Transcript 슬라이드 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
Oct 28th, KIAS workshop
Acknowledgements
Collaborators
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. Littlewood (Cambridge U)
P. B. Allen (SUNY, Stony Brook)
Oct 28th, KIAS workshop
Jaejun Yu
Outline
1. Motivation : long-standing puzzles in (La,Y)MO3
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
Oct 28th, KIAS workshop
Single-band Hubbard model for correlated electrons
Kinetic energy
correlation
Dynamic MFT
Mott insulator (U >> W)
U
op
()
O 2p
op
LHB
UHB
U
p–d transition

Georges et al., Rev. Mod. Phys. (1996)
Oct 28th, KIAS workshop
Multi-peak structures in () for numerous oxides
V2O3
Perovskite structure
4 eV
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 28th, KIAS workshop
Charge transfer and correlation peaks in LaMO3
Arima and Tokura, JPSJ (1995).
1.
2.
3.
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Large reduction
the d-d transition
How to of
understand
these energies
Disappearance
the d-d transition
for LaCrO3
somewhat of
anomalous
behaviors
Abnormal energy
in parameter
LaMO ? for LaMO3
3
Outline
1. Motivation : long-standing puzzles in (La,Y)MO3
2. Orbitally degenerate Hubbard model
* Multiple peak structure in LaMO3
3. Applications of ODHM to the 2 eV peak of RMnO3
* 2 eV peak in LaMnO3
* Probing Orbital/Spin correlations in RMnO3
4. Summary
Oct 28th, KIAS workshop
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.
Oct 28th, KIAS workshop
Orbital degeneracy: d-electron in a cubic crystal field
3z2-r2
eg
2
2
x -y
3d, 4d
10Dq
l=2
m=-2,-1,0,1,2
xy
yz
zx
t2g
10Dq : Electrostatic potential
due to ligand anions
“crystal field splitting”
Degeneracy of eg/t2g orbitals is common in cubic perovskite structure.
Oct 28th, KIAS workshop
The orbitally degenerate Hubbard model (ODHM)
U
U
U’(=U-2J)
U’-J (=U-3J)
if J’ = J
Oct 28th, KIAS workshop
from a simple atomic picture
Spin/Orbital configurations for t2g1 system
Ferro-orbital (FO)
Antiferro-orbital (AFO)
Oct 28th, KIAS workshop
FM/FO
AFM/FO
FM/AFO
AFM/AFO
Orbital selection rule for interatomic d-d transitions
1 ()  i  f | f | x | i |2
Hopping between the different orbitals
is not allowed.
Hopping between the same orbitals
is allowed.
Oct 28th, KIAS workshop
Orbital multiplicity effects based on the simple atomic picture
Example
LaTiO3 (t2g1)
multiplet final states and energy costs
Optical processes
t2g2
t2g1 + t2g1  t2g0 + t2g2
(LaTiO3)
Schematically,
U – 3JH
U
U – 3JH
Oct 28th, KIAS workshop
t2g2
t2g2
U –2JH
U
U –2JH
Forbidden
Orbital multiplicity effect on the t2g2-configuration
1A
1
t2g2
1T
3T
2
1
U+2JH [=A+10B+5C]
1E
U-JH [=A+B+2C]
U-3JH [=A-5B]
(U=A+4B+3C JH=3B+C)
Wavefunctions of t2g2-configuration
(3T1 M=1) = |dxy()dxy()|
(3T1 M=0) =1/2(|dxy()dxy()|-|dxy()dxy()|)
(3T1 M=-1) = |dxy()dxy()|
(1T2) =1/2(|dxy()dxy()|+|dxy()dxy()|)
(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()|)
Oct 28th, KIAS workshop
Energy values
U-3JH
U-JH
U+2JH
Orbital multiplicity effects on the inter-site d-d transitions
Example
LaTiO3 (t2g1)
Optical processes
t2g1 + t2g1  t2g0 + t2g2
(LaTiO3)
Schematically,
multiplet final states and energy costs
t2g2 (3T1)
t2g2 (1E, 1T2)
t2g2 (1A1)
U – 3JH
U –JH
U + 2JH
U + 2JH
U – 3JH
Oct 28th, KIAS workshop
U –JH
Forbidden
Understanding of d-d transitions under orbital multiplicity
3.20
1.28
RTi3+O3 (t2g1) :
(JH=0.64 eV)
U-3JH
1.92
U -JH
U +2JH
T. Arima and Y. Tokura, JPSJ (1995).
Oct 28th, KIAS workshop
Orbital multiplicity effects on the inter-site d-d transitions II
multiplet final states and energy costs
Optical processes
t2g1 + t2g1  t2g0 + t2g2
t2g2 (3T1)
t2g2 (1E, 1T2)
t2g2 (1A1)
U – 3JH
U –JH
U + 2JH
t2g3 (4A2)
t2g3 (2E, 2T1)
t2g3 (2T2)
(LaTiO3)
t2g2 + t2g2  t2g1 + t2g3
(LaVO3)
t2g3 + t2g3  t2g2 + t2g4
(LaCrO3)
U – 3JH
U
U + 2JH
t2g2 (3T1) / t2g4 (3T1)
U + 2JH
For more information, see
J. S. Lee, M. W. Kim, and T. W. Noh, New Journal of Physics 7, 147 (2005)
Oct 28th, KIAS workshop
Understanding of d-d transitions under orbital multiplicity
RCr3+O3 (t2g3) :
(JH=0.72 eV)
U+2JH
3.40
2.04
(t2g :
(JH=0.68 eV)
RV3+O3
1.36
2)
U -3JH
U
U +2JH
3.20
1.28
(t2g :
(JH=0.64 eV)
RTi3+O3
1.92
1)
U-3JH
U -JH
U +2JH
Arima and Tokura, JPSJ (1995).
The broad (multiple) correlation peaks can be explained .
Oct 28th, KIAS workshop
Outline
1. Motivation : long-standing puzzles in (La,Y)MO3
2. Orbitally degenerate Hubbard model
* Multiple peak structure in LaMO3
3. Applications of ODHM to the 2 eV peak of RMnO3
* 2 eV peak in LaMnO3
* Probing Oribital/Spin correlations in RMnO3
4. Summary
Oct 28th, KIAS workshop
Some explanations on 2.0 eV peak in LaMnO3
Arima and Tokura, JPSJ (1995).
LaMO3
1) Charge transfer peak ?
Arima and Tokura, PRB (1995)
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 28th, KIAS workshop
A explanation of the 2.0 eV peak based on the ODHM
LaMO3
(t2g3eg1) (t2g3eg1) (t2g3eg0) (t2g3eg2)
(LaMnO3)
t2g3eg2 (6A1)
~ U – 3JH
t2g3eg2 (4A1, 4E)
~ U +2JH
t2g3eg2 (4A2)
~ U + 4JH
5.60
4.0
M=Mn (t
(JH=0.80 eV)
3 1
2g eg )
Arima and Tokura, JPSJ (1995).
Oct 28th, KIAS workshop
1. 60
:
U -3JH
U +2JH
U+4JH
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)
Oct 28th, KIAS workshop
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
M. W. Kim et al. submitted to PRL
Oct 28th, KIAS workshop
ODHM explanation for 2 eV peak of LaMnO3
1. Ground state
schematic configurations for possible transitions
(a) FM/FO
c
(b) FM/AFO
b
a
Forbidden
A-type AFM spin order
6A
1
lowest energy
(c) AFM/FO
(d) AFM/AFO
c
b
4E
a

4A

C-type orbital order
Oct 28th, KIAS workshop
4A

4E

ODHM explanation for 2 eV peak of LaMnO3
2. Anisotropic optical conductivity
Tobe et al. PRB (2001)
c
b
a
Oct 28th, KIAS workshop
Kovaleva et al., PRL (2004)
-1
Absorption Coefficient (cm )
ODHM explanation for 2 eV peak of LaMnO3
3. Temperature dependence
Spectral weight show distinct
suppression as crossing the
antiferromagnetic ordering T.
M. W. Kim et al. NJP (2004)
5
2.0x10
10 K
50 K
100 K
125 K
150 K
200 K
250 K
300 K
5
1.5x10
5
1.0x10
4
5.0x10
0.0
0.5
1.0
Tobe et al. Phys. Rev. B (2001)
-1
Spectral Weight (eVcm)
LaMnO3
1.5
2.0
2.5
Photon Energy (eV)
3.0
3.5
5
2.65x10
5
2.60x10
5
2.55x10
5
2.50x10
0
Oct 28th, KIAS workshop
50
100 150 200 250
Temperature (K)
300
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)
1. The peak energy change is small.
2. The spectral weight change is large.
-1
 (cm )
2.0x10
5
1.5x10
5
1.0x10
5
5.0x10
4
LaMnO3
PrNdGdTb-
300 K
0.0
0
1
2
Photon Energy (eV)
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3
R-ion dependence of the integrated spectral weight
absorption coefficient
Oct 28th, 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 (eV)
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
2
I ( ) 


 f P i
2
  (  Ei  f )
f
Large R-ion
Small R-ion
Electric dipole transition probability
Wi f    f | P | i 
~   f | i 
2
2
Orbital rotation
eg 2
empty
occupied
 Mn i  sin
eg 2
eg 1

2
x 2  y 2  cos
eg 1

2
3z 2  r 2
Jahn-Teller distortion and
GdFeO3 type distortion can
suppress the electron hopping
in the ab-plane.
Orbital Mixing
Oct 28th, KIAS workshop
Rotation of orbital due to the buckling of MnO6 octahedra
Electric dipole transition probability
Wi f    f | P | i 
~   f | i 
2
2
cf. Goodenough and Kanamori rule
Oct 28th, 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.
(a.u.)
W
0.6
S
0.8
0.4
SW
0.2
S W ( f)
(exp.)
0.0
1.20
1.16
R-ion radius (A)
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1.12
1.08
Orbital mixing due to the Jahn-Teller distortion
z
x
i  cos
Oct 28th, KIAS workshop
i
2
3z  r
2
2
 sin
i
2
x2  y2
Spectral weight change due to the bond-angle and orbital mixing angle
Y
1.0
0.8
S (a.u)
0.6
X
0.4
0.2
0.0
105
40
30
θ
110
(d
eg
.)
10
115
S    f | i 
Oct 28th, KIAS workshop
g.)
20
0
–Φ
(π
de
/2 (
)
2
Rotation of needle-like
orbital controls the charge
motion
Spectral weight change due to the bond-angle and orbital mixing angle
y2
Y
1.0
0.8
x1
X
x2
0.6
S (a.u)
y1
0.4
0.2
0.0
105
40
30
θ
110
(d
20
eg
.)
10
115
S    f | i 
Oct 28th, KIAS workshop
2
0
–
(π
Φ
g.)
(de
2
/
)
Spectral weight change due to the bond-angle and orbital mixing angle
LaMnO3
y2
Y
1.0
x1
y1
0.8
X
x2
S (a.u)
0.6
0.4
0.2
0.0
105
40
30
θ
110
(d
eg
.)
10
115
S    f | i 
Oct 28th, KIAS workshop
2
g.)
20
0
–Φ
π
(
de
/2 (
)
TbMnO3
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.
(a.u.)
W
0.6
S
0.8
0.4
SW
0.2
S
0.0
(exp.)
W
( f)
S W ( f, )
1.20
1.16
R-ion radius (A)
Oct 28th, 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 28th, 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)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.
Oct 28th, KIAS workshop