Some interesting physics in transition metal oxides: charge ordering, orbital ordering and spin-charge separation

C. D. Hu

Department of physics

National Taiwan University

1. Introduction to double-exchange interaction (DE) 2. Introduction to charge ordering 3. Introduction to orbital ordering and orbital dynamics4. Interplay between double-exchange interaction, charge ordering, and orbital ordering

Double-exchange interaction

La1-xDxMnO3 D: divalent elements 3-d

Lan(1-x)Sr1+nxMnnO3n+1 n = # of layers. 2-d

Phase diagram

OOI

CMR: Temperature Dependence

The electrical resistance depends strongly on applied magnetic field. As the temperature is increased through the ferromagnetic Curie temperature Tc, the MR ration rises sharply.

Manganites Structure

LaMnO3 La+3 Mn+3 O-23

Mn+3 3d4 xy, yz, zx orbitals form t2g band, localized spin 3/2 x2-y2, 3z2-r2 form eg band, mobile spin 1/2 S=3/2+1/2 -------doping-----

La1-xCaxMnO3 La+3 Ca+2 Mn+4 O+23

Mn+3 3d4 xy, yz, zx orbitals form t2g band, localized spin 3/2 S=3/2.

atom

Crystal

field

eg

t2g

Jahn-Teller

distortion

x2-y2

3z2-r2

xy

xz, yz

Mn

YT

Mn OMn Mn OMn

10, eVtJJcctHji i

ijiDE

iσS

Zener, Anderson, Hasegawa: Double-Exchange interaction

Mean field picture

Recent Development (PRB 64,054406(2001))

From the point of view of the total spin on a site.

2 2(2 1)

total localized conduction

total

S S s

S

|S=3/2,m> and |1/2,+1/2> |S=2,m+1/2>|S=3/2,m> and |1/2,-1/2> |S=2,m-1/2>

Slave fermion

., iiiiii fcfc

Schwinger bosons

.,|2/1,2/1|

,,|2/1,2/1|

mSmSmSB

mSmSmSA

SffBBAA

fBBAAfS

tH

iiiiii

jijjijiiDE

2

)(12

Finally

combine α or β with the localized spin.

'. . . .i iH K E U n n J S s J T

1

( )2 1

. .

2

i i j i j ji j

i i

i i i i i i i i

H t f A A B B fS

U n n J T

A A B B f f f f S

pkpkkppkikiDEi

ti

jijjijiiDE

fAccAfkEN

ipHiF

dttFFeimne

fBBAAfS

tH

,

)(,11

)(12

2

22 )/(10 TKcm

Similar to one-magnon process.

Saito, et. al., PRB 62,1039 (2000).

Experimental results II: ARPES shape of Fermi edge (1) Different from that of Gold (metal).(2) Temperature sensitive

f

f

f

f

f

f

ff f

Charge ordering

• Many compounds• cuperates• manganites• magnetites

Nd doped La2-xSrxCuO4 (Niemoller et. al.)

ac-plane, Stripe in b-directuion

Charge-ordered stripes seen in La0.33Ca0.67MnO3 by Uehara, Mori, Chen and Cheong, Nature399, 560 (1999).

DV2O4 D: divalent elements

New J. Phys. 7, 53. Radaelli

PRL 93 157206. Tchernyshyov

cubic to monoclinic

Miles, et. al.Rev. Mod. Phys. 29, 279

Orbital ordering Fe3O4 Verway transition

Fe3O4 Verway transition

O O-2

O A-type: 1/3 Fe+2

O B-type: 1/3 Fe+2 O B-type: 1/3 Fe+3

Orbital ordering

Manganite, Spinel (AB2X4, MgTi2O4, FeSc2S4), R1-xAxTiO3, TiOX (X=Cl,BR),

V2O3, LiNiO2, NaTiO2, Ca3Ru2O7, KCuF3, Fe3O4,

Fe3O4

PRL 93, 156403. Jen, Guo, Huang

PRB 66, 214422. Wright, Attfield, Radaelli

z-directiontz

x, y-directiontx(y)

0 0'

0 1t

3 3

4 3 1

t

(PR. 93, 1498. Slater, Koster)

† † †. . ( )z x yi a j i a j i a jK E t c c t c c t c c

2 (cos cos ) 2 / 3(cos cos ). .

2 / 3(cos cos ) 2 / 3(cos cos ) 'cos

x y x y

x y x y z

t k a k a t k a k aK E

t k a k a t k a k a t k

simple cubic lattice

Interplay between DE and OO

La0.5Ca0.5MnO3

La0.5Sr1.5MnO4

PR 100, 545. Wollen, Koehler PR 100, 564. Goodenough

: Mn4+, : spin,

lobes: orbitals of Mn3+

Summary

1. A lot of interesting phenomena.2. Orbital dynamics is simple.3. With the new form of DE, the system seems to be managable.

PRL. 88 167204Kim et. al.

PRL. 81, 1517x=0.3

Feathures:Drude peak and broad peak

polaron?

small polaron large polaron

orbital?

PRB. 58, 11841Kilian and Khaliulin

J. Phys. Soc. Jpn. Shiba et. al.

Probing the orbital ordering

Resonant x-ray scattering (RXS) :An Incident photon excites an electron to a higher level. The Electron emits a photon and falls to a lower state.

La0.5Sr1.5MnO4 1s4p (PRL 80, 1932. Murakami et. al.)

1. The energy of 4p state is affected by the electrons at 3d state.2. The energies of 4p state of Mn3+ and Mn4+ are different.3. Intensity varies with the direction of polarization due to the Aj coupling.4. Incident photon: polarization. z-axis: b direction. orbitals: y2-z2 and x2-z2.