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