Title: Multiferroics

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Title Multiferroics ??????? ??? (C. D.
Hu) Abstract Multiferroics is the type
of material which possesses several long-range
orders. These long-range orders, such as
ferroelectric order, (anti)ferromagnetic order,
ferroelastic order are coupled with each other
and give rise to interesting physical phenomena.
Experiments such as magnetic susceptibility
measurement, spin-polarized neutron scattering
and synchrotron radiation can give us important
information of the cause of multiferrroics.
Several theoretical models of the mechanism will
be introduced. The emphasis will be on the
"spin-current" model in which spin-orbit
interaction will play the essential role. 1.
Introduction. 2. Experiments. 3. Models. 4.
Conclusion.
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1. Introduction
Multiferroics The kind of material which have
several long-range orders such as
antiferromagnetism and ferroelectricity.
http//physics.aps.org/ articles/v2/20 Physics 2,
20 (2009) Daniel Khomskii
Illustration Alan Stonebraker
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Ferroelectricity Material which has net electric
polarization.
BiFeO3 lone-pair of 6s-electrons of
Bi(3) YMnO3 tilting of MnO5
BaTiO3 movement of Ti(4) TbMn2O5 dimerization
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Antiferromagnetism Material which has no net
magnetization but has long-range magnetic order.
Sinusoidal Cycloidal spiral Proper screw
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There are more than 100 multiferroic compounds.
Type I multiferroics High Tc and large electric
polarization, but weak coupling between
electricity and magnetism.
Type II multiferroics Low Tc and small electric
polarization, but strong coupling between
electricity and magnetism.
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K.F. Wan, J.-M. Liu and Z.F. Ren, Advances in
Physics 58, 321448 (2009)
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2. Experiments
RMnO3 orthorhombic
c b a
O Oxygen R Rare earth elements Mn Manganese
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Kimura et. al. PRB 71 224425 (2005), TN41K,
Tlock28K.
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Kenzelmann et. al. PRL 95, 087206 (2005)
neutron scattering
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3. Models
Why are electric polarization and magnetic order
coupled?
Maxwell's equations
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A. Atomic displacement (lattice distortion)
Ca3CoMnO6
Choi et. al., PRL 100, 047601 (2008)
face-sharing octahedra along c-axis
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4 2 4 2 4 2 4
2 4 Mn Co
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B. Spin current model
H. Katsura, N. Nagaosa and A. V. Balatsky, PRL
95, 057205
z
TM1 O TM2
S1
y
S2
x
p
V
?
eg
eg
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d-orbitals under crystal field of cubic symmetry
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hybridization
Hunds coupling
Sj local spin Direction sj mobile spin
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spin-orbit interaction
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electronic origin
? ?
? ? ? ?
P
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z
Result
y
x
spiral spin
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spin current
spin current ? electric field ? electric
polarization
AC (Aharonov-Casher) effect
charge accumulation
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Spiral Spin and Orbital Ordering
The spin current model gives a very small
electric polarization. It is due to cancellation
of the contribution of entire energy band.
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Conclusion 1. Multiferroics is a field of rich
physics. 2. Multiferroics is a field driven by
experiments. 3. The theoretical models are not
complete. 4. Multiferroics is related to a lot
other physical phenomena such as, lattice
distortion, charge order, orbital order,
spintronics, and magnetic properties.
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Polarization and Dzyaloshinskii-Moriya
interaction I. Dzyaloshinskii, J. Phys. Chem.
Solids 4, 241 (1958).Tôru Moriya, Phys. Rev.
120, 91 (1960)
exchange interaction with spin-orbit coupling
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SO
?E
SO
V
D?(?/?E) (t2/U), D/JSE??g/g
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Relation between multiferroics and DM
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DM interaction
Spin current
i bond direction
Gauge field AC effect
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z y x
Eeff,z
s
jxy
Mn O Mn