Jeroen van den Brink

Bond- versus site-centred ordering and

possible ferroelectricity in manganites

Leiden 12/08/2005

Outline

Coupling of orbital degrees of freedom to:

-- Lattice

-- Spins

-- Charge

Orbital induced ferroelectricity in manganites

Dima Efremov, JvdB, Daniel Khomskii, Nature Materials 3, 853 (2004)

Lottermoser et al., Nature 430, 541 (2004).Van Aken et al., Nature Mat. 3, 164 (2004).Kimura et al., Nature 426, 55 (2003).Hur et al., Nature 429, 392 (2004).Zheng et al., Science 303, 661 (2004).Fiebig et al., Nature 419, 818 (2002).Wang et al., Science 299, 1719 (2003).Spaladin, Physics World, April 2004.

Magnetic Ferroelectrics

Possible application:switching of magnetic bits by electric field

Why study them?

Fundamental interest: why rare? How to get around?

Magnetic ferroelectrics are very rare!

What is a ferroelectric? dipole

disorderferroelectric

Breaking of inversion symmetry

Valence electrons are in localized 3d orbitals

R a correlated electron systems

R a

a

R >>a

R >> a conventional metals, semiconductors

What is special about manganites?

Do atomic physics first, include translation symmetry later

3d orbitals of a Mn- ion

• eg orbitals

• t2g orbitals

Large Coulomb interaction between electrons on the ion

Large Atomic Hund’s rule exchange

Electron Spins

Parallel

Orbitals behave like electron spins

Compare orbitals and spins....

Orbitals are extra degree of freedomImpact on physical properties

•Order-disorder•Thermodynamics•Magnetism•Lattice distortions Ferro-electricity

PossibleMultiferroicbehavior

Orbitals and spins

Similarities

Angular momentum SU(2) algebra: [Sx,Sy]=iSz

Localized momentemergent from electron-electron interactions

Spin-spin and orbital-orbital interaction due to superexchange

Possibility of long range ordering

Orbitals and spins

Differences

Spins Orbitals

coupling to latticeWeak Strong

Symmetry of HamiltionianHigh Low

ExcitationsGapless Gaped

Frustration of orderSometimes Always

10

Mn4+ / Mn3+

Oxygen2- La3+/Ca2+

Perovskite crystal structure of La1-xCaxMnO3

• t2g orbitals

Cubic Crystal field splitting

––

––

–– ––

––––

Local considerations

5xeg

t2g

5xeg

t2g

Mn (3+) = 3d4 Mn (4+) = 3d3

• eg orbitals

Mn4+ / Mn3+

Orbital induced ferroelectricity in manganiteswith doping near x=1/2

Mn (3+) = 3d4 eg1

Mn (4+) = 3d3 eg0

E.O. Wollan and W.C. Koeler, Phys. Rev. 100, 545 (1955)

Charge ordering

Ferro zig-zag chainsMagnetic CE-type order

Interplay orbital, spin and charge

eg

t2g

Bond center

Ferro

teg

t2g

Site center

Antiferro

JvdB, Khomskii, PRL 82, 1016 (1999)

JAF

Formally: DDEX model

,S SJ c c H jiijDDEX

ijjiijij t

41,

//ij,// ,1

2222

zzx

zzzij

. 43,

//

2222

yxyxxij

ij cosJ S SJ ji

2 cos ijij tt

DDEX model

Near x=0.4 : Bond-centered charge ordering

A.Daoud-Aladine et al., PRL 89 97205 (2002)

eg

t2g

Dimer

Near x=0.5 : Site-centered charge ordering

E.O. Wollan and W.C. Koeler, Phys. Rev. 100, 545 (1955)

Ferroelectric?

x=0.5x=0.4

Site centered CO

Bond centered CO

Ferro-electricgroundstate

0.4 < x < 0.5

intermediate

It is allowed by symmetry: Can happen Will happen

Magnetic structure of Zener polaron?

CE type ?

Or:

Jaffet-Kittel structure “orthogonal”structure

Magnetic Structure

x=0.5x=0.4

0.4 < x < 0.5

intermediate

JvdB, Khaliullin, Khomskii, PRL 83, 5118 (1999)

Calculated phase diagram

Dima Efremov, JvdB, Daniel Khomskii, Nature Mat. (2004)

Continous transition from

Site centered CO

Bond centered CO

to

“In between” centered CO

Breaking of inversion symmetry in the intermediate phase

Ferro-electricity Magnetism

Prediction for manganites:

Multiferroic phase appears close to x=1/2

Conclusions

Between bond- and site-centered charge order:

ferroelectric phase

Calculated magnetic structure

From: To:

We find a continous transition as function of doping

x=0.4 x=0.5

Crystal field splitting of eg levels Jahn-Teller distortion

Lifting of degeneracy: lattice

5x3x

2xeg

t2g

5x3x

2xeg

t2g

x=0.5 : Site-centered charge ordering

JvdB, Khaliullin, Khomskii, PRL 83, 5118 (1999); PRL 82, 1016 (1999)

Goodenough (1963) Orbital order in plane

Orbital order LaMnO3Order by disorder