Tae Won Noh Research Center for Oxide Electronics & School of physics, Seoul National University

1. The roles of orbital in the optical and magnetic properties of RMnO3 (R = rare earth ions) Tae Won Noh Research Center for Oxide Electronics & School of physics, Seoul National University Seoul, Korea

2. Acknowledgements Collaborators Jaejun Yu M. W. Kim S. J. Moon J. H. Jung (Inha Univ.) & S. Parashar (ReCOE, SNU) P. Murugavel (ReCOE, SNU) Valuable discussion with G. Khaliullin (Max Plank Institute) K. Ahn (Argonne NL) J. Goodenough (U. Texas) P. B. Allen (SUNY, Stony Brook) P. Littlewood (Cambridge U)

3. Outline • 2. Orbitally degenerate Hubbard model (ODHM) • * Multiple peak structure in LaMO3 • 3. Applications of ODHM to the 2 eV peak of RMnO3 • * 2 eV peak in LaMnO3 • * Probing orbital correlations in RMnO3 • 4. Summary 1. Motivation : long-standing puzzles in (La,Y)MO3

4. Single-band Hubbard model for correlated electrons Mott insulator (U >> W) () U U op op p–d transition Dynamic MFT O 2p LHB UHB  Georges et al., Rev. Mod. Phys. (1996) Kinetic energy correlation

5. V2O3 Perovskite structure 4 eV Arima, Tokura, and Torrance, PRB (1993). Rozenberg et al., PRL (1994). Multi-peak structures in () for numerous oxides Correlation peaks : broad and/or multiple peak structures  Cannot be simply explained in terms of the single band picture

6. Charge transfer and correlation peaks in LaMO3 Arima and Tokura, JPSJ (1995). How to understand these somewhat anomalous behaviors in LaMO3? • Large reduction of the d-d transition energies • Disappearance of the d-d transition for LaCrO3 • Abnormal energy parameter for LaMO3

7. Outline • Motivation : long-standing puzzles in (La,Y)MO3 • 3. Applications of ODHM to the 2 eV peak of RMnO3 • * 2 eV peak in LaMnO3 • * Probing Orbital/Spin correlations in RMnO3 • 4. Summary 2. Orbitally degenerate Hubbard model * Multiple peak structure in LaMO3

8. Optical anisotropy due to orbital ordering Tokura et al., SCIENCE 288 462 (2000) La1.5Sr0.5MnO4 : CE-type OO Polarized microscopy Large optical anisotropy due to the orbital ordering below TCO Optical properties will be strongly dependent on the orbital degrees of freedom.

9. 3z2-r2 eg x2-y2 3d, 4d 10Dq l=2 m=-2,-1,0,1,2 xy yz t2g zx 10Dq : Electrostatic potential due to ligand anions “crystal field splitting” Orbital degeneracy: d-electron in a cubic crystal field Degeneracy of eg/t2g orbitals is common in cubic perovskite structure.

10. U U U’(=U-2J) U’-J (=U-3J) if J’ = J from a simple atomic picture The orbitally degenerate Hubbard model (ODHM)

11. Ferro-orbital (FO) FM/FO AFM/FO AFM/AFO FM/AFO Antiferro-orbital (AFO) Spin/Orbital configurations for t2g1 system

12. Hopping between the different orbitals is not allowed. Hopping between the same orbitals is allowed. Orbital selection rule for interatomic d-d transitions

13. LaTiO3 (t2g1) Example Optical processes t2g1 + t2g1 t2g0 + t2g2 (LaTiO3) Orbital multiplicity effects based on the simple atomic picture multiplet final states and energy costs t2g2 t2g2 t2g2 U – 3JH U –2JH U U U –2JH Schematically, Forbidden U – 3JH

14. 1A1 U+2JH[=A+10B+5C] 1T2 1E U-JH [=A+B+2C] 3T1 U-3JH [=A-5B] (U=A+4B+3C JH=3B+C) Wavefunctions of t2g2-configuration Energy values (3T1 M=1) = |dxy()dxy()| (3T1 M=0) =1/2(|dxy()dxy()|-|dxy()dxy()|) (3T1 M=-1) = |dxy()dxy()| U-3JH (1T2) =1/2(|dxy()dxy()|+|dxy()dxy()|) U-JH (1Ev) =1/2(|dyz()dyz()|-|dzx()dzx()|) (1Eu) =1/6(-|dyz()dyz()|-|dzx()dzx()|+2|dxy()dxy()|) (1A1) =1/3(|dyz()dyz()|+|dzx()dzx()|+|dxy()dxy()|) U+2JH Orbital multiplicity effect on the t2g2-configuration t2g2

15. LaTiO3 (t2g1) Example multiplet final states and energy costs Optical processes t2g2(3T1) t2g2(1E, 1T2) t2g2(1A1) t2g1 + t2g1 t2g0 + t2g2 U – 3JH U –JH U + 2JH (LaTiO3) Orbital multiplicity effects on the inter-site d-d transitions U –JH Schematically, U + 2JH Forbidden U – 3JH

16. 3.20 1.28 1.92 RTi3+O3 (t2g1) : (JH=0.64 eV) U-3JH U -JH U +2JH Understanding of d-d transitions under orbital multiplicity T. Arima and Y. Tokura, JPSJ (1995).

17. multiplet final states and energy costs Optical processes t2g2(3T1) t2g2(1E, 1T2) t2g2(1A1) t2g1 + t2g1 t2g0 + t2g2 U – 3JH U –JH U + 2JH t2g3(4A2) t2g3(2E, 2T1) t2g3(2T2) t2g2 + t2g2 t2g1 + t2g3 (LaVO3) U – 3JH U U + 2JH t2g3 + t2g3 t2g2 + t2g4 t2g2(3T1) / t2g4(3T1) U + 2JH (LaCrO3) Orbital multiplicity effects on the inter-site d-d transitions II (LaTiO3) For more information, see J. S. Lee, M. W. Kim, and T. W. Noh, New Journal of Physics 7, 147 (2005)

18. 3.20 1.28 1.92 RTi3+O3 (t2g1) : (JH=0.64 eV) U-3JH U -JH U +2JH 3.40 2.04 1.36 RV3+O3 (t2g2) : (JH=0.68 eV) U -3JH U U +2JH RCr3+O3 (t2g3) : (JH=0.72 eV) U+2JH Understanding of d-d transitions under orbital multiplicity Arima and Tokura, JPSJ (1995). The broad (multiple) correlation peaks can be explained .

19. Outline 1. Motivation : long-standing puzzles in (La,Y)MO3 2. Orbitally degenerate Hubbard model * Multiple peak structure in LaMO3 4. Summary 3. Applications of ODHM to the 2 eV peak of RMnO3 * 2 eV peak in LaMnO3 * Probing Oribital/Spin correlations in RMnO3

20. Some explanations on 2.0 eV peak in LaMnO3 Arima and Tokura, JPSJ (1995). • Charge transfer peak ? • Arima and Tokura, PRB (1995) • Tobe et al., PRB (2001) LaMO3 2) Band picture: inter-atomic peak coupled with the local spin alignment? Ahn and Millis PRB (2000) 3) Intramolecular peak due to Frank-Condon process ? Allen and Perebeinos, PRL (1999) Krüger et al., PRL (2004)

21. 5.60 (t2g3eg1) (t2g3eg1) (t2g3eg0) (t2g3eg2) 4.0 1. 60 M=Mn (t2g3eg1) : (JH=0.80 eV) U+4JH U -3JH U +2JH (LaMnO3) t2g3eg2 (6A1) t2g3eg2 (4A1, 4E) t2g3eg2 (4A2) ~ U – 3JH ~ U +2JH ~ U + 4JH A explanation of the 2.0 eV peak based on the ODHM LaMO3 Arima and Tokura, JPSJ (1995).

22. Other experiment supports our picture on 2 eV peak The 2 eV peak in Resonant Inelastic X-ray Scattering: Energy and Momentum dependences well agree with the picture of inter-band transition between Hubbard bands. Inami et al., PRB (2003)

23. M. W. Kim et al. submitted to PRL Merits of ODHM explanation for 2 eV peak of LaMnO3 1. Ground state spin/orbital configuration 2. Anisotropic optical conductivity 3. Temperature dependence of the spectra 4. Rare earth doping effects on optical spectra

24. ODHM explanation for 2 eV peak of LaMnO3 schematic configurations for possible transitions 1. Ground state c b a A-type AFM spin order lowest energy c b a C-type orbital order

25. Kovaleva et al., PRL (2004) Tobe et al. PRB (2001) c b a ODHM explanation for 2 eV peak of LaMnO3 2. Anisotropic optical conductivity

26. M. W. Kim et al. NJP (2004) 5 2.0x10 ) 10 K LaMnO3 -1 50 K 100 K 5 1.5x10 125 K 150 K 200 K Absorption Coefficient (cm 5 1.0x10 250 K 300 K 4 5.0x10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Photon Energy (eV) 5 ) 2.65x10 -1 5 2.60x10 Spectral Weight (eVcm 5 2.55x10 5 2.50x10 0 50 100 150 200 250 300 Temperature (K) ODHM explanation for 2 eV peak of LaMnO3 3. Temperature dependence Spectral weight show distinct suppression as crossing the antiferromagnetic ordering T. Tobe et al. Phys. Rev. B (2001)

27. 1. The peak energy change is small. 2. The spectral weight change is large. ODHM explanation for 2 eV peak of LaMnO3 4. Rare earth substitution effects M. W. Kim et al., PRL (submitted) Kimura et al. PRB (2003)

28. absorption coefficient La Pr Photon Energy (eV) 0 1 2 3 La 1.0 Gd Pr Tb 0.8 Nd 0.6 Gd Spectral weight (norm.) Tb 0.4 0 1 2 3 0.2 0.0 1.08 1.23 1.20 1.17 1.14 1.11 Ionic radius of R-site (A) R-ion dependence of the integrated spectral weight Kimura et al. Phys. Rev. B (2003)

29. Small R-ion Large R-ion Orbital rotation Electric dipole transition probability eg2 eg2 empty Jahn-Teller distortion and GdFeO3 type distortion can suppress the electron hopping in the ab-plane. occupied eg1 eg1 Orbital Mixing Orbital pattern dependent optical matrix element

30. Electric dipole transition probability Rotation of orbital due to the buckling of MnO6 octahedra cf. Goodenough and Kanamori rule

31. R-ion dependence of the integrated spectral weight 10 deg. Bond angle of <Mn-O-Mn> (deg.) 155.2 151.1 150.0 146.5 145.3 La Pr Nd Gd Tb 1.0 “Orbital rotation” cannot alone explain the drastic change. 0.8 0.6 (a.u.) W (exp.) 0.4 S S W 0.2 f S ( ) W 0.0 1.20 1.16 1.12 1.08 R-ion radius (A)

32. Orbital mixing due to the Jahn-Teller distortion z x

33. Spectral weight change due to the bond-angle and orbital mixing angle Rotation of needle-like orbital controls the charge motion

34. Spectral weight change due to the bond-angle and orbital mixing angle

35. LaMnO3 TbMnO3 Spectral weight change due to the bond-angle and orbital mixing angle

36. R-ion dependence of the integrated spectral weight 10 deg. Bond angle of <Mn-O-Mn> (deg.) 155.2 151.1 150.0 146.5 145.3 La Pr Nd Gd Tb 1.0 “Orbital rotation” and “Orbital mixing” can explain the drastic change. 0.8 0.6 (a.u.) W (exp.) 0.4 S S W f S ( ) 0.2 W f q S ( , ) W 0.0 1.20 1.16 1.12 1.08 R-ion radius (A)

37. Spectral weight change vs. magnetic phase diagram Bond angle of <Mn-O-Mn> (deg.) 155.2 151.1 150.0 146.5 145.3 150 SW (measured) La 1.0 TN (A-type) Pr TN (E-type) 0.8 SW (a.u.) TIC (sine-wave) 100 Nd 0.6 TN (K) Sm 0.4 Gd Ho 50 A-AF Tb The magnetic phase diagram is reproduced from the work by Kimura et al. PRB (2003) 0.2 E-AF ? 0 0.0 1.20 1.15 1.10 1.05 ionic radius of R-site (Å ) Hexagonal Orthorhombic

38. Summary 1. Based on the orbitally degenerate Hubbard model, we could explain optical spectra of (La,Y)MO3 (M = 3d transition metal). 2. We showed that features of 2 eV peak of LaMnO3 can be explained within the orbitally degenerate Hubbard model. 3. We proposed that the orbital correlations could affect R-ion size dependentspectral weight change and magnetic properties of RMnO3. 4. Optical spectroscopy is a good experimental technique to probe the orbital correlation in strongly correlated electron systems.