The roles of orbital in the optical and

The roles of orbital in the optical and magnetic properties of RMn. O 3 (R = rare earth ions) Tae Won Noh Research Center for Oxide Electronics & School of physics, Seoul National University Seoul, Korea Oct 28 th, KIAS workshop

Acknowledgements Collaborators M. W. Kim & S. J. Moon J. H. Jung (Inha Univ. ) S. Parashar (Re. COE, SNU) P. Murugavel (Re. COE, SNU) Valuable discussion with G. Khaliullin (Max Plank Institute) K. Ahn (Argonne NL) J. Goodenough (U. Texas) P. Littlewood (Cambridge U) P. B. Allen (SUNY, Stony Brook) Oct 28 th, KIAS workshop Jaejun Yu

Outline 1. Motivation : long-standing puzzles in (La, Y)MO 3 2. Orbitally degenerate Hubbard model (ODHM) * Multiple peak structure in La. MO 3 3. Applications of ODHM to the 2 e. V peak of RMn. O 3 * 2 e. V peak in La. Mn. O 3 * Probing orbital correlations in RMn. O 3 4. Summary Oct 28 th, KIAS workshop

Single-band Hubbard model for correlated electrons Kinetic energy correlation Dynamic MFT Mott insulator (U >> W) U op ( ) O 2 p Georges et al. , Rev. Mod. Phys. (1996) Oct 28 th, KIAS workshop op LHB U p–d transition

Multi-peak structures in ( ) for numerous oxides V 2 O 3 Perovskite structure 4 e. V Rozenberg et al. , PRL (1994). Arima, Tokura, and Torrance, PRB (1993). Correlation peaks : broad and/or multiple peak structures Cannot be simply explained in terms of the single band picture Oct 28 th, KIAS workshop

Charge transfer and correlation peaks in La. MO 3 Arima and Tokura, JPSJ (1995). 1. 2. 3. Oct 28 th, KIAS workshop Large reduction the d-d transition How to of understand these energies Disappearance the d-d transition for La. Cr. O 3 somewhat of anomalous behaviors Abnormal energy in parameter La. MO ? for La. MO 3 3

Outline 1. Motivation : long-standing puzzles in (La, Y)MO 3 2. Orbitally degenerate Hubbard model * Multiple peak structure in La. MO 3 3. Applications of ODHM to the 2 e. V peak of RMn. O 3 * 2 e. V peak in La. Mn. O 3 * Probing Orbital/Spin correlations in RMn. O 3 4. Summary Oct 28 th, KIAS workshop

Optical anisotropy due to orbital ordering Tokura et al. , SCIENCE 288 462 (2000) La 1. 5 Sr 0. 5 Mn. O 4 : 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. Oct 28 th, KIAS workshop

Orbital degeneracy: d-electron in a cubic crystal field 3 z 2 -r 2 x 2 -y 2 eg xy yz zx t 2 g 3 d, 4 d 10 Dq l=2 m=-2, -1, 0, 1, 2 10 Dq : Electrostatic potential due to ligand anions “crystal field splitting” Degeneracy of eg/t 2 g orbitals is common in cubic perovskite structure. Oct 28 th, KIAS workshop

The orbitally degenerate Hubbard model (ODHM) U U U’(=U-2 J) U’-J (=U-3 J) if J’ = J Oct 28 th, KIAS workshop from a simple atomic picture

Spin/Orbital configurations for t 2 g 1 system Ferro-orbital (FO) Antiferro-orbital (AFO) Oct 28 th, KIAS workshop FM/FO AFM/FO FM/AFO AFM/AFO

Orbital selection rule for interatomic d-d transitions Hopping between the different orbitals is not allowed. Hopping between the same orbitals is allowed. Oct 28 th, KIAS workshop

Orbital multiplicity effects based on the simple atomic picture Example La. Ti. O 3 (t 2 g 1) multiplet final states and energy costs Optical processes t 2 g 2 t 2 g 1 + t 2 g 1 t 2 g 0 + t 2 g 2 (La. Ti. O 3) Schematically, U – 3 JH U U – 3 JH Oct 28 th, KIAS workshop t 2 g 2 U – 2 JH U U – 2 JH Forbidden

Orbital multiplicity effect on the t 2 g 2 -configuration 1 A t 2 g 2 U+2 JH [=A+10 B+5 C] 1 1 T 3 T 2 1 1 E U-JH [=A+B+2 C] U-3 JH [=A-5 B] (U=A+4 B+3 C JH=3 B+C) Wavefunctions of t 2 g 2 -configuration (3 T 1 M=1) = |dxy( )| (3 T 1 M=0) =1/ 2(|dxy( )|-|dxy( )|) (3 T 1 M=-1) = |dxy( )| (1 T 2) =1/ 2(|dxy( )|+|dxy( )|) (1 Ev) =1/ 2(|dyz( )|-|dzx( )|) (1 Eu) =1/ 6(-|dyz( )|-|dzx( )|+2|dxy( )|) (1 A 1) =1/ 3(|dyz( )|+|dzx( )|+|dxy( )|) Oct 28 th, KIAS workshop Energy values U-3 JH U-JH U+2 JH

Orbital multiplicity effects on the inter-site d-d transitions Example La. Ti. O 3 (t 2 g 1) Optical processes t 2 g 1 + t 2 g 1 t 2 g 0 + t 2 g 2 (La. Ti. O 3) Schematically, multiplet final states and energy costs t 2 g 2 (3 T 1) t 2 g 2 (1 E, 1 T 2) t 2 g 2 (1 A 1) U – 3 JH U –JH U + 2 JH U – 3 JH Oct 28 th, KIAS workshop U –JH Forbidden

Understanding of d-d transitions under orbital multiplicity 3. 20 RTi 3+O 3 (t 2 g 1) : (JH=0. 64 e. V) 1. 28 U-3 JH 1. 92 U -JH U +2 JH T. Arima and Y. Tokura, JPSJ (1995). Oct 28 th, KIAS workshop

Orbital multiplicity effects on the inter-site d-d transitions II multiplet final states and energy costs Optical processes t 2 g 1 + t 2 g 1 t 2 g 0 + t 2 g 2 (3 T 1) t 2 g 2 (1 E, 1 T 2) t 2 g 2 (1 A 1) U – 3 JH U –JH U + 2 JH t 2 g 3 (4 A 2) t 2 g 3 (2 E, 2 T 1) t 2 g 3 (2 T 2) (La. Ti. O 3) t 2 g 2 + t 2 g 2 t 2 g 1 + t 2 g 3 (La. VO 3) t 2 g 3 + t 2 g 3 t 2 g 2 + t 2 g 4 (La. Cr. O 3) U – 3 JH U U + 2 JH t 2 g 2 (3 T 1) / t 2 g 4 (3 T 1) U + 2 JH For more information, see J. S. Lee, M. W. Kim, and T. W. Noh, New Journal of Physics 7, 147 (2005) Oct 28 th, KIAS workshop

Understanding of d-d transitions under orbital multiplicity RCr 3+O 3 (t 2 g 3) : (JH=0. 72 e. V) U+2 JH 3. 40 (t 2 g : (JH=0. 68 e. V) RV 3+O 3 2. 04 2) U -3 JH 1. 36 U U +2 JH 3. 20 (t 2 g : (JH=0. 64 e. V) RTi 3+O 3 1) 1. 28 U-3 JH 1. 92 U -JH U +2 JH Arima and Tokura, JPSJ (1995). The broad (multiple) correlation peaks can be explained. Oct 28 th, KIAS workshop

Outline 1. Motivation : long-standing puzzles in (La, Y)MO 3 2. Orbitally degenerate Hubbard model * Multiple peak structure in La. MO 3 3. Applications of ODHM to the 2 e. V peak of RMn. O 3 * 2 e. V peak in La. Mn. O 3 * Probing Oribital/Spin correlations in RMn. O 3 4. Summary Oct 28 th, KIAS workshop

Some explanations on 2. 0 e. V peak in La. Mn. O 3 Arima and Tokura, JPSJ (1995). La. MO 3 1) Charge transfer peak ? 2) Arima and Tokura, PRB (1995) 3) Tobe et al. , PRB (2001) 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) Oct 28 th, KIAS workshop

A explanation of the 2. 0 e. V peak based on the ODHM La. MO 3 (t 2 g 3 eg 1) (t 2 g 3 eg 0) (t 2 g 3 eg 2) (La. Mn. O 3) t 2 g 3 eg 2 (6 A 1) ~ U – 3 JH M=Mn (t (JH=0. 80 e. V) 3 1 2 g eg ) Arima and Tokura, JPSJ (1995). Oct 28 th, KIAS workshop t 2 g 3 eg 2 (4 A 1, 4 E) ~ U +2 JH 4. 0 : U -3 JH t 2 g 3 eg 2 (4 A 2) ~ U + 4 JH 5. 60 1. 60 U +2 JH U+4 JH

Other experiment supports our picture on 2 e. V peak The 2 e. V 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) Oct 28 th, KIAS workshop

Merits of ODHM explanation for 2 e. V peak of La. Mn. O 3 1. Ground state spin/orbital configuration 2. Anisotropic optical conductivity 3. Temperature dependence of the spectra 4. Rare earth doping effects on optical spectra M. W. Kim et al. submitted to PRL Oct 28 th, KIAS workshop

ODHM explanation for 2 e. V peak of La. Mn. O 3 1. Ground state schematic configurations for possible transitions c b a A-type AFM spin order c b a C-type orbital order Oct 28 th, KIAS workshop lowest energy

ODHM explanation for 2 e. V peak of La. Mn. O 3 2. Anisotropic optical conductivity Tobe et al. PRB (2001) c b a Oct 28 th, KIAS workshop Kovaleva et al. , PRL (2004)

-1 Absorption Coefficient (cm ) ODHM explanation for 2 e. V peak of La. Mn. O 3 3. Temperature dependence Spectral weight show distinct suppression as crossing the antiferromagnetic ordering T. -1 Spectral Weight (e. Vcm) Tobe et al. Phys. Rev. B (2001) M. W. Kim et al. NJP (2004) 5 2. 0 x 10 10 K 50 K 100 K 125 K 150 K 200 K 250 K 300 K 5 1. 5 x 10 5 1. 0 x 10 La. Mn. O 3 4 5. 0 x 10 0. 5 1. 0 1. 5 2. 0 2. 5 Photon Energy (e. V) 3. 0 3. 5 5 2. 65 x 10 5 2. 60 x 10 5 2. 55 x 10 5 2. 50 x 10 0 Oct 28 th, KIAS workshop 50 100 150 200 250 Temperature (K) 300

ODHM explanation for 2 e. V peak of La. Mn. O 3 4. Rare earth substitution effects Kimura et al. PRB (2003) M. W. Kim et al. , PRL (submitted) 1. The peak energy change is small. 2. The spectral weight change is large. Oct 28 th, KIAS workshop

R-ion dependence of the integrated spectral weight absorption coefficient Oct 28 th, KIAS workshop Spectral weight (norm. ) Kimura et al. Phys. Rev. B (2003) 0. 8 0. 6 0. 4 Tb Gd 0 1. 0 Pr La 1 1 2 3 0 Photon Energy (e. V) 2 3 La Pr Nd Gd Tb 0. 2 0. 0 1. 23 1. 20 1. 17 1. 14 1. 11 Ionic radius of R-site (A) 1. 08

Orbital pattern dependent optical matrix element Large R-ion Small R-ion Electric dipole transition probability Orbital rotation empty occupied eg 2 eg 1 Jahn-Teller distortion and Gd. Fe. O 3 type distortion can suppress the electron hopping in the ab-plane. Orbital Mixing Oct 28 th, KIAS workshop

Rotation of orbital due to the buckling of Mn. O 6 octahedra Electric dipole transition probability cf. Goodenough and Kanamori rule Oct 28 th, KIAS workshop

R-ion dependence of the integrated spectral weight 10 deg. Bond angle of <Mn-O-Mn> (deg. ) 155. 2 La 151. 1 150. 0 Pr Nd 146. 5 145. 3 Gd Tb 1. 0 “Orbital rotation” cannot alone explain the drastic change. S (a. u. ) W 0. 8 0. 6 (exp. ) 0. 4 SW 0. 2 S W ( f) 0. 0 1. 20 1. 16 R-ion radius (A) Oct 28 th, KIAS workshop 1. 12 1. 08

Orbital mixing due to the Jahn-Teller distortion z x Oct 28 th, KIAS workshop

Spectral weight change due to the bond-angle and orbital mixing angle Rotation of needle-like orbital controls the charge motion Oct 28 th, KIAS workshop

Spectral weight change due to the bond-angle and orbital mixing angle Oct 28 th, KIAS workshop

Spectral weight change due to the bond-angle and orbital mixing angle La. Mn. O 3 Tb. Mn. O 3 Oct 28 th, KIAS workshop

R-ion dependence of the integrated spectral weight 10 deg. Bond angle of <Mn-O-Mn> (deg. ) 155. 2 La 151. 1 150. 0 Pr Nd 146. 5 145. 3 Gd Tb 1. 0 “Orbital rotation” and “Orbital mixing” can explain the drastic change. S (a. u. ) W 0. 8 0. 6 (exp. ) 0. 4 SW 0. 2 S 0. 0 W ( f) S W ( f, q) 1. 20 1. 16 R-ion radius (A) Oct 28 th, KIAS workshop 1. 12 1. 08

Spectral weight change vs. magnetic phase diagram Bond angle of <Mn-O-Mn> (deg. ) SW (a. u. ) 1. 0 151. 1 150. 0 146. 5 145. 3 SW (measured) 150 TN (A-type) La Pr 0. 8 TN (E-type) TIC (sine-wave) 100 Nd 0. 6 Sm 0. 4 Gd A-AF Tb Ho 50 0. 2 0. 0 ? 1. 20 1. 15 1. 10 ionic radius of R-site ( Å ) Orthorhombic Oct 28 th, KIAS workshop TN (K) 155. 2 E-AF 0 1. 05 The magnetic phase diagram is reproduced from the work by Kimura et al. PRB (2003) Hexagonal

Summary 1. Based on the orbitally degenerate Hubbard model, we could explain optical spectra of (La, Y)MO 3 (M = 3 d transition metal). 2. We showed that features of 2 e. V peak of La. Mn. O 3 can be explained within the orbitally degenerate Hubbard model. 3. We proposed that the orbital correlations could affect R-ion size dependent spectral weight change and magnetic properties of RMn. O 3. 4. Optical spectroscopy is a good experimental technique to probe the orbital correlation in strongly correlated electron systems. Oct 28 th, KIAS workshop