), Y. Ren et al. PRB 62, 6577 (00);

6. Phase diagram of cubic vanadates RVO3 S. Miyasaka et al. (2003), T. Yasue et al. (2008) Control: GdFeO3 distortion Control: Jahn-Teller distortion C-type SO G-type OO G-type SO C-type OO

7. Superexchange in cubic Vanadates: Interplay of spins & orbitalsKugel-Khomskii type spin-orbital model • Transitions across Hubbard gap determine magnetism. • Two t2g electrons in ground state: V3+ 1 electron in xy, 2nd electron in xz or yz • Spin 1 due to Hund interaction JH • Only electrons in xz and yz orbitals can hop along c-direction. (active orbitals xz & yz) • Exchange of a (xy,yz) into (yz,xy) pair leads to strong orbital fluctuation along c-axis. C-Spin (G-Orbital) favored by superexchange !! Occupied xy-orbital not shown! G.Khaliullin, P.H., A.M.Oles, PRL 86, 3879 (2001).

8. G-C phase transition in YVO3 Orbital lattice coupling: JT & GdFeO3 distortion • Superexchange favors C-phase • Vc favors low T G-phase ! • 1st order transition: entropy controlled • Smaller excitation energy in high-T C-phase Spin & orbital waves : LSWT G-phase (Low T) • Free energy : Vc=1.3 J, Va=0.65 J, h=JH/U C-phase G. Khaliullin et al., PRL 86, 3879 (01) A.M. Oles et al., PRB 75, 184434 (07)

9. Magnons: Evidence for Orbital Peierls State in YVO3 Neutron scattering: C. Ulrich et al., PRL 91, 257202 (2003) • Low-T phase: G-type antiferromagnetism • Jc=5.7 meV, Jab=5.7 meV • C-Phase: Splitting of magnon in acustic and optic branch • Orbital Peierls dimerization! • No evidence for significant dimerization of the lattice ! • Yet symmetry group (Raman) consistent with dimerization: (Tsvetkov et al 2004) • Strong ferro-coupling along c! • Jab=2.6 meV, Jc1=-2.2 meV, Jc2=-4 meV

10. Two Ground States Shen, Xie, Zhang, PRL 88, 027201 (2002) Oles, P.H., Khaliullin, Acta Phys. Pol. B34, 857 (02) Khaliullin, P.H., Oles, PRL 86, 3879 (2001).

11. Orbital-Peierls Dimerization in C-Phase at finite temperature • Nearest neighbor spin- and orbital-correlation functions are dimerized at finite temperature in the C-phase • Dimerization of FM chain only possible at finite T by simultaneous formation of orbital singlet pairs: • Magnetic structure factor S(q,w): • Magnons at q=p/2 (along c) are split as result of the orbital dimerization. • High-energy structure due to orbital excitations. P.H., G. Khaliullin, A.M. Oles, PRL 91, 257203 (2003) ; TMRG: J. Sirker & G. Khaliullin, PRB 67, 100408 (2003)

12. Effective spin model Coupling constants determined by orbital correlations: Magnons in C-Phase of YVO3 (T=85 K): Linear spin-wave theory. Exp. Ulrich et al. (2007) A.M.Oles et al PRB 75, 184434 (07)

13. IntermezzoWhat can be learned from optics about magnetism?

14. Optical spectra ofLaVO3 High anisotropy! E||c strong T-dependence Schematic:d-d Multiplet Transitions U~2.1 eV vs. 3.8 eV Spectral weight of LaVO3 Miyasaka, Okimoto, Tokura (2002) Controlled by magnetism !

15. Partial optical sum rules from superexchange Optical spectral weights for different multiplet transitions n=1,2 &3: Partial sum rules at finite JH follow from the individual multiplet contributions: • Virtual transitions across the Hubbard gap determine magnetism. • Same d-d transitions appear in optics. • Strength of absorption into different multiplet states linked to the magnetic order. J=t2/U, h=JH/U, R=1/(1-3h), r=1/(1+2h)

16. Comparison of optical weights and superexchange energy: LaVO3 • Optical weights for c-polarization • At low temperature all weight in high-spin transition n=1 • Kinetic energy K(c) amplified by orbital fluctuations along c. • Exp. Points: Miyasaka et al. (2002) • Strong variation at TN=143 K • J~40 meV from kinetic energy in high-spin multiplet transition. • Optical weights for a(b) polarization • High anisotropy G.Khaliullin, P.H., A.M. Oles, Phys. Rev. B 70, 195103 (2004)

17. Phase diagram of cubic vanadates: dependence on cation radius

18. Phase Diagram of Vanadates & Spin-Orbital Model • Orbital-lattice couplings: • Ez : GdFeO3 distortion, Q=(p,p,0) • Vab & Vc: Jahn-Teller & GdFeO3 distortion Ez & Vc favor orbital-C structure & competes with superexchange interaction. • Hu: orthorhombic distortion u=(b-a)/a (NEW) V-O-V angle: GdFeO3-distortion versus R-ion radius: rR= r0- a sin2(2J) ; r0=1.5 A, a=0.95 A & assume j=J/2 PH, Oles, Khaliullin & Feiner, PRL (08)

19. GdFeO3 distortion and crystal field Crystal field splitting of xz and yz orbitals from point charge model

20. Orthorhombic distortion: u=(b-a)/a Sm Y Sm La Transverse field favors M.H.Sage et al. PRL 96 ,036401 (06); PRB 76,195102 (07) G.R. Blake et al, PRL 87, 245501 (01) Y. Ren et al. PRB 67, 014107 (03) M. Reehuis et al. PRB 73, 094440 (06) P. Bordet et al. J.Sol.St.Chem. 106, 253 (93) P. Munoz et al. J. Mater. Chem. 13, 1234 (03)

21. Order parameter vs. Temperature TN1 Too SmVO3 • La: TO=TN1 fixed by choice of Vc • At TO no discontinuity of <tx> for Sm • Decrease of <tx> below TN1 M.H.Sage et al. PRL 96 ,036401 (06);

22. Variation of coupling constants & orthorhombicity u(J) Result confirms our assumption that g and K are independent of J, i.e., • Relation 0.03 geff=u(J) yields g= 30 J • Relation 15<tx>=3 geff/J yields c(T)=0.2/J • Given K=8 eV/A2 (SrTiO3) the orbital contribution is about 5%

23. Conclusions • Phase-diagram controlled by interplay of superexchange & orbital-lattice couplings (JT, GdFeO3, orthorhombic distortion competes with xz & yz order  nonmonotonous Too) • Extreme anisotropy of magnetic C-phase due to quasi-1D orbital fluctuations. • Temperature dependence of partial optical sum rules can be obtained from spin-orbital model. • Orbital and spin degrees of freedom usually cannot be factorized! (entanglement, orbital-Peierls) – Cluster mean-field theory (ED)

24. Spin-orbit coupling: Orientation of spins • Orbital moments are quenched except for contribution from degenerate xz, yz orbitals which contribute to Lz. P.H., Khaliullin, Oles, PRL 91, 257203 (2003)

25. Goodenough-Kanamori rules JAF ~ 4 t2/U JF ~ -4 t2/U (JH/U) Usually FM interactions smaller by factor JH/U Conjecture for C-phase: Strong 1D (singlet) orbital fluctuations along c-axis support and amplify ferromagnetism along c!! G.Khaliullin, P.H., A.M.Oles, PRL 86, 3879 (2001).