Spin-polarization coupling
in
multiferroic transition-metal oxides
Shigeki Onoda (U. Tokyo)
Chenglong Jia (KIAS)
Jung Hoon Han (SKKU)
Naoto Nagaosa (U. Tokyo)
March Meeting 2007
Multiferroics with noncollinear magnetic and ferroelectric phase
Material
TbMnO3
(Kimura et al Nature 2003;
Kenzelman et al PRL 2005)
Ni3V2O8
(Lawes et al PRL 2005)
Ba0.5Sr1.5Zn2Fe12O22
(Kimura et al PRL 2005)
CoCr2O4
(Yamasaki et al. PRL 2006)
MnWO4
(Taniguchi et al. PRL 2006)
CuFeO2
(Kimura et al PRB 2006)
LiCuVO4
(Naito et al cond-mat/0611659)
LiCu2O2
(Park et al PRL 2007)
d-electron
Polarization
(C/m2); Q
Specifics
d4 (t2g)3 (eg)1
800; q~0.27
Orbital order
d8 (t2g)6 (eg)2
100; q~0.27
Kagome
d5 [(t2g)3 (eg)2]?
150 (B=1T); N/A
N/A
Co2+ : d7 (e)4 (t2)3
Cr3+ : d3 (t2g)3
2; [qq0] q~0.63
ferrimagnetic
d5 (t2g)3 (eg)2
50;
q=(-.214, .5, .457)
N/A
d5 (t2g)3 (eg)2
400 (B>10T);
1/5<q<1/4
2D triangular;
Field-driven
d9 (t2g)6 (eg)3
N/A; q~0.532
1D chain
d9 (t2g)6 (eg)3
<10; q~0.174
1D chain
RED = magnetic ions
March Meeting 2007
Common & uncommon features
Common
Involves 3d transition metal
magnetic ions (Fe, Mn, Ni, Co,
Cr, Cu)
Onset of ferroelectricity
concomitant with that of
noncollinear magnetic order
Not Common
Different d-electron
configurations
(d1-d9,
t2g, eg, mixed t2g-eg)
Spin-polarization coupling
seems universal, irrespective
of d-electron number
March Meeting 2007
In this talk
A microscopic theory of
spin-polarization coupling for
arbitrary d-electron configuration
is presented
March Meeting 2007
Existing theories
Phenomenological theories of Mostovoy & Harris provide general ground for
writing down the spin-polarization coupling
Microscopic derivation first given by Katsura, Nagaosa, Balatsky (2005)
Physical origin: spin-orbit interaction
March Meeting 2007
Developing a Microscopic Theory
A linear chain consisting of alternating M(agnetic) and O(xygen) atoms is a
reasonable model for magneto-electric insulators
M
O
M
O
M
O
M
O
M
O
M
O
M
O
M
The building block is a single M-O-M cluster.
We solve this model as exactly as possible for realistic d-electron
configurations: t2g, eg, mixed t2g-eg
Previous theory of KNB based on t2g orbitals
March Meeting 2007
Our Result
Jia, Onoda, Nagaosa, Han, cond-mat/0701614
March Meeting 2007
Classification of spin-orbit interactions
d-electron
Mechanism
t2g
Spin-orbit within 3-fold degenerate t2g
subspace (SOM)
eg
No SO allowed within eg subspace,
invoke SO at ligand ion (SOL)
Partially filled t2g & eg; SOM can mix t2g
and eg levels and the new eg levels
become “active”
t2g-eg
In all instances we find non-zero Psp associated with
noncollinear magnetic order
Psp is reallly UNIVERSAL
March Meeting 2007
t2g
t2g
t2g
p
Both Porb and Psp are found
March Meeting 2007
eg
eg
eg
p
Only Psp exists due to oxygen
p-orbital spin-orbit interaction
Relevant to d8 NVO; d9 LiCu2O2 ,LiCuVO4
March Meeting 2007
Mixed t2g-eg: Model for TbMnO3
Ingredients:
(1) Orbital ordering takes place at high temperature ->
Inversion symmetry is broken; two-sublattice structure to begin with ->
Need to generalize theory for two-sublattice orbitals
(2) d4 (t2g)3 (eg)1 configuration gives rise to (t2g)-(eg) mixing and polarization
(3) Spin-orbit coupling at oxygen gives rise to polarization
March Meeting 2007
Loss of Inversion Symmetry
A new term along the cluster axis due to lack of inversion symmetry;
No spin-orbit interaction is required
March Meeting 2007
t2g-eg mixing (C.D.Hu, cond-mat/060470; Our work)
Mixing of
occupied spin-up eg state and
unoccupied spin-down t2g state
Gives rise to Psp
Numerical estimate using realistic parameters of TbMnO3
consistent with experimentally measured polarization
Same mechanism may be relevant for
CuFeO2 (t2g)3 (eg)2 MnWO4 (t2g)3 (eg)2
March Meeting 2007
Relevance for X-ray scattering
For a helical spin pattern at wavevector Q, there arises lattice modulations due to
induced polarization at various wavevectors;
Fourier harmonics
Polarization
Two-sublattice structure gives further peaks at
Spin-current type of polarization is the only UNIFORM POLARIZATION
March Meeting 2007
Summary
A general theory of magnetism-induced dipole moment is presented
The mechanisms can be classified according to t2g, e g, and mixed t2g-e g
configurations
One can identify the origin of improper ferroelectricity in diverse d-electron
configurations as follows:
d-electron configuration
Mechanism
(t2g)3 (eg)n (n=1,2,3)
t2g-eg mixing; Ligand SO
(t2g)6 (eg)n (n=1,2,3)
Ligand SO
(t2g)n (n=1,2,4,5)
Magnetic SO
March Meeting 2007