Vector spin chirality in classical

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Vector spin chiralityin classical quantum
spin systems
Jung Hoon Han (SKKU)
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Collaboration
Jung Hoon Kim, Jin Hong Park (SKKU) Shigeki Onoda
(RIKEN) Naoto Nagaosa (U. Tokyo) Chenglong Jia
(Germany) Raoul Dillenschneider (Augsburg)
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Motivation
A class of materials with strong coupling of spin
lattice (orbital) degrees of freedom were
(re)discovered. One stark manifestation of the
coupling is the control of ferroelectric
polarization using only the magnetic field.
Nature 426, 55 (2003)
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Two types of improper multiferroics

• Exchange-striction-driven (RMn2O5)
• Spin-chirality-driven

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Vector spin chirality (vSC)
It was soon realized that the relevant physics
was in the coupling of the local dipole moment to
the local vector spin chirality (vSC)

• Noncollinear magnetic states possess a nonzero
  vSC
• Idea of non-magnetic, but vSC-ordered magnetic
  state goes back as early as Villain, J. Phys. C
  10, 4793 (1977). Other theoretical works on vSC
• S. Miyashita and H. Shiba, J. Phys. Soc. Jpn.
  53, 1145 (1984).
• H. Kawamura and M. Tanemura, Phys. Rev. B 36,
  7177 (1987).
• H. Kawamura, J. Phys. Condens. Matter 10, 4707
  (1998).

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Connection to ferroelectricity
Connection of vSC to local dipole moment, or
ferroelectricity, was noticed after some key
neutron experiment
T
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Same symmetry !

• With spiral magnetism one can define a SENSE of
  ROTATION, which is equivalent to the vSC
• The forward-rotating spins produce UP
  polarization, the backward-rotating spins produce
  DOWN polarization, or vice versa.
• Symmetry arguments for multiferroic materials are
  worked out in
• A. B. Harris, Phys. Rev. B 76, 054447 (2007).
• T. Arima, JPSJ 76, 073702 (2007) CuFeO2

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Bookkeeping of chiral multiferroics
Material d-electron Polarization (?C/m2) Q Specifics
TbMnO3 (Kimura et al Nature 2003 Kenzelman et al PRL 2005) d4 (t2g)3 (eg)1 800 q0.27 Orbital order
Ni3V2O8 (Lawes et al PRL 2005) d8 (t2g)6 (eg)2 100 q0.27 Kagome
Ba0.5Sr1.5Zn2Fe12O22 (Kimura et al PRL 2005) d5 (t2g)3 (eg)2 150 (B1T) N/A N/A
CoCr2O4 (Yamasaki et al. PRL 2006) Co2 d7 (e)4 (t2)3 Cr3 d3 (t2g)3 2 qq0 q0.63 ferrimagnetic
MnWO4 (Taniguchi et al. PRL 2006) d5 (t2g)3 (eg)2 50 q(-.214, .5, .457) N/A
CuFeO2 (Kimura et al PRB 2006) d5 (t2g)3 (eg)2 400 (Bgt10T) 1/5ltqlt1/4 2D triangular Field-driven
LiCuVO4 (Naito et al JPSJ 2007) d9 (t2g)6 (eg)3 N/A q0.532 1D chain
LiCu2O2 (Park et al PRL 2007) d9 (t2g)6 (eg)3 lt10 q0.174 1D chain
RED magnetic ions
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Microscopic Theories (mean-field)
TbMnO3
Mn d orbitals are orbitally ordered Magnetic
interaction contain both ferro and
antiferro Exchanges fertile ground for
frustrated magnetism
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Microscopic Theories (mean-field)
For general d-electron configurations
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Microscopic Theories

• H. Katsura, N. Nagaosa, and A. V. Balatsky, PRL
  95, 057205 (2005)
• JONH, PRB 74, 224444 (2006)
• JONH, PRB 76, 023708 (2007)

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Microscopic Theories (LDA)
Mean-field calculation reflects distortion of
electronic wave functions due to spiral magnetic
order The mechanism is the spin-orbit
coupling The wave function distortion would
generically lead to internal electric field,
which would tend to displace ions, and generate
dipole moments LDA calculation reflects the
atomic movement better than MF calculation (Xiang
Whangbo, PRL (2007)
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Microscopic Theories (LDA)
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Existing Experiments
Often, there is a first magnetic transition to
COLLINEAR spin states, for which no polarization
is induced A second transition at a lower
temperature to spiral spin states cause nonzero
polarization
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Whats possible
Can we envision a phase without magnetic order,
but still has the remnant of vSC (vector spin
chirality) ? Theoretically certainly possible.
vSCL (vector spin chiral liquid)
Chiral spin states !
T, frustration
Magnetic
Chiral
Paramgnetic
Ferroelectric
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Villains idea of vSC
Villain, JPhysC (1977)
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Ginzburg-Landau theory of vSCL
Recent work Ginzburg-Landau calculation showed
possibility of a chiral spin liquid phase with
sufficient frustration
Onoda Nagaosa PRL 99, 027206 (2007)
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Quantum spin S1/2 Multiferroic
Seki et al. arXiv0801.2533
Park et al. PRL (2007)
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Quantum spin S1/2 Multiferroic
Enderle et al. EPL (2005)
Naito et al JPSJ (2007)
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Search for models of vSCL
Both materials are exciting due to quantum nature
of S1/2 spins and the 1D character of spin
network However, the ferroelectricity is
concomitant with spiral magnetic ordering Not a
true vSCL yet
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vSCL found ?
Cinti et al. PRL 100, 057203 (2008)
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Search for models of vSCL
In light of recent developments, search for model
Hamiltonians (both classical quantum) where the
ground state supports ordered vSC but no ordering
of magnetic moments There is already some
evidence from GL theory A 1D microscopic
calculation exists for a 1D spin model We know
little about 2D vSCL A classical 2D model with
ordered vSC but no magnetic moment may have been
found (arXiv0804.4034)
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1D model of vSCL (quantum)
XXZ spin chain (S1/2) with nearest and
next-nearest neighbor exchange
Hikihara et al. JPSJ 69, 259 (2000)
vSCL found for XY-like, J2-dominant regime of
the model
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Furukawa et al. arXiv0802.3256v1
A recent calculation of Furukawa et al. confirmed
existence of vCSL phase in the same model
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2D model of vSCL (quantum) ??
In 2D we do not seem to have any idea how to
write down a quantum spin model with long-range
vSC correlation 2D vSC solid state can be
generated easily with Dzyaloshinskii-Moriya
interaction
1D example
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Analogy with persistent current
For S1/2, Jordan-Wigner mapping gives
Spin chirality maps onto bond current
A current-flowing ground state in the fermion
picture corresponds to vSC-ordered state in the
spin picture (Dillenschneider et al.
arXiv0705.3993)
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2D model of vSCL (classical)
A similar manipulation can be made in 2D to
obtain vSCS A true vSCL state is still out of
reach We recently re-examined AFM XY model on
triangular lattice with huge bi-quadratic
exchange
Magnetic order -gt vSC order But can vSC order
first before magnetism does?
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J1-J2 model on triangular lattice
PONH, arXiv0804.4034
vSC ordering occurs below RED curve Magnetic
ordering occurs below BLACK BLUE curve The
region xgtxc supports vSCL phase with condensation
of vSC, but no magnetic ordering has yet occurred
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Summary

• We have come a long way since the initial
  discovery of multiferroicity in
• understanding the coupling of vSC and local
  electric dipoles
• An interesting possibility of purely vSC-ordered
  liquid phase is opening up
• (GL theory, 1D quantum spin models and
  compounds)
• A 2D classical model which supports vSCL phase
  seems feasible
• (2D AFM XY on triangular lattice)
• 2D quantum model with vSCL ground state will be
  exciting