Tae Won Noh

Research Center for Oxide Electronics & School of physics, Seoul National UniversitySeoul, KoreaThe roles of orbital in the optical and magnetic properties of RMnO3 (R = rare earth ions)

CollaboratorsS. J. MoonJaejun YuP. Murugavel (ReCOE, SNU)S. Parashar (ReCOE, SNU)J. H. Jung (Inha Univ.)AcknowledgementsG. Khaliullin (Max Plank Institute)K. Ahn (Argonne NL)J. Goodenough (U. Texas)P. Littlewood (Cambridge U)Valuable discussion withM. W. Kim&P. B. Allen (SUNY, Stony Brook)

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. Summary1. Motivation : long-standing puzzles in (La,Y)MO3

Single-band Hubbard model for correlated electrons Kinetic energy correlation

Multi-peak structures in () for numerous oxidesCorrelation peaks : broad and/or multiple peak structures Cannot be simply explained in terms of the single band picture

Large reduction of the d-d transition energies Disappearance of the d-d transition for LaCrO3Abnormal energy parameter for LaMO3How to understand thesesomewhat anomalous behaviorsin LaMO3?Charge transfer and correlation peaks in LaMO3Arima and Tokura, JPSJ (1995).

OutlineMotivation : 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. Summary2. Orbitally degenerate Hubbard model * Multiple peak structure in LaMO3

Optical anisotropy due to orbital ordering Polarized microscopy

Large optical anisotropy due to the orbital ordering below TCO

Optical properties will be strongly dependent on the orbital degrees of freedom.Tokura et al., SCIENCE 288 462 (2000)La1.5Sr0.5MnO4 : CE-type OO

Orbital degeneracy: d-electron in a cubic crystal fieldDegeneracy of eg/t2g orbitals is common in cubic perovskite structure.

The orbitally degenerate Hubbard model (ODHM)

Spin/Orbital configurations for t2g1 system

Orbital selection rule for interatomic d-d transitions

U 3JHU 2JH Ut2g2 t2g2 t2g2 multiplet final states and energy costs Orbital multiplicity effects based on the simple atomic pictureU 3JHU U 2JHForbiddenSchematically,

t2g2 Orbital multiplicity effect on the t2g2-configuration

Orbital multiplicity effects on the inter-site d-d transitions U 3JHU + 2JHU JHForbiddenSchematically,

Understanding of d-d transitions under orbital multiplicityT. Arima and Y. Tokura, JPSJ (1995).

(LaTiO3) Orbital multiplicity effects on the inter-site d-d transitions IIFor more information, see

J. S. Lee, M. W. Kim, and T. W. Noh, New Journal of Physics 7, 147 (2005)

Understanding of d-d transitions under orbital multiplicityArima and Tokura, JPSJ (1995).The broad (multiple) correlation peaks can be explained .

Outline1. Motivation : long-standing puzzles in (La,Y)MO3

2. Orbitally degenerate Hubbard model * Multiple peak structure in LaMO3

4. Summary3. Applications of ODHM to the 2 eV peak of RMnO3 * 2 eV peak in LaMnO3* Probing Oribital/Spin correlations in RMnO3

Some explanations on 2.0 eV peak in LaMnO3Arima and Tokura, JPSJ (1995).LaMO3Charge transfer peak ?Arima and Tokura, PRB (1995)Tobe et al., PRB (2001)3) Intramolecular peak due to Frank-Condon process ?Allen and Perebeinos, PRL (1999)Krger et al., PRL (2004)2) Band picture: inter-atomic peakcoupled with the local spin alignment?Ahn and Millis PRB (2000)

A explanation of the 2.0 eV peak based on the ODHMArima and Tokura, JPSJ (1995).LaMO3

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

Merits of ODHM explanation for 2 eV peak of LaMnO31. Ground state spin/orbital configuration3. Temperature dependence of the spectra2. Anisotropic optical conductivity4. Rare earth doping effects on optical spectra

ODHM explanation for 2 eV peak of LaMnO31. Ground statelowest energycabcabA-type AFM spin orderC-type orbital orderschematic configurations for possible transitions

ODHM explanation for 2 eV peak of LaMnO32. Anisotropic optical conductivity

ODHM explanation for 2 eV peak of LaMnO3Tobe et al. Phys. Rev. B (2001)Spectral weight show distinct suppression as crossing the antiferromagnetic ordering T.3. Temperature dependence

4. Rare earth substitution effectsM. W. Kim et al., PRL (submitted)Kimura et al. PRB (2003)ODHM explanation for 2 eV peak of LaMnO3

R-ion dependence of the integrated spectral weightKimura et al. Phys. Rev. B (2003)

Orbital pattern dependent optical matrix element

Rotation of orbital due to the buckling of MnO6 octahedracf. Goodenough and Kanamori rule

R-ion dependence of the integrated spectral weightBond angle of (deg.)10 deg.Orbital rotation cannot alone explain the drastic change.1.201.161.121.080.00.20.40.60.81.0146.5145.3150.0151.1155.2LaR-ion radius (A) SW (a.u.) SW (f) SW (exp.)TbGdNdPr

Orbital mixing due to the Jahn-Teller distortionzx

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

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

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

R-ion dependence of the integrated spectral weightBond angle of (deg.)10 deg. Orbital rotation and Orbital mixing can explain the drastic change.1.201.161.121.080.00.20.40.60.81.0146.5145.3150.0151.1155.2LaR-ion radius (A) SW (a.u.) SW (f) SW (exp.) SW (f,q)TbGdNdPr

Spectral weight change vs. magnetic phase diagramThe magnetic phase diagram is reproduced from the work by Kimura et al. PRB (2003)?E-AF1.101.151.20050100150ionic radius of R-site ( )TN (K)LaPrNdTbSmTN (A-type)Gd155.2151.1150.0146.5145.3Bond angle of (deg.)SW (a.u.)TN (E-type)0.00.20.40.60.81.0 SW (measured)A-AF1.05HoOrthorhombicHexagonalTIC (sine-wave)

Summary2. 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 dependent spectral weight change and magnetic properties of RMnO3.1. Based on the orbitally degenerate Hubbard model, we could explain optical spectra of (La,Y)MO3 (M = 3d transition metal). 4. Optical spectroscopy is a good experimental technique to probe the orbital correlation in strongly correlated electron systems.