Role of the Octahedra Rotation on the
Electronic Structures of 4d Transition
Metal Oxides
Changyoung Kim
Dept. Physics, Yonsei University
B. J. Kim1, J. Yu1, S. J. Oh1, H. Koh2, I. Nagai3, S. I. Ikeda3,
Eun Jung Ko4, Hyung Joon Choi4
1School
of Physics and Center for Strongly Correlated Materials Research,
Seoul National University, Seoul, Korea
2Advanced Light Source, Lawrence Berkeley National Laboratory,
Berkeley, California 94720, USA
3National Institute of Advanced Industrial Science and Technology,
Tsukuba, Ibaraki 305-8568, Japan
4Department of Physics, Yonsei University
Outline
• Background - (Sr,Ca)2RuO4
• ARPES data from Sr2RhO4 – Missing dxy Fermi Surface
• Comparison with Band Calculation
• Implication to (Sr,Ca)2RuO4
• (Sr,Ba)2RhO4 - Band Structure Manipulation
• Summary
Sr2RuO4: spin-triplet superconductor
Layered perovskite superconductor like La2CuO4
CuO2-plane
RuO2-plane
Y. Maeno et al., Nature 372, 532 (1994)
LaO
SrO
CuO2
RuO2
LaO
SrO
Phase diagram of Ca2-xSrxRuO4
S. Nakatsuji et al, Phys. Rev. Lett. 84, 2666 (2000).
Mott transition
Orbital Selective Mott Transition (OSMT)?
Structural distortion of Ca2-xSrxRuO4
Various ground states are realized by structural distortions.
4d transition-metal oxide
•Large spatial extent of 4d orbitals
→large bandwidth, large 10Dq.
→tends to be weakly-correlated.
•Low-spin configuration is expected.
x2-y2
3z2-r2
Ca2-xSrxRuO4
Sr2RhO4
xy
yz, zx
Rotation of Octahedra
Rotation brings about:
• Doubling of the unit cell
• Decrease of M-O-M bond angle
which cause:
• Band folding
• Bandwidth narrowing
Unit cell doubling and band folding
−π/2a
−π/2a
1D
a
2a
−π/a
0
π/a
2D
(π,π)
Γ
Band width narrowing
Octahedra rotation
t
Metal, small U/W
Decrease of M-O-M bond angle
Decrease in hopping energy t
t
Increase in U/t
Insulator, large U/W
Angle-resolved photoemission spectroscopy (ARPES)
z
hν
Kinetic Energy
Final State
Direct Mapping of
“Band” (ARPES)
ϑ
hν
y
Energy
Ef
ϕ
x
From momentum/energy conservation rules:
k pe = − k N −1
BE
Initial State
Momentum
E
hv − E pe = E N −1 − E N
ky
kx
ARPES data on Ca-doped SRO
ARPES is a powerful tool to study the electronic structure.
S.-C. Wang et al. PRL 93,177007 (2004)
Sr2RuO4
Ca1.5Sr0.5RuO4
However, the disorder effects introduced by doping have discomforting
effects in ARPES: the signals are generally broad and weak.
Sr2RhO4
• Share same crystal structure with Sr2RuO4.
• 5 electrons in 4d orbitals.
• Rotation angle ~ 10º.
• No supeconductivity.
Sr2RhO4 presents an opportunity to study
the effect of rotation without disorder.
Electrical resistivity
・Large anisotropy
Similar to ρ(T) in Sr2RuO4
T (K)
T (K)
(b) Sr RhO
2
4.00
10
14 0
14
17
20
22 25
ab
ρ
20
12
11
0 100 200 300 400 500 600 700
10
9
7
0
100 200 300 400 500 600 700
2
2
T 2 (K2)
0.2
ρ
ρ
c
400
0.1
ρ
200
0
0.3
T (K )
600
ab
0
50
100
150
T (K)
200
250
300
2
ρ = 8.6 µΩcm
0
c
25
15
0.4
ρ ab(T ) A0 = 6.26×10-3 µΩcm/K2
ab
26
8
800
Fitting with ρ = ρ 0+AT
13
c
1000
17 20 22 25 26
0.5
ρ ( Ω cm )
ρ (m Ωcm)
1200
10 14
(µΩcm)
30 0
( µΩ cm )
・T 2- dependence
Sr2RhO4
1400
ab
ρ c/ ρ ab (3K) = 2400
ρ c(T )
ρ 0 = 20.1 mΩcm
Ac = 10.55 mΩcm/K2
・Below ~250 K, ρ c decreases with
lowering temperature.
because of suppression of thermal
scattering between quasiparticles
and phonon ?
・No superconducting transition was
observed down to 36 mK.
Sr2RhO4 is a two-dimensional Fermi liquid.
Expected FS of Sr2RhO4
By doping one electron: (rigid-band model)
FS of Sr2RuO4
Sr2RuO4
α
Sr2RhO4
β
A. Damascelli et al. Phys. Rev. Lett. 85, 5194-5197 (2000)
γ
Hase et al. J. of solid state chemistry 123,186 (1996)
C Bergemann et al, PRL 84, 2662 (2000)
We expect basically similar FS topology in Sr2RhO4
ARPES measurements
High energy ARPES
• ALS BL 7
• Analyzer : Scienta 100
• Temperature : 40K
• Total Energy Resolution : 40 meV
• Angular Resolution : 0.25o
• Photon energy : 85 eV
• Sample cleaved in situ
low energy ARPES
• SSRL BL
• Analyzer : Scienta 2002
• Temperature : 20K
• Total Energy Resolution : 40 meV
• Angular Resolution : 0.25o
• Photon energy : 20 eV
• Sample cleaved in situ
FS of Sr2RhO4 (ALS ARPES)
M
X
X
Fermi Surface Mapping
Γ
Γ
Γ
M
1.2
0.8
0.4
0.0
1.2
0.8
0.4
0.0
1.2
0.8
0.4
0.0
M
X
Binding Energy (eV)
Missing xy-band(γ)
FS in Sr2RhO4!
B.J. Kim et al., to be published in PRL
LDA calculation (I4/mmm)
WITHOUT distortion (rotation of octahedra)
a hole pocket formed by
xz/yz orbital band. (α)
an electron pocket formed by x2-y2
orbital band. (δ)
two electron pockets formed by
xy (γ) and yz,zx band (β)
Occupation :
α
β
γ
δ
94.8%
66.8%
72.5%
7.1%
Effects of the rotational distortion
undistorted
undistorted
+band folding
distorted
LDA calculation shows disappearance of xy-band (γ) FS.
exp and calc.
F. Baumberger et al., PRL 96, 246402 (2006)
Effects of the rotational distortion
Effects of the rotational distortion
FS of Sr2RhO4 (ARPES)
Γ
Γ
X
X
Observation of xy-band sunken under Ef
Effects of the rotational distortion
Complete filling of the xy-band
→ transfer of electrons from the yz/zx band to xy band
xy
yz, zx
Electron occupation
α
β
γ
δ
94.8%
66.8%
72.5%
7.1%
α
β
γ
δ
96.2%
51.5%
100%
0%
Effects of the rotational distortion
Hybridization between the xy and x2-y2 band
→ Increase in the orbital occupation of the x2-y2 state
x2-y2
3z2-r2
Strongly hybridized
xy
yz, zx
Destabilizes the elongation of the octahedra along c-axis
Structural instability
As temperature is lowered:
a-axis
contracts
by 0.35%
c-axis
expands
by 0.08%
rotation angle increases
HOWEVER,
Rh-O(1)
contracts
only by
0.2%
O(2)
O(1)
Rh-O(2)
contracts
by 0.26%
Summary – Sr2RhO4
• Rotation of the octahedra leads to hybridization of xy and x2-y2
bands.
• Hybridization of xy and x2-y2 bands results in:
(1) transfer of electrons from yz/zx to xy band and
(2) disappearance of the xy Fermi surface.
• eg states play vital role in determining electronic structures near Ef,
and therefore should be included in the theoretical models that
deals with 4d TMOs.
Implications to CSRO system
•Orbital-selective Mott-transition at x=0.5?
•Magnetic ground state and origin of localized spin.
→depends critically on nxy,nyz/zx ,and the crystal structure.
Band structure (Sr end)
Same physics apply here!
Experimental evidences
S.-C. Wang et al. PRL 93,177007 (2004)
γ Sheet changes from electron-like to hole-like
Orbital-selective Mott transition?
Anisimov et al. Eur. Phys. J. B 25,191 (2002)
Region III (2>x>0.5)
Region II (0.5>x>0.2)
Region I (0.2>x>0)
yz, zx
2
xy
2
xy
yz, zx
1
3
xy
yz, zx
Contradicts with our finding!
4/3
8/3
Structural phase transition (x=0.2)
Flattening of octahedra at x=0.2
3z2-r2
x2-y2
x2-y2
3z2-r2
yz, zx
xy
yz, zx
xy
Unstable!
Strong hybridization with eg states drives the structural phase
transition and thus the Mott transition.
Summary
• Rotation of the octahedra leads to hybridization of xy and x2-y2
bands also in CSRO.
• Hybridization of xy and x2-y2 bands results in dramatic change in
the Fermi surface topology.
• eg states play vital role in determining electronic structures near Ef,
and therefore should be included in the theoretical models that
deals with 4d TMOs.