Tae Won Noh

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
S. J. Moon
M. W. Kim
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
Kinetic energy
correlation
5
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
Orbital degeneracy d-electron in a cubic crystal
field
Degeneracy of eg/t2g orbitals is common in cubic
perovskite structure.
10
The orbitally degenerate Hubbard model (ODHM)
11
Spin/Orbital configurations for t2g1 system
12
Orbital selection rule for interatomic d-d
transitions
13
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
Orbital multiplicity effect on the
t2g2-configuration
t2g2
15
Orbital multiplicity effects on the inter-site
d-d transitions
U JH
U 2JH
Schematically,
Forbidden
U 3JH
16
Understanding of d-d transitions under orbital
multiplicity
T. Arima and Y. Tokura, JPSJ (1995).
17
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
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)
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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)
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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
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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
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ODHM explanation for 2 eV peak of LaMnO3
2. Anisotropic optical conductivity
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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)
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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)
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R-ion dependence of the integrated spectral weight
Kimura et al. Phys. Rev. B (2003)
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Orbital pattern dependent optical matrix element
30
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 ltMn-O-Mngt (deg.)
155.2
146.5
145.3
150.0
151.1
La
Nd
Pr
Tb
Gd
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
S
(
f
)
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
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 ltMn-O-Mngt (deg.)
146.5
145.3
150.0
151.1
155.2
La
Nd
Pr
Tb
Gd
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 ltMn-O-Mngt (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.)
100
TIC (sine-wave)
Nd
0.6
TN (K)
Sm
0.4
Gd
Ho
50
Tb
A-AF
The magnetic phase diagram is reproduced from the
work by Kimura et al. PRB (2003)
0.2
E-AF
?
0
0.0
1.10
1.15
1.20
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 dependent spectral 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.