LaOFeAs -- multiferroic manganites
Jeroen van den Brink
Gianluca Giovannetti,Luuk Ament,Igor Pikovski,Sanjeev
Kumar,Antoine Klauser,Carmine Ortix
George Sawatzky,Frank Kruger,Ilya Elfimov,Jan Zaanen
Krakaw 19/6/2008
LaOFeAs
Layered crystal structure
Fe
S=2
d6
tetrahedral
surrounding
t2g
t2g
eg
eg
S=1
S=0
exp. ordered moment: 0.4 B
C-type magnetic order
(bad) metal
LaOFeAs: LDA+U, C-type magnetic order
Fe 3d-band width ~4 eV
gap ~0.5 eV
S=2
Giovannetti, Kumar, JvdB, arXiv:0804.0866
Phys B. doi:10.1016 (2008)
Stochiometric LaOFeAs
S=2, Mott insulator
high spin Fe found in XAS
Bernd Buchner, Martin Knupfer
arXiv:0806.2625
Experimental small moment and “metallicity”
are due to off-stochiometry
Giovannetti, Kumar, JvdB, Phys B. doi:10.1016 (2008)
Multiferroics = Magnetic Ferroelectrics
Why study them?
Magnetic ferroelectrics are very rare!
Fundamental interest: Why rare? How to get around?
How to get strong coupling between magnetic and
ferroelectric orderparameter?
Van Aken et al., Nature 449, 702 (2007)
Cheong and Mostovoy, Nature Mat. 6, 13 (2007)
Eerenstein et al., Nature 442, 759 (2006)
Pimenov et al., Nature Phys. 97, 100 (2006)
Ikeda et al., Nature 436, 1136 (2005)
Lottermoser et al., Nature 430, 541 (2004)
Zheng et al., Science 303, 661 (2004)
Kimura et al., Nature 426, 55 (2003)
Hur et al., Nature 429, 392 (2003)
Observed multiferroic couplings
-- BiFeO3 and BiMnO3
Tmagnetic<<Tferroelectric
orderparameters barely couple
-- TbMnO3 , DyMnO3 , Ni3 V2 O8
Tferroelectric=Tmagnetic
magnetism induces FE
chiral magnetic order (spin spiral) does the job
Maxim Mostovoy, PRL 96, 067601 (2006)
-- Pr1-xCaxMnO3 , HoMn2O5
magnetism induces FE, but:
no chiral symmetry breaking
???
HoMn2O5
Mn3+
Mn4+
Mn3+
Mn4+
HoMn2O5
conceptual picture
Mn3+
- +
Mn4+
- +
- +
electronic and ionic
displacements due to dislocated SDW / magneto-striction
ferroelectric polarization
Betouras, Giovannetti, JvdB, PRL 98, 257601 (2007)
Ab initio bandstructure computations ~1200 nC/cm2
experimental polarization ~80 nC/cm2
ferroelectric domains?
Incorporating electron
correlation effects with
LDA+U fixes the problem
small polarization due to
near cancellation of Pion and Pelec
Gianluca Giovannetti and JvdB, PRL 100, 227603 (2008)
Perovskite crystal structure of Pr1-xCaxMnO3
0.4 < x < 0.5
Oxygen2-
Pr3+/Ca2+
Mn4+ / Mn3+
11
Near x=0.4 : Bond-centered charge/spin ordering
eg
t2g
Dimer
A.Daoud-Aladine et al., PRL 89 97205 (2002)
Near x=0.5 : Site-centered charge/spin ordering
E.O. Wollan and W.C. Koeler, Phys. Rev. 100, 545 (1955)
Ferroelectric?
x=0.4
x=0.5
Bond centered
spin/CO
Site centered
spin/CO
0.4 < x < 0.5
intermediate
Ferro-electric
groundstate
It is allowed by symmetry:
can happen
observed to happen
will happen
Jooss et al., PNAS 104, 13597 (2007)
....and it first happened in microscopic DDEX model
H DDEX  ij t ijij c i c j  J ijSi  S j
 
J Si  S j  J cos  ij

tij  t cos ij 2

z2, z2
ij //z
1,

z2, z2
ij //x
 ,
1
4

x 2 y 2 , x 2 y 2
ij // x
 43
JvdB, Khomskii, PRL 82, 1016 (1999)
 stabilization of dislocated SDW phase
multiferroicity
Efremov, JvdB, Khomskii, Nature Mat. (2004)
Computed phase diagram of Pr1-xCaxMnO3
Continous transition from
Site centered CO
to
Bond centered CO
“in between order”
Breaking of inversion symmetry in the intermediate phase
Ferro-electricity
Magnetism
Efremov, JvdB, Khomskii, Nature Mat. (2004)
Giovannetti, Kumar, JvdB, Picozzi, preprint (2008)
Conclusions
we predict....
LaOFeAs to be Mott insulator with Fe high spin
La1/2Ca1/2MnO3 to be strongly multiferroic
Simple 1D Picture
longitudinal
charge displacements
suggests FE in quasi-1D organic charge transfer salts
which is observed!
e.g.: S. Brazovskii, Physics of Organic
Superconductors and Conductors
Springer Series in Materials Sciences (2008).
Perovskite HoMnO3 with GdFeO3 distortion
Magnetic E-phase
S. Picozzi et al., Phys. Rev. Lett. 99, 227201 (2007).
Simple 1D Picture
Superexchange
strengthens bonds of
antiparallel spins
all oxygens move
down!
transversal
charge
displacements
Double
exchange
strengthen bonds of
parallel spins
JvdB and Daniel Khomskii, J. Phys. C.M., in press (2008)
HoMn2O5
ICM + PE
QuickTime™ and a CM+FE
TIFF (LZW) decompressor
are needed to see this picture.
ICM+PE
Kimura, Kamada, Noda, Kaneko, Metoki, Kohn
cond-mat/0602226 (2006)
1. Phenomenological approach
Magneto-electric coupling: Ginzburg-Landau
Electric polarization
Magnetization
Pr 
M r 
couple these two
orderparameters
Free
 energy must be invariant for:
time reversal
t  t
M M

P  P 
spatial inversion
r  r
P  P
MM
 
Magneto-electric coupling: Ginzburg-Landau
P, , M, M
To build an invariant we need

 

FME (r )  P   ( M 2 )   M ( M )  (M  ) M  ...

We are interested
in ferroelectrics:
uniform electric polarization so that
P r   p0
which implies that:
 drP  ( M
3
V
2
)  p0 
 dr ( M
3
V
2
)M
2
surface
Our key observation:


FME (r )  P   ( M )
2
becomes active if
SDW dislocated
M  M0 cos(qm x )
magnetization is shifted with respect
to the lattice (but inversion invariant)

Betouras, Giovannetti, JvdB, PRL 98, 257601 (2007)
Giovannetti and JvdB, PRL 100, 227603 (2008)
Minimize Free Energy


FME (r )  P   ( M )
2
with

with Ansatz for polarization

gives finite p0 and p1
Pr 
2
FE (r ) 
2E r 
M  M0 cos(qm x )
P  p0  p1 cos(qx)
only when qm = q/2

For multiferroic
coupling it is
sufficient to have commensurate dislocated magnetic order
YMn2O5
ICM
CM:
commensurate
ICM
CM
ICM:
incommensurate
magnetic ordering
indeed only commensurate magnetic phase is ferroelectric!
Chapon, Radaelli, Blake, Park, Cheong
Phys. Rev. Lett. 96, 097601 (2006)