electronic structure of layered t electron systems (thin...

Electronic structure of layered t2g electron systems (thin films) studied by x-ray photoemission

and x-ray absorption spectroscopy

Takashi MizokawaDepartment of Complexity Science and Engineering

Orbital ordering in 1D, 2D, and 3D t2g electron systems

Orbital degrees of freedom

d orbitals under Oh or Td crystal fieldeg 3z2-r2, x2-y2 t2g yz, zx, xy

partially filled eg or t2g orbitalsorbital-dependent superexchange interaction

=> orbital ordering (Kugel-Khomskii)=> orbital-driven Peierls state

lattice distortion lifts the orbital degeneracy Jahn-Teller distortiondimer formation

Orbital-dependent superexchange interaction

H = -t ∑ ci,mσ†ci+1,mσ + u ∑ ni,m↑ni,m↓ + u’∑ ni,m↑ni,m’↓ + (u’-j) ∑ ni,mσ ni,m’ σ

E aa↑↑= 0 E ab↑↑= -2t2/(u’-j)

E aa↑↓= -2t2/u E ab↑↓= - 2t2/u’

ab

K. Kugel and D. I. Khomskii: Zh. Eksp. Teor. Fiz. 15, (1973) 1429 [Sov. Phys. JETP. 37, (1973) 725].

ba

high-spin d4 configuration (eg system)

elongatedoctahedronatom octahedron

3z2-r2, x2-y23z2-r2, x2-y2 3z2-r2

yz, zx, xy x2-y2

xy

yz, zx, xy yz, zx

Jahn-Teller effect for eg system (ExE)

H = -Aq(σx sinθ+σz cosθ) + Mω2q2/2 + A3 q3 cos 3θ

z

x

y

Q2Q3

In many cases, it is elongated. => A3 <0d-type or a-type ?

d1 configuration (t2g system)

elongatedoctahedronatom octahedron

3z2-r2, x2-y23z2-r2, x2-y2 3z2-r2

yz, zx, xy x2-y2

xy

yz, zx, xy yz, zx

ExT2 pseudo Jahn-Teller effect

p-d model for transition-metal oxide

pddp HHHH ++=..,

,,,,,

,,, cHppVppH lk

llklk

ppllklk

lklk

pkp ++= ′

′>

+′

+ ∑∑ σσ

σσσ

σε

↓+

↓′↑′′≠

+↑

↓′+

↓↑′′≠

+↑

′+

′′≠

+

↓′+

↓′↑′≠

+↑

↓+

↓↑+

↑

∑

∑

∑

∑

∑

+

′+

−′+

′+

+

mimimimmi

mi

mimimimmi

mi

mimimimmi

mi

mimimimmi

mi

mimimimi

mi

ddddj

ddddj

ddddju

ddddu

ddddu

αααα

α

αααα

α

σασασασα

σα

ααασαα

αααα

α

,,

,,

,,,

,,,

,,

)(

..,,,,

cHpdVH klmlk

mkpd

mklpd += ∑ +σ

σασαα

σασα

σαε mimi

midd ddH ∑ +=,,,

p-d charge transfer energy∆ = ed – ep + nU

d-d Coulomb interactionU = u – 20j/9

For Co3+

∆ = εd ‐ εp+ 6U = 2.0 eVU = u ‐20/9j = 7.5 eV(pdσ) = ‐2.2 eV, (pdπ) = 1.0 eV,(ppσ) = 1.0 eV, (ppπ) = ‐0.25 eV

corner-sharing case

Layered Perovskite (2D)Ca2RuO4 Ru4+ 3d4 TMI = 350 K, TN = 110 K AFISr2VO4 V4+ 3d1 Matsuno-Okimoto-Kawasaki-Tokura, APL 2003.

Perovskite (3D)YTiO3 Ti3+ 3d1 TC = 30 K FILaVO3 V3+ 3d2 TN = 140 K C-AFIYVO3 V3+ 3d2 TN = 77 K G-AFI, 77 K-116 K C-AFI(LaMnO3 Mn3+ 3d4 TN = 145 K A-AFI)(BiMnO3 Mn3+ 3d4 TC = 103 K FI)(YNiO3 Ni3+ 3d7 TMI = 582 K,TN = 210 K AFI)

Perovskite structure(a)

c

ab

c

ab

(b)

ヤン・テラー歪み

GdFeO3 型歪み

a 型 d 型

サイト１サイト２

サイト３サイト４

GdFeO3-type distortion

Jahn-Teller-type distortion

a-type d-type

Site 3

Site 1 Site 2

Site 4

LaMnO3 (d-type JT) and BiMnO3 (no JT)

LaMnO3BiMnO3

LaMnO3, YVO3 (d-type JT) and LaVO3 (a-type JT)

LaMnO3

Tilting Angle (degree)0 5 10 15

Rel

ativ

e E

nerg

y E

d -E

a (m

eV)

-40

-30

-20

-10

0

10

without JT and A-site shiftwith JT, without A-site shiftwith JT and A-site shift

LaVO3 and YVO3

Tilting Angle (degree)

0 5 10 15

Rel

ativ

e E

nerg

y E

d-E

a (m

eV)

-20

-15

-10

-5

0

5

10

"d-type"G-type AFM

C-type AFM"a-type"

GdFeO3-type distortion => Jahn-Teller effect => orbital ordering => spin (superexchange)

Ener

gy

3

A-O

GdFeO -type distortion

d-typecovalency

LaVO YVO YTiO 333

Ener

gy

3

A-O

GdFeO -type distortion

a-type

d-typesuper-exchange

covalency

LaMnO3

a-type JT distortion

super-exchange

LaMnO3

(a)

c

ab

c

ab

(b)


GdFeO3 型歪み

a 型 d 型





a-type d-type

3x2-r2

3x2-r2 3y2-r2

3y2-r2

LaVO3

(a)

c

ab

c

ab

(b)


GdFeO3 型歪み

a 型 d 型





a-type d-type

xy, yz

xy, zx xy, yz

xy, zx

YVO3

(a)

c

ab

c

ab

(b)


GdFeO3 型歪み

a 型 d 型





a-type d-type

xy, zx

xy, zx xy, yz

xy, yz

Layered perovskite

PM

PI

AFI

RuO

x

yz

Tem

per

ature

(K

)

x in Ca2-xSrxRuO4

0.20.1

TMI

TN

apical

in-plane

370

300

77

elongated

compressed

0.0

Phase diagram of Ca2-xSrxRuO4 (Nakatsuji and Maeno, 2000)

O 1s XAS across the MI transitionA: apical oxygen B: in-plane oxygen

530529528527Photon Energy (eV)

210K

200K

190K

180K

170K

160K

150K

Ca1.91Sr0.09RuO4

A

B cooling

O 1s XAS normal


120K

140K

150K

160K

170K

180K

200K

210K

190K

Ca1.91Sr0.09RuO4

A

B

heating

O 1s XAS normal

Angle dependence of the O 1s XAS spectra


Ca1.91Sr0.09RuO4 θ=0

o

θ=15o

θ=30o

77KAFI

300KPM

O 1s XAS

A

B


Ca2RuO4

370KPM

77KAFI

300KPI

O 1s XAS θ=0

o

θ=15o

θ=30o

A

B

Angle dependence and the orbital symmetry

x

yz

4dyz

Px

Py

Pz

Pz

Px

Py

nyz/zxcos2θ

nxycos2θnyz/zxsin2θ

Iapical = nyz/zxcos2θ

Iin-plane = nxycos2θ + nyz/zxsin2θ

4dxy4dzx

Iapical/Iin-plane = nyz/zx/(nxy + nyz/zxtan2θ)

nxy + nyz/zx = 2

Angle dependence of the apical/in-plane ratio

4

3

2

1

0

Rel

ativ

e In

tens

ity (a

pica

l/in-

plan

e)

3020100

Angle to normal θ

Ca2RuO4 77K AFI Ca2RuO4 300K PI Ca2RuO4 370K PM Ca1.91Sr0.09RuO4 77K AFI Ca1.91Sr0.09RuO4 300K PM

Orbital population of the unoccupied t2g orbitals

1.250.75Ca1.91Sr0.09RuO4 77 K (AFI)

0.81.2Ca1.91Sr0.09RuO4 300 K (PM)

1.40.6Ca2RuO4 77 K (AFI)

1.10.9Ca2RuO4 300 K (PI)

0.81.2Ca2RuO4 370 K (PM)

nyz/zxnxy

Jahn-Teller => orbital ordering => spin ordering

Ca2RuO4 JT compressed xy orbital

Sr2VO4 JT compressed? xy orbital?JT elongated ? yz/zx orbital?

YTiO3 d-type JT elongated FI

LaVO3 a-type JT elongated C-AFI

YVO3 d-type JT elongated G-AFI

LaMnO3 d-type JT elongated A-AFI

BiMnO3 no JT FI (pure superexchange)

edge-sharing case

Pyroxene (1D)NaTiSi2O6: Ti3+ 3d1 TNM=210 K MI-NMILiTiSi2O6: Ti3+ 3d1 TNM=230 K MI-NMI

M. Isobe et al., JPSJ 71, 1423 (2002).

triangular lattice (2D) Ca3Co4O9 Co4+,Co3+ 3d5,3d6

NaTiO2 Ti3+ 3d1

(LiMnO2 Mn3+ 3d4)

spinel lattice (3D)MgTi2O4 Ti3+ 3d1 TMI = 260 K M-NMI

M. Isobe et al., JPSJ 71, 1848 (2002).M. Schmidt et al., PRL 92, 056402 (2004).

LiV2O4 V4+,V3+ 3d1,3d2 MI under pressureCuIr2S4 Ir4+,Ir3+ 3d5,3d6 TMI = 226 K M-NMI

Pyrochlore (3D)Lu2V2O7 V4+ 3d1 FI

pyroxine (1D) NaTiSi2O6 xy-xy dimerization

orbital-driven Peierls state?zig-zag lattice is important

Shirakawa, Ohta, and Mizokawa 2003

triangular lattice (2D) layered Co oxides

NaCo2O4 Ca3Co4O9 Bi2Sr2Co2O9

x ~ 0.5 x ~ 0.67?, 0.33?, 0.15? x ~ 0.4Bad metalT. Yamamoto et al., 2000

Good metalI. Terasaki et al., 1997.

Insulating at low temperatureY. Miyazaki et al., 2002

O 1s XAS of (Bi,Pb)-Sr-Co-OIn

tens

ity

531530529528

Photon Energy (eV)

Bi-Sr-Co-O normal Bi-Sr-Co-O off-normal (Bi,Pb)-Sr-Co-O normal (Bi,Pb)-Sr-Co-O off-normal

O 1s XAS

a1g

eg

eg

eg'

a1gt2g

eg

trigonal field

CoO2 layer

normal

off-normal60o

Inte

nsity


Ca3Co4O9 Co 2p XAS

2p3/2

2p1/2

0 deg. 30 deg. 60 deg.

Inte

nsity


Ca3Co4O9O 1s XAS


αβ

γ

CoO2 layerlow-spin Co3+

low-spin Co4+

a1g hole

CoO layer low-spin Co3+

CoO2 layerlow-spin Co3+

low-spin Co4+

a1g holeIn

tens

ity


NaCo2O4O 1s XAS


α

γ

βIn

tens

ity


NaCo2O4 Co 2p XAS


2p1/2

2p3/2

φa1g = (φyz + φzx + φxy)

φyz = ( φ321 + φ32-1) = yz/r2 R32(r)

φzx = ( φ321 - φ32-1) = zx/r2 R32(r)

φxy = ( φ322 - φ32-2) = xy/r2 R32(r)

φ3z2-r2 = φ320= (3z2- r2)/r2 R32(r)

φx2-y2 = ( φ322 + φ32-2) = (x2- y2)/r2 R32(r)

2i

2i

−2

1−

21

π415

π415

π415

π1615

π1615

31

Charge ordering in the triangular lattice

Co3+ Co4+ S=1/2 Co3+ : Co4+ = 2 : 1Ferromagnetic

Co3+ : Co4+ = 1 : 2antiferromagnetic

Hole concentration x :Ca349 > Na124 > Bi2229x=0.6, 0.5, 0.4

dimer formation => orbital ordering => singlet formation Jahn-Teller distortion => orbital ordering => spin ordering

NaTiSi2O6 xy-xy dimer NMI

NaTiO2 xy-xy dimer NMI

Ca3Co4O9 xy+yz+zx ordering AFI

CuIr2S4 xy-xy dimer NMI

MgTi2O4 yz-yz and zx-zx dimer NMI

Lu2V2O7 yz/zx/yz/zx ordering FI

LiV2O4 xy,yz/xy,zx ordering? AFI

electronic structure of layered t electron systems (thin...

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