Spin, Charge, and Orbital Ordering of Transition Metal Oxides

黃迪靖國家同步輻射研究中心清華大學物理系 (合聘)

清華大學物理系演講 Oct. 5, 2005

Outline:

•Verwey transition and charge-orbital

ordering of Fe3O4•Multiferroics in TbMn2O5

-- coexistence and strong coupling of ferroelectricityand antiferromagnetism

Phenomena of electron-correlated materials

CMR

T

RB = 0

B = 15 T

HTSC MIT

RR

T T

Colossal Magneto-Resistance

High Temperature SuperConductivity

Metal-to-Insulator Transition

metalssuper-conductors

Physical properties of solids are primarily determined by valence electrons in a lattice.

Electronic structure of correlated materials:

•bandwidth

•Coulomb interaction

•charge transfer energy

W

Density of States

Imada, Fujimori & TokuraRev. Mod. Phys. (1998)

TM

O

BandwidthW Fermi level

Metals, from the view point of band theory

Correlated-Electron Materials: U > W

TM

Oxygen

On-site Coulomb energyU

din dj

n

i j

djn dj

n+1 L

Charge-transfer energy∆

j

din−1 dj

n+1

W

Density of States

Imada, Fujimori & TokuraRev. Mod. Phys. (1998)

TM

O

Mott-Hubbard insulator

Coulomb energyU

CoO:insulator

Band theory is insufficient to explain the physical properties of strongly correlated-electron systems.

3z2-r2

x2-y2 TM

eg

xy

zx yz

OJT

3d crystal field

t2g

spin

charge

orbital

lattice

Charge ordering: spatial localization of the charge carriers on certain sites

2+

3+

Orbital ordering:periodic arrangement of specific electron orbitals

soft x-ray absorption & scattering

TM: 2p 3dO: 1s 2p

direct, element-specific probing of electronic structure of TMO

TM 2p

The Electromagnetic Wave Spectrum

103 101 10-1 10-3 10-5 10-7 10-9 10-11 10-13 10-15

10-9 10-7 10-5 10-3 10-1 101 103 105 107 109

Radio waves

Visible lightVisible light

Infrared Ultra-violet Hard-X-rays Gamma raysSoft X-rayMicro-waves

SynchrotronRadiation

(eV)

物體大小

建築物

波長(米)

光 源

粒子加速器

棒球 昆蟲 細胞 病毒 蛋白質 分子 原子核 質子 夸克？原子

放射性源X射線管電 燈無線電天線 微波管

光子能量(電子伏特)

ElectronBeam

N

S

N

S

Bending Magnet

Synchrotron radiation is the electromagnetic waves emitted from charge particles when they move in a curved path.

SynchrotronRadiation

This light has been called “synchrotron radiation”, since it was accidentally discovered in an electron synchrotron in 1947.

Insertion Device

Elliptically Polarized Undulator 5.6

N

S

ElectronBeam

Synchrotron Radiation

11

2233

44

55

6677

88

99

1010

99 1010

中心設施 11 大門 22 行政大樓 33 研光大樓 44 儀光大樓 55 增能環館 儲存環館 77 機電館 88 招待所

鄰近單位 高速電腦中心 交通大學

66

國家同步輻射研究中心

Research Highlights

• Electronic structure of half-metal oxidesHuang et al., PRB (2003) Chen et al., PRB (2004)Chang et al., PRB (2005)

• Orbital ordering of manganitesHuang et al., PRL (2004)

• Spin and orbital moments of magnetic oxidesHuang et al., PRB (2002) Huang et al., PRL (2004)

• Orbital symmetry and electron correlation of cobaltatesWu et al., PRL (2005)

• The Verwey transition• Multiferroics in TbMn2O5

Verwey transition and charge-orbital ordering of Fe3O4

macroscopic manifestation of the Verwey transition in Fe3O4

Weiss and Forrer (1929)

Millar (1929)

Okamura (1932)

100 200 T(K)

Recent Reviews

Imada, Fujimori, and TokuraRev. Mod. Phys. (1998)Tsuda, Nasu, Fujimori, and Siratori“Electronic Conduction in Oxides” (2000)F. Walz, J. Phys: Condens. Matter (2002)J. Garcia & G. Subias, J. Phys: Condens. Matter (2004)

The Verwey transition of magnetite (Fe3O4)

T > TV ~ 120 K

Inverted spinel structure (cubic)1/3: tetrahedral (A-site) ) Fe3+2/3: octahedral (B-site) Fe3+, Fe2+

A-site , B-site , TC ~ 860K

Verwey model:

charge order-disorder transition of B-site Fe (Verweyn & Haayman, 1941)

oxygen

Fe3O4 is believed to be a classic example of charge ordering.

a2

a2a

aaa 222 ××

aaa ××T > TVcubic,

T < TVmonoclinic

supercellwith space group Cc

neutron scatteringFujii et al. (1975)

low T phaseC = 2a

(4 0 1/2)c

unit cell

k k’∆k = q

2a sinθ = λ =

2k sinθ = 2πa

2πk

momentumtransfer q =

2πa

θ

Basic concept of diffraction

a

lattice doubling half-order diffraction

k k’∆k’ = q’

2(2a) sinθ’ = λ =

2k sinθ = 2πa

2πk

q’ = 2πa

12

12

2a

Does Fe3O4 exhibit charge ordering?Neutron diffuse scattering [Siratori et al., J. Phys. Soc. Jpn. (1998)]The atomic displacements are not of localized character, but spread over at least several unit cells, indicating the itinerant character of the 3d electrons.

NMR results [ Novak et al., PRB (2000) ]The states of Fe ions on the B sublattice are mixed so strongly that the notion of 2+ and 3+ valencymay lose its meaning.

X-ray scattering [ Garcia et al., PRL (2000) ]The octahedral Fe atoms are electronically equivalent in a time scale lower than 10-16 sec.

Refinement of x-ray and neutron diffraction

2a

Charge ordering was deduced from the Fe-O distance.

4 independent B sites of Fe used; B1, B2, B3, B4(B1 and B4 have 2.4 valence, B2 and B3 have 2.6 valence)

suggest:1.(0 0 1)c and (0 0 1/2)c

charge modulation along the c-axis

2.Breakdown of Anderson’s criterion

Fe2+

Fe3+

Wright, Attfield, and Radaelli, PRL (2001), PRB (2002)

3.815.485.4Fe B33.905.415.4Fe B23.395.585.6Fe B43.45 5.575.6Fe B1

LDA+Uspin moment

LDA+Uvalence charge

Wright et al.valence charge

monoclinic

cubic

Fe2+

Fe3+

LDA+U calculations

Jeng, Guo, and Huang, PRL (2004)

•gap ~ 0.2 eV

•charge ordering of B-Fe

cf: Leonov et al., PRL (2004)

LDA+U calculations: charge-orbital ordering

Jeng, Guo, and Huang, PRL (2004)

Fe3+

OFe3+

electron-rich Fe4O4 cube(3 B-Fe2+ and 1 B-Fe3+)

electron-poor Fe4O4 cube(3 B-Fe3+ and 1 B-Fe2+)

Fe2+

Fe3+Fe3+

Fe3+

Fe3+

z = 0

a2

2/a

2/a

A Fe3+B Fe3+

B Fe2+ O

Breakdown of Anderson’s criterion can be explained by the existence of orbital ordering.

X-ray scattering

kkqvvv −= '

drrrq

rqrnf i∫ ⋅⋅

= 2)sin()(4 vvvv

π

'kv

kv )(rni : electron density

Fe3O4: charge disproportionation ∆Q= 0.2 e∆Q/Qtotal ~ 1/550

kv

'kv

0

i∑ Γ−−−

⋅⋅∆

⋅⋅

i i

rkirki

iEEeriier

f)(

0'0~

0

'

ωεε

h

vvvv vvvvempty valence

core level

Resonant X-ray scattering

to extract the valence disproportionationand to learn about the spatial distribution of i

Subias et al., PRL (2004)Resonant X-ray scattering

Fe K-edge resonant X-ray scattering failed to observe any charge ordering.

(0 0 l+1/2)C ?

??

1s 3d

1s 4p

Subias et al., PRL (2004)Resonant X-ray scattering

(0 0 l+1/2)c ?

??

1s 3d

1s 4p

Fe K-edge resonant X-ray scattering failed to observe any charge ordering.

The existence of charge ordering in Fe3O4remains controversial.

No freezing of the soft phonon mode has been observed.[Samuelsem, & Steinsvoll (1974)]

Mechanism of the Verwey transition?

egt2g

Fe 4p

1sK-edge resonant x-ray scattering

charge-orbital ordering

Fe 3d

Fe

Fe 2p

Fe L-edge and O K-edgeresonant soft x-ray scattering directly probes Fe 3d and O 2pwith high sensitivity.

O 2p

O 1s

Strong hybridization between Fe 3d and O 2pChen et al., PRB (2004)

monoclinic

DOS from LDA+U calculations

B-Fe t2g

States between EF and 1 eV above + 2a periodicity(0 0 ½)c resonant diffraction

Iso-surface of O 2p in Fe3O4integrated between EF and 1 eV above

z = 0

a2

2/a

2/a

B Fe3+

z = a B Fe2+

O

z = 0

monoclinic P2/c structure LDA+U calculations: H.T. Jeng

Summary

•The Verwey transition is a transition of charge-orbital ordering.

•Experimental discovery of orbital-ordering mechanism for the Verweytransition, resolving the long-lasting debate.

Outline:

•Verwey transition and charge-orbital

ordering of Fe3O4•Multiferroics in TbMn2O5

-- coexistence and strong coupling of ferroelectricityand antiferromagnetism

The magnetoelectric effect:the induction of magnetization by an electric field; induction of polarizationby a magnetic field.- first presumed to exist by Pierre Curie in 1894

πρ

ππ

40

1

)4(14

=⋅∇

=⋅∇∂∂

−=×∇

+∂∂

+=×∇

EB

tB

cE

PEtc

jc

H

v

v

vv

vvvv

Nature, 426, 55 (2003)

TbMnO3

2 0

2 5

3 0

3 5

0 1 0 2 0 3 0 4 0

-4 0

-2 0

0

2 0

4 0

0

(b )

(a )

0 T 1 T 3 T 5 T 7 T 9 T

E //b , H //a (F C )1 k H z

w a r m in g

ε

P1

P2T

P

0

40

-80

40

P1

P2T

P

0

40

-80

40

E p o le //+ bH //a (Z F C )

P (n

C/cm

2 )

T (K )

• 3 transitions on cooling. • Magnetic field induces a sign reversalof the electric polarization.

TbMn2O5 Nature, 429, 392 (2004)

Recently discovery in the coexistence and strong coupling of antiferromagnetismand ferroelectricity in frustrated spin systems such RMnO3 and RMn2O5(R=Tb, Ho , …)

revived interest in “multiferroic” systems

The mechanism has not been yet clarified, although magnetic competing interactions are believed to be the key ingredient.

Tb

O

Mn4+O6octahedron

• orthorhombic structure (a b c, α = β = γ = 90°)

•AFM insulator (TN=42 K )

AFM square lattice with asymmetrical next-nearest-neighbor interactions, i.e. geometrically frustrated

•Magnetization in the ab plane,

•Tb ferromagnetic below 10 K

•Spontaneous polarization P // b

•AFM modulation vector k ⊥ PMn3+O5pyramid

TbMn2O5

Tb3+Mn4+ , Mn3+O2-

kP

3 AFM phases with different propagation vectors in the ac plane. k = (kx 0 kz)

propagation vectors kin units of (2π/a 0 2π/c):33 K < T 42 K k ~ (1/2 0 0.30) incommensurate

24 K < T

Summary

•Resonant soft x-ray scattering of TbMn2O5Two incommensurate orderings at T < 24:

AFM ordering, consistent with neutron diffractions.A new type of ordering,

--- charge-orbital ordering ?.

•The AFM ordering is closely related to the dielectric response.

Collaborators

Jun Okamoto (國家同步輻射研究中心)趙國勝 (交通大學電子物理研究所)林宏基、黃志謀、徐嘉鴻、陳建德 (國家同步輻射研究中心)吳文斌 (交通大學電子物理研究所)

LDA+U:鄭弘泰 (中研院物理所)郭光宇 (台灣大學物理系)

Resistivity measurements (Fe3O4):林大欽 (淡江大學物理系)

TbMn2O5: S. W. Cheong (Rutgers Univ.)

歡迎有興趣的研究生加入我們的研究團隊!

Thank you !