Spin-Orbital-Charge Coupled Dynamics in t 2g -electron Systems

1. Spin-Orbital-Charge Coupled Dynamics in t2g-electron Systems Yoshi Tokura Dept of Appl Phys, Univ Tokyo ERATO Multiferroics Project, JST and Cross-Correlation Materials Research Group (CMRG), RIKEN Orbitally-active t2g2 systems with Mott criticality: Orbital order and dynamics in (hole-doped) perovskite RVO3 Diffuse charge dynamics on frustrated double-exchange system R2Mo2O7 Collaborators Univ. Tokyo S.Iguchi, J. Fujioka, T. Yasue, K. Sano, S. Kumakura N. Hanasaki (now @ Okayama Univ), S. Miyasaka(now @Osaka Univ) Univ. Budapest RIKEN- CMRG AIST-CERC I. Kezsmarki, S. Bordacs Y. Taguchi, C. Terakura N. Takeshita

2. Interplay of charge, spin and orbital degree of freedom 3d orbital charge x2-y2 3z2-r2 charge Orbital Spin yz Orbital zx Spin xy • Superconductivity • Colossal magnetoresistance (CMR) • Charge and orbital ordering • Non-Fermi liquid Role of orbital degree of freedom on versatile phase

3. (b) YVO3 (a) LaVO3 (d) BiMnO3 (c) LaMnO3 t2g oribtal spin C-type orbital G-type spin G-type orbital C-type eg orbital

4. Electronic phase in CMR manganites eg orbital system Too>>Tso Strong Jahn-Teller interaction Charge dynamics coupled with lattice degree of freedom t2g orbital system Too~Tso Jahn-Teller interaction orbital exchange interaction spin-orbit interaction Comparable Y. Tokura, Rep. Prog. Phys. 69, (2006) 797 spin-orbital coupled phenomena

5. O V V O eg La dzx dyz dxy Electronic structure in perovskite LaVO3 Perovskite structure V3+ (3d 2) LaVO3 eg t2g dxy1dyz1/ dxy1dzx1 Orbital ordering in dyz and dzx orbitals

6. Spin and orbital ordering in LaVO3 TSO=143K Spin C-type SO T Orbital G-type OO TOO=141K E || c E ⊥ c Quasi-one-dimensional (1D) electronic structure along c-axis originating from the C-type SO and G-type OO Y. Motome et al., Phys. Rev.Lett, 90,146602(2003) Quasi-1D orbital exchange interaction S. Miyasaka et al, J. Phys. Soc Jpn, 71, 2086(2002)

7. The orbital excitation (two-orbiton) c orbital -G c k pseudospinon 1.96eV excitation • One-dimensionality • Orbital exchange interaction and the Jahn-Teller energy S. Miyasaka, et al., Phys. Rev. Lett, 94, 076405(2005)

8. Van Hove singularity of spinon band H.Suzuura, H.Yasuhara, A.Furusaki, N.Nagaosa, and Y.Tokura , PRL(96). c.f.J.Lorenzana and R.Eder, PRB(97). Spin-phonon coupling (Lorezana-Sawatzky) Heisen. accurate estimate of J XY spinon interband trasnitions (two-magnon band) showing up as the sideband of phonon J~0.26eV optical phonon

9. Optical (Raman) probe for quantum orbital chains S.Onoda-N.Nagaosa ECJT/J=0.15 EDJT dynamical Jahn-Teller ECJT classical Jahn-Teller pseudo spion (orbital version of spinon) gapping due to Jahn-Teller distortion   /2 0

10. Orbital excitations in NdVO3 as probed by Raman spectra

11. Filling-Control Metal-Insulator Transition antiferromagnetic metal phase (AFM) (no oribtal order) decrease of carrier density mass enhancement cf. γ~ 40mJ/K2V-unit in V2-δO3 Miyasaka et al. PRL (2001).

12. Doping variation of the electronic structure in La1-xSrxVO3 c C-type SO G-type OO Lightly doped region • Doped hole occupies dyz/dzx orbital and forms a self-trapped state accompanying the modification in lattice, spin, and orbital sector • Anisotropic hole dynamics, reflecting the one-dimensionality of the orbital exchange interaction • On the verge of insulator- • metal transition doped holes nearly equivalently occupy dxy, dyz and dzx orbital

13. Electronic structure in the lightly doped systems c C-type SO G-type OO dyz, dzx • Large T dependence of the mid-IR peak in E || c spectra. • Minimal T dependence of the E⊥c spectra. • The doped holes predominantly occupy the dyz or dzx orbital • large kinetic energy along c-axis, reflecting one-dimensional orbital exchange interaction.

14. Spin-orbital phase diagram for RVO3( R=rare-earth ion ) YVO3 (c) R VO 3 Eu Gd Y Tb Sm Ho Dy Er 200 Nd Yb Pr T Lu OO1 G-type OO La (K) T OO SO1 T , 100 SO c T T = T SO2 OO2 b C-type SO G-type OO G-type SO a C-type OO 1.15 1.2 1.25 1.3 1.35 (Å) r R SO : Spin Ordering OO : Orbital Ordering G-type OO C-type SO G-type OO G-type SO C-type OO • Control of the orthorhombic lattice distortion by changing R ion • Variation of the spin and orbital ordered phase

15. Optical conductivity spectra for YVO3 TSO2, TOO2=77K TSO1=115K TOO1=200K Spin G-type SO G-type OO disorder C-type OO Orbital C-type SO T G-type SO, C-type OO C-type SO, G-type OO Spin-orbital disordering Nearly isotropic orbital exchange interaction in magnitude 1D-orbital exchange interaction Nearly isotropic charge dynamics

16. Spin-orbital phase diagram for RVO3( R=rare-earth ion ) (c) R VO 3 Eu Gd Y Tb Sm Ho Dy Er 200 Nd Yb Pr T Lu OO1 G-type OO La (K) T OO SO1 T , 100 SO c T T = T SO2 OO2 b C-type SO G-type OO G-type SO a C-type OO 1.15 1.2 1.25 1.3 1.35 (Å) r R SO : Spin Ordering OO : Orbital Ordering G-type OO C-type SO G-type OO G-type SO C-type OO • Control of the orthorhombic lattice distortion by changing R ion • Variation of the spin and orbital ordered phase

17. R=Dy z y x Reentrant orbital ordering transitions in DyMnO3 Miyasaka et al. PRL(2007)

18. G-type OO G-type OO G-type OO C-type SO G-type OO C-type SO C-type OO G-type SO C-type OO G-type SO hysteresis region hysteresis region Magnetic field induced orbital-state switching in DyMnO3 Coincident with metamagetic trasnsition of Dy Ising moments contribution from Gd f moments via the f-d exchange interaction H//b H//a

19. Spin-orbital phase diagrams of hole-doped RVO3 C-type SO G-type OO G-type OO G-type SO C-type OO G-type SO, C-type OO state is extremely fragile against doping W Insulator-metal transition point dependent on W paramagnetic G-type OO phase • Change of band-filling • Quenched disorder Fujioka et al. PRB (2006).

20. Optical conductivity spectra in Y1-xCaxVO3 inner-gap exc. 1D M-H gap x>0.02 : Anisotropic Mott-gap excitation reflecting the quasi-1D orbital exchange interaction Nearly isotropic hole dynamics

21. (111) Mo eg eg O2- 4d eg’ t2g a1g D3d Oh Pyrochlore-type structure : R2 Mo2 O7 Mo-sublattice, composed of corner-sharing teterahedra. (111)-plane is Kagome lattice. R Mo Double-excange int. + frsturation

22. eg eg’ a1g D3d Electronic band structure based on DFT I.V. Solovyev PRB (2003) (conduction electron) t2g manifold a1glocal spin nearly half-metallic EF EF EF up-spin t2g- band

23. Metal-insulator phomena dependent on R-ion size

24. (d) randomness vs. frustration in double-exchange systems bandwidth Perovskite Mn AF FM Pyrochlore Mo phase competition Y. Tomiokaet al. Randomness Spin glass Spin frustration Spin glass (on frustrated lattice) (size mismatch of RE and AE ions)

25. eg 4d t2g Oh D3d eg eg a1g Importance of electron correlation orbital dependent Mott transition conduction/localized electron local spin Mo-Mo distance P (hydrostatic pressure) a1g bandwidth (JAF) eg’ bandwidth(W/U) Mo-O-Mo bond angle rA (chemical pressure)

26. Y2Mo2O7 Sm2Mo2O7 Eg～0.1 eV EF Mo 4d Mo 4d O 2p O 2p Optical conductivity spectra for Mott gap and CT exitation ・large enegy scale (=1 eV) over which electronic structure is reconstructed. O2p →Mo4d UH Mott-Hubbard type (as opposed to CT type) Taguchi-YT PRB (2002)

27. Mott gap variation in R2Mo2O7 Drude Kezsmarki et al.PRL (2004)

28. Drude component near the Mott criticality Kezsmarki et al.PRL (2004)

29. Optical phase diagram in R2Mo2O7 Drude weight charge gap incoherent metal low-energy spectral weight around ωM Kezsmarki et al.PRL (2004)

30. scrutinizing phase boundary・・・ mass enhancement (~×3） in FM state (orbital fluctuation?) Curie-Weiss temperature ferromagnetic(eg’mediated) vs. antiferromagnetic(a1g mediated) ferromagnetic fluctuation spin flipping time of spin glass from atomic to cluster-like Hanasaki et al. PRL (2007).

31. eg 4d t2g Oh D3d P (hydrostatic pressure) a1g bandwidth (JAF) eg eg’ bandwidth(W/U) eg a1g rA (chemical pressure) Effect of Pressures orbital dependent Mott transition conduction/localized electron local spin

32. Pressure effects FM SGI Nd2Mo2O7 metallic & ferromagnetic -> metallic & spin glassy -> metallic & paramagnetic 3kHz Ferromag. Spin glass anomalously T-independent bad conductivity Paramag.

33. FM SGI Pressure effects metallic & ferromagnetic -> metallic & spin glass -> metallic & paramagnetic Sm2Mo2O7 Ferromag. Spin glass anomalously T-independent bad conductivity Paramag.

34. Spinglass to paramagnetic metal transition in pressurized Gd2Mo2O7 Gd2Mo2O7 FM SGI anomalously T-independent bad conductivity in paramagnetic metal state

35. Phase diagram multicritical feature incoherent (non Fermi Liquid?) metal conduction electrons interacting with glassy or flctuating local spins on the frustrated lattice (b)

36. eg (d) 4d t2g Oh D3d eg eg ambient pressure a1g DE model on frustrated lattice? W,U JAF <<JH paramag. metal (non-FL?) spin-glass insulator JAF ferromag. metal W/U large finite scattering rate in T=0 limit

37. eg (d) 4d t2g Oh D3d eg eg ambient pressure a1g DE model on frustrated lattice? W,U JAF <<JH paramag. metal (non-FL?) spin-glass insulator JAF ferromag. metal W/U

38. minute spin anisotropy leads to non-Fermi-liquid behavior α=0,0.3,0.5,0.7,1

39. Rich electric phases in t2g –electron frustrated systems all close to the metal-insulator transition (Mott, charge/orbital order) supercond. (Tc=14K) LiTi2O4 d0.5 pyrochlore lattice ferromag. Mott ins. (orbital order) Lu2V2O7 d1 heavy electron d1.5 LiV2O4 Mott transition spin chirality (anomalous Hall) Nd2Mo2O7 d2 Y2Mo2O7 entanglement in spin & orbital sectors Kugel-Khomskii type and spin-orbit interactions scalar spin chirality Si・(Sj×Sk),vector spin chilarity Si×Sj, spin current, orbital current?