Multiferroic behavior in spin-chirality- and exchange-striction-driven compounds

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Multiferroic behavior in spin-chirality-
andexchange-striction-driven compounds
Jung Hoon Han (SungKyunKwan U, Korea)
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Collaboration
Jung Hoon Kim, Jin Hong Park (SKKU) Kee Hoon Kim
(SNU) 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 or electronic degrees of freedom were
(re)discovered. One stark manifestation of the
coupling is the control of ferroelectric
polarization using only the magnetic field.
TbMnO3
Nature 426, 55 (2003)
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Motivation
TbMn2O5
Magnetic field along a switches polarization
from b to -b axis in TbMn2O5
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Two types of multiferroics

• Exchange-striction-driven,
• symmetric spin exchange
• (e.g. TbMn2O5)
• Spin-chirality-driven,
• anti-symmetric spin exchange
• (e.g. TbMnO3)

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Part I

• Spin-chirality-driven,
• anti-symmetric spin exchange
• (e.g. TbMnO3)

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From spin chirality to ferroelectricity
Connection of spin chirality (for noncollinear
magnetism) to local dipole moment, or
ferroelectricity, was noticed after some key
neutron experiment
T
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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 vSC breaks inversion symmetry, preserves
time-reversal, thats the same symmetry as the
local dipole moment
Mostovoy PRL96, 067601 (2006)
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Microscopic Theories (mean-field)
For general d-electron configurations
M
O
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Microscopic Theories (mean-field)
Spiral, helical, conical spins give uniform
polarization

• 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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vSC-driven 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 (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)
• Recent LDA works on TbMnO3

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Existing Experiments
Often, there is first a 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
T, frustration
Spiral Magnetic
Collinear Magnetic
Paramagnetic
Ferro- electric
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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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Villains idea of vSC
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vSC liquid (vSCL) ?
Can we have an example of non-magnetic,
chirality-ordered phase? There had been
discussions of vSCL in classical models of AFM
with frustration No analogous efforts for
quantum spin cases until recently It is entirely
possible that coupling to ferroelectric moment
occurs in non-magnetic, yet vSC-ordered phase (a
exotic new matter?) Perhaps low-D, small-S
(highly quantum), highly frustrated spin systems
are a good place to look for vSCL
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vSCL found ?
Cinti et al. PRL 100, 057203 (2008)
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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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1D model of vSCL (quantum)
XXZ spin chain (S1) with nearest and
next-nearest neighbor exchange
Hikihara et al. JPSJ 69, 259 (2000)
vSC correlation is long-ranged vSCL found for
XY-like, J2-dominant regime of the model
J2/J1
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Furukawa et al. arXiv0802.3256v1
A recent calculation of Furukawa et al. confirmed
existence of vSCL phase in the same model with
S1/2
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2D model of vSCL (classical)
We recently re-examined AFM XY model on
triangular lattice with huge bi-quadratic
exchange
Magnetic ordering naturally leads to vSC, but can
the converse be also true?
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J1-J2 model on triangular lattice
PONH, arXiv0804.4034
PM paramagnetic aM (algebraic ordered)
magnetic aN (algebraic ordered) nematic C
chirality-ordered
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Chirality for J1-J2 model
Introduce a vector potential
From the corresponding free energy define the
spin current
Staggered sum of the spin current is the vSC
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Monte Carlo results for chirality
Finite- Size Scaling
Binder cumulant
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Summary (Part I)

• 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

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Exchange-striction-driven Multiferroics
TbMn2O5
Magnetic field along a switches polarization
from b to -b axis in TbMn2O3
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Exchange-striction-driven Multiferroics
Radaelli et al. PRB (2005) PRL (2004,2006)
Two types of Mn ions Mn3 (oxygen tetrahedron)
Mn4 (oxygen octahedron)
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Looking at the Mn Lattice
Mn3 (RED) Mn4 (BLUE) Interactions along
c-axis either FM or AFM (no frustration)
Project down to 2D (ab plane) without loss of
generality
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Frustrated Mn spin interactions
Intra-chain interaction is AFM (no
frustration) Inter-chain is also AFM, every other
bond is frustrated Shifting the spin orientation
by one lattice does not lower energy -gt 2-fold
degeneracy between every chains -gt macroscopic
degeneracy
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Exchange-striction Primer
J
J
According to pure Heisenberg exchange, the middle
spin is frustrated
J?J
J-?J
It can choose one spin orientation and move
toward atoms of opposite spins, lowering the
overall exchange energy
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Lifting of Degeneracy by Exchange-striction
Exchange striction causes displacement of Mn3
resulting in net polarization along b axis
(consistent with exp.) Lifts macroscopic degener
acy All this well known (S.-W. Cheong,
Radaelli, etc.) before I got interested
OR
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Effects of B field along a-axis on BiMn2O5
Kee Hoon Kim et al. Submitted
Dielectric constant along b-axis shows pronounced
increases where P0.
Electric polarization, initially along b,
reverses direction due to magnetic field
(magneto-electric coupling)
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Scaling
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Phase diagram of BiMn2O5
First-order PT
Pgt0 and Plt0 regions are separated by a line as if
by a phase transition Genuine 2nd order PT is
impossible
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What we need to know
Why P changes sign under H field? Why apparent
critical behavior near Hc ?
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Understanding Polarization Reversal
In an ordinary AFM, H field will cause spin flop.
All spins will rotate either CW or CCW as to be
orthogonal to B field The relative spin
orientations will be the same after spin flop,
hence no change in exchange striction force (Si
Sj) -gt Cant explain experiment Suggestion
Perhaps each spin chain undergoes spin flop with
different sense of rotations (possible since
inter-chain coupling is weak)
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Preliminary MC data
The spins do rotate CW for even chains, CCW for
odd chains good pairs become bad pairs and vice
versa -gt explains polarization reversal Surprisin
gly, susceptibility (dielectric constant) shows a
peak!
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Summary (Part II)

• A class of compounds RMn2O5 are examples of
  exchange-striction-driven multiferroicity
• An interesting polarization reversal and sharp
  increase in dielectric susceptibility was
  observed in high-field experiment on BiMn2O5
• A model with both frustrated spin-spin
  interaction and exchange-striction coupling with
  reasonable agreement with experimental findings
• The precise critical nature of P remains to be
  understood

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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)