Role of the Octahedra Rotation on the Electronic Structures of 4d Transition

Metal Oxides

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, Korea2Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA3National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan4Department of Physics, Yonsei University

Changyoung KimDept. 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

Y. Maeno et al., Nature 372, 532 (1994)

CuO2

LaO

LaORuO2

SrO

SrO

Layered perovskite superconductor like La2CuO4CuO2-plane RuO2-plane

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

xy

yz, zx

Ca2-xSrxRuO4

Sr2RhO4

Rotation of Octahedra

• Doubling of the unit cell

• Decrease of M-O-M bond angle

Rotation brings about:

which cause:

• Band folding

• Bandwidth narrowing

Unit cell doubling and band folding

a

−π/a π/a0

2a

−π/2a −π/2a1D

2D

Γ

(π,π)

Band width narrowing

Decrease of M-O-M bond angle

Octahedra rotation

Decrease in hopping energy t

Increase in U/t

Metal, small U/W

Insulator, large U/W

t

t

BE

Kin

etic

Ene

rgy

Initial StateMomentum

Ener

gy

Ef

Direct Mapping of“Band” (ARPES)

hν

Final State

Angle-resolved photoemission spectroscopy (ARPES)

y

x

z

ϑ

ϕ

hν

1−−= Npe kk

NNpe EEEhv −=− −1

From momentum/energy conservation rules:

E

kx

ky

ARPES data on Ca-doped SRO

ARPES is a powerful tool to study the electronic structure.

However, the disorder effects introduced by doping have discomforting effects in ARPES: the signals are generally broad and weak.

S.-C. Wang et al. PRL 93,177007 (2004)

Sr2RuO4 Ca1.5Sr0.5RuO4

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.

ρ c/ ρ ab (3K) = 2400

Fitting with ρ = ρ 0+AT 2

ρ 0 = 8.6 µΩcmAab = 6.26×10-3 µΩcm/K2

ρ 0 = 20.1 mΩcmAc = 10.55 mΩcm/K2

Sr2RhO4

Electrical resistivity

・Large anisotropy

・T 2- dependence

・Below ~250 K, ρ c decreases with lowering temperature.

ρ ab(T )

ρ c(T )

because of suppression of thermal scattering between quasiparticlesand phonon ?

・No superconducting transition was observed down to 36 mK.

Similar to ρ(T) in Sr2RuO4

0

200

400

600

800

1000

1200

1400

0

0.1

0.2

0.3

0.4

0.5

ρab

ρc

ρ c (Ω

cm )

ρ ab (

µΩcm

)

Sr2RhO

4.00 (b)

7

8

9

10

11

12

13

14

0 100 200 300 400 500 600 700

ρ ab ( µ

Ωcm

)

T 2 (K2)

14 22 25 260T (K)

201710

15

20

25

30

0 100 200 300 400 500 600 700

ρ c (m

Ωcm

)

T 2 (K2)

10 14 17 20 22 25 260T (K)

0 50 100 150 200 250 300

T (K)

Sr2RhO4 is a two-dimensional Fermi liquid.

Expected FS of Sr2RhO4

FS of Sr2RuO4

A. Damascelli et al. Phys. Rev. Lett. 85, 5194-5197 (2000)

α

γ

β

By doping one electron: (rigid-band model)

We expect basically similar FS topology in Sr2RhO4

Hase et al. J. of solid state chemistry 123,186 (1996)

Sr2RuO4 Sr2RhO4

C Bergemann et al, PRL 84, 2662 (2000)

ARPES measurements

• 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

• SSRL BL

• Analyzer : Scienta 2002

• Temperature : 20K

• Total Energy Resolution : 40 meV

• Angular Resolution : 0.25o

• Photon energy : 20 eV

• Sample cleaved in situ

High energy ARPES

low energy ARPES

FS of Sr2RhO4 (ALS ARPES)

Missing xy-band(γ)FS in Sr2RhO4!

1.2 0.8 0.4 0.0

M

X

1.2 0.8 0.4 0.0

Γ

X

1.2 0.8 0.4 0.0

Γ

M

Binding Energy (eV)

Γ

X

M

Fermi Surface Mapping

B.J. Kim et al., to be published in PRL

LDA calculation (I4/mmm)

a hole pocket formed by xz/yz orbital band. (α)

two electron pockets formed by xy (γ) and yz,zx band (β)

an electron pocket formed by x2-y2

orbital band. (δ)

WITHOUT distortion (rotation of octahedra)

α 94.8%β 66.8%γ 72.5%δ 7.1%

Occupation :

Effects of the rotational distortion

undistorted undistorted+band folding

distorted exp and calc.

LDA calculation shows disappearance of xy-band (γ) FS.

F. Baumberger et al., PRL 96, 246402 (2006)

Effects of the rotational distortion

Effects of the rotational distortion

FS of Sr2RhO4 (ARPES)

Observation of xy-band sunken under Ef

Γ X

Γ

X

Effects of the rotational distortion

Complete filling of the xy-band → transfer of electrons from the yz/zx band to xy band

α 94.8%β 66.8%γ 72.5%δ 7.1%

α 96.2%β 51.5%γ 100%δ 0%

Electron occupation

xy

yz, zx

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

xy

yz, zx

Strongly hybridized

Destabilizes the elongation of the octahedra along c-axis

Structural instability

rotation angle increases

a-axis contracts by 0.35%

c-axis expands by 0.08%

As temperature is lowered:

HOWEVER, O(1)

O(2)Rh-O(2) contractsby 0.26%

Rh-O(1) contracts only by 0.2%

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

γ Sheet changes from electron-like to hole-like

S.-C. Wang et al. PRL 93,177007 (2004)

Orbital-selective Mott transition?

Region III (2>x>0.5)Region II (0.5>x>0.2)Region I (0.2>x>0)

xy

yz, zx xyyz, zx

xyyz, zx

Contradicts with our finding!

Anisimov et al. Eur. Phys. J. B 25,191 (2002)

2

2 3

1

8/3

4/3

Structural phase transition (x=0.2)

xy

yz, zx

Flattening of octahedra at x=0.2

xyyz, zx

x2-y2

3z2-r2 x2-y2

3z2-r2

Strong hybridization with eg states drives the structural phase transition and thus the Mott transition.

Unstable!

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.