Transcript Multiferroic behavior in spin-chirality and exchange-striction

Multiferroic behavior in
spin-chirality- and
exchange-striction-driven
compounds
Jung Hoon Han
(SungKyunKwan U, Korea)
ISSP TASSP workshop Jun 19, 2008
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)
ISSP TASSP workshop Jun 19, 2008
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
Nature 429, 392 (2004)
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)
ISSP TASSP workshop Jun 19, 2008
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, that’s 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)
ISSP TASSP workshop Jun 19, 2008
vSC-driven multiferroics
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 JPSJ 2007)
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
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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
Spiral
Magnetic
Collinear
Magnetic
Paramagnetic
T, frustration
Ferroelectric
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What’s 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 !
Magnetic
Chiral
Paramgnetic
T, frustration
Ferroelectric
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Villain’s idea of vSC
Villain, JPhysC (1977)
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Villain’s 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 nonmagnetic, 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 S=1/2
Multiferroic
Seki et al. arXiv:0801.2533
Park et al. PRL (2007)
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Quantum spin S=1/2
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 S=1/2 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 (S=1) with nearest and next-nearest neighbor exchange
J1 , 
J2 , 
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. arXiv:0802.3256v1
A recent calculation of Furukawa et al. confirmed existence of vSCL phase
in the same model with S=1/2
ISSP TASSP workshop Jun 19, 2008
2D model of vSCL (classical)
We recently re-examined AFM XY model on triangular lattice with huge biquadratic 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, arXiv:0804.4034
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
FiniteSize
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
Nature 429, 392 (2004)
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 -> 2-fold
degeneracy between every chains -> 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
(c)
(a)
R
L
R
L
R
L
R
L
R
L
R
L
R
L
R
L
R
L
R
L
R
L
R
L
OR
(b)
L
R
L
R
L
R
R
L
R
L
R
L
L
R
L
R
L
R
R
L
R
L
R
L
D
D
D
U
U
U
Exchange
striction
causes
displacement
D
D
U
U ofD
U
Mn3+ resulting in
D
D
U
U
D
netUpolarization
along
bDaxisU
D
U
D
U
(consistent with exp.)
B
Lifts macroscopic
(d) D
D
U
U
D
U
degeneracy
U
D
U
D
U
D
U
D
U
D
U
D
All this well known
(S.-W.
Cheong,
D
U
D
URadaelli,
D
U etc.)
before I got interested…
B
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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 P=0.
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
P>0 and P<0 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
(c)
(a)
R
L
R
L
R
L
R
L
R
L
R
L
R
L
R
L
R
L
R
L
R
L
R
L
D
D
D
U
U
U
In an ordinary
AFM,
H field
will
cause
spin flop. All spins will rotate either CW
D
D
D
U
U
or CCWUas to be orthogonal
to B field
U
D
U
D
U
D
The relative spin orientations will be the
same after spin
flop, hence no change
D
D
U
U
D
U
in exchange striction force (~Si * Sj)
B
-> Can’t explain experiment
(b)
L
R
L
R
L
R
R
L
R
L
R
L
L
R
L
R
L
R
R
L
R
L
R
L
(d)
D
U
D
U
D
U
Suggestion: Perhaps each spin chain
D
D
D
U
U
U
undergoes
spin flop
with different
sense
of rotations… (possible since inter-chain
D
U
D
U
D
U
coupling is weak)
U
D
U
D
U
D
B
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Preliminary MC data
70
4
60
Susceptibility
3
2
P
1
0
-1
-2
50
40
30
20
10
0
-3
0
1
2
3
H
4
5
0
1
3
2
4
5
H
The spins do rotate CW for even chains, CCW for odd chains; good pairs
become bad pairs and vice versa -> explains polarization reversal
Surprisingly, susceptibility (dielectric constant) shows a peak!
ISSP TASSP workshop Jun 19, 2008
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 S=1/2, Jordan-Wigner mapping gives
Spin chirality maps onto bond current
A current-flowing ground state in the fermion picture corresponds to vSCordered state in the spin picture (Dillenschneider et al. arXiv:0705.3993)
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