Magnetic transitions of multiferroics revealed by photons

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Magnetic transitions of multiferroics revealed by
photons

• ???
• ????????
• ???????

• Multiferroicity
• Soft x-ray magnetic scattering
• Magnetic transitions and switch of spin chirality

May 9, 2007
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Collaborators National Synchrotron Research
Center J. Okamoto, K. S. Chao, H. H. Wu, H.-J.
Lin, and C. T. Chen
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National Tsing Hua Univ. C. Y. Mou
???
Rutgers Univ. S. Park, J. Y. Choi, and S-W.
Cheong
Acknowledgement C. D. Hu, National Taiwan
University
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Magnetism ordering of spins
Magnetization can be induced by H field
Ferroelectricity polar arrangement of charges
Electric polarization can be induced by E field
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Magnetoelectric effect
Induction of magnetization by an electric field
induction of polarization by a magnetic field.
- first presumed to exist by Pierre Curie in 1894
on the basis of symmetry considerations
M. Fiebig, J. Phys. D Appl. Phys 38, R123 (2005)
Materials exhibiting ME effect Cr2O3 BiMnO3 BiFeO
3 ..
However, the effects are typically too small to
be useful in applications!
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(Ferro)magnetism vs. (Ferro)electricity

Pauli vs. Coulomb
Magnetic moment
unfilled d bands impurities
(La,Sr)MnO3 spins from 3d3 or 3d4
Exchange interactions
-
superexchange
TM
O
TM
Mn
double exchange
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Large displacement often involved in
ferroelectricity
Pb-O plane
Ti-O plane

• PbTiO3
• Pb-O covalent bond

cubic 800 K
Ti4
tetragonal 300 K
O
Pb
TC763 K
Kuroiwa et al, PRL87 217601 (2001)
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(Ferro)magnetism vs. (Ferro)electricity

Classic examples BaTiO3 or PbTiO3 polarization
from cation/anion paired diploes
Ti4 3d0
O 2p2
Filled or empty d band, no room for magnetism!
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Two contrasting order parameters
Magnetization time-reversal symmetry broken
Polarization inversion symmetry broken
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Recently discovery in the coexistence and
gigantic coupling of antiferromagnetism and
ferroelectricity in frustrated spin systems such
RMnO3 and RMn2O5 (RTb, Ho , )
TbMnO3 Kimura et al., Nature 426, 55, (2003)
TbMn2O5 Hur et al., Nature 429, 392 (2004)
revived interest in multiferroicity
Magnetism and ferroelectricity coexist in
materials called multiferroics.

• TC lt TN
• Frustrated magnetic systems.

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spin frustration
J gt0
?
geometrically frustrated magnetization
Normal antiferromagnet
frustrated spin chains
FM
AFM
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TbMnO3 antiferromagnetic TN42 K
H // b
TC27 K
Kimura et al. Nature, 426, 55 (2003)
collinear magnetic order, inversion symmetric
TN42 K
non-collinear magnetic order, inversion symmetry
broken
T35 K
Kenzelmann et al., PRL 95, 087206 (2005)
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TbMn2O5 Nature, 429, 392 (2004)
antiferromagnetic TN42 K
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Frustrated magnets RMnO3, RMn2O5 TC lt TN ?
polarization governed by magnetism ?
Issues -What is the underlying mechanism of
the gigantic ME effect? -What kind of spin
configurations supports electric polarization?
Mostovoy PRL (2006)
L
spiral ?
collinear ?
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Phenomenological Ginzburg-Landau approach
Lowest order in the expansion of the free energy
internal field from spins
magnetization at modulation vector
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Symmetry properties
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Phenomenological Ginzburg-Landau approach
Okamoto et al., PRL 98, 157202 (2007)
noncollinear spins, e.g. spiral
Mostovoy PRL(2006)
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Microscopic theory

• Atomic displacement antisymmetric exchange
  interaction Sergienko and Dagotto PRB 73,
  094434 (2006) Sergienko,Sen and Dagotto PRL
  97, 227204(2007)

• Spin current Katsura et. al., PRL 95,
  057205 (2005) Jia et. al. PRB 74, 224444

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How to induce polarization without involving
atomic displacement?
Essential Physics Motion of magnetic moments
induces electric dipoles! the intrinsic
Aharonov-Casher Effect
Einstein and Laub (1908) A magnetic dipole
moment m that moves with constant velocity should
develop an electric dipole moment
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Hirsch, PRL 83, 1834 (1999)
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Electric polarization induced by spin current
What is spin current?
Heisenberg Model
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The spin-current model
Katsura et. al., PRL 95, 057205 (2005)
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Magnetic transitions and switch of spin
chirality in CoCr2O4
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CoCr2O4
field cooling 0.01 T
spinel
Yamasaki et al. PRL 96, 207204(2006)
conical spin structure
ferrimagnetic
TC 93 K
TS 26 K
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CoCr2O4
Yamasaki et al. PRL (2006)
001
P//-110
q// 110
The spin-current model
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interlayer spacing of (110) lattice planes
L
L110
reciprocal space
(110)
a
real space
b (2p/a)
a (2p/a)
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(2-d, 2-d, 0)d0.63
Tomiyasu et al. PRB (2006)
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Soft x-ray magnetic scattering
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Elastic x-ray scattering
elastic scattering
momentum transfer
A volume element at will
contribute an amount to the scattering field
with a phase factor .
scattering form factor
Fourier transform of charge distribution.
Bragg condition q modulation vector of
charge, spin , or orbital order
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Scattering accumulates microscopic effects and
reveals macroscopic properties.
magnetization at modulation vector
X-ray scattering
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Elastic x-ray scattering
elastic scattering
momentum transfer
A volume element at will
contribute an amount to the scattering field
with a phase factor .
scattering form factor
Fourier transform of charge distribution.
Detectable with x-ray?
Bragg condition q modulation vector of
charge, spin , or orbital order
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X-ray magnetic scattering
spin density
Relevant interactions
Spin-orbit interactions
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X-ray magnetic scattering
kinetic energy
m.B
SO
Non-resonant
Blume, J. Appl. Phys. (1985)
Resonant
for ?? 600 eV
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Resonant X-ray magnetic scattering
electric dipole transitions
Hannon et al., PRL(1988)
F1,1 F1,-1
scattering amplitudes
As a result of spin-orbit and exchange
interactions, magnetic ordering manifests itself
in resonant scattering.
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Resonant soft x-ray scattering of CoCr2O4
X-ray absorption
X-ray scattering q(0.63, 0.63, 0)
3d
778 eV
2p3/2
Co
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001
P // -110
q // 110
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reciprocal space
For a given x, switch of chirality d ? - d
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Summary
We can see spin order of TMOs by using
photons.

• Multiferroicity

• ME from an internal field determined by
  .

• CoCr2O4

• Magnetic lock-in transition revealed with
  resonant soft x-ray scattering
• Switch of spin chirality.