ISSP TASSP workshop Jun 19, 2008 Multiferroic behavior in spin-chirality- and...
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Transcript of ISSP TASSP workshop Jun 19, 2008 Multiferroic behavior in spin-chirality- and...
ISSP TASSP workshop Jun 19, 2008
Multiferroic behavior in spin-chirality- and
exchange-striction-driven compounds
Jung Hoon Han (SungKyunKwan U, Korea)
ISSP TASSP workshop Jun 19, 2008
CollaborationCollaboration
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
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.
MotivationMotivation
Nature 426, 55 (2003)
TbMnO3
ISSP TASSP workshop Jun 19, 2008
Magnetic field along a switches
polarization from +b to -b axisin TbMn2O5
Nature 429, 392 (2004)
TbMn2O5
MotivationMotivation
ISSP TASSP workshop Jun 19, 2008
• Exchange-striction-driven, symmetric spin exchange (e.g. TbMn2O5)
• Spin-chirality-driven, anti-symmetric spin exchange (e.g. TbMnO3)
Two types of multiferroicsTwo types of multiferroics
ISSP TASSP workshop Jun 19, 2008
• Spin-chirality-driven, anti-symmetric spin exchange (e.g. TbMnO3)
Part IPart I
ISSP TASSP workshop Jun 19, 2008
Connection of spin chirality (for noncollinear magnetism) to local dipole moment, or ferroelectricity, was noticed after some key neutron experiment
T
From spin chirality to ferroelectricityFrom spin chirality to ferroelectricity
ISSP TASSP workshop Jun 19, 2008
It was soon realized that the relevant physics was in the coupling of the local dipole moment to the local vector spin chirality (vSC)
Vector spin chirality (vSC)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)
ISSP TASSP workshop Jun 19, 2008
For general d-electron configurations
Microscopic Theories (mean-Microscopic Theories (mean-field)field)
M O
ISSP TASSP workshop Jun 19, 2008
Microscopic Theories (mean-field)Microscopic Theories (mean-field)
• H. Katsura, N. Nagaosa, and A. V. Balatsky, PRL 95, 057205 (2005)• JONH, PRB 74, 224444 (2006)• JONH, PRB 76, 023708 (2007)
Spiral, helical, conical spins give uniform polarization
ISSP TASSP workshop Jun 19, 2008
Material d-electronPolarization(C/m2); Q
Specifics
TbMnO3
(Kimura et al Nature 2003;Kenzelman et al PRL 2005)
d4 (t2g)3 (eg)1 800; q~0.27 Orbital order
Ni3V2O8
(Lawes et al PRL 2005)d8 (t2g)6 (eg)2 100; q~0.27 Kagome
Ba0.5Sr1.5Zn2Fe12O22
(Kimura et al PRL 2005)d5 (t2g)3 (eg)2 150 (B=1T); N/A N/A
CoCr2O4 (Yamasaki et al. PRL 2006)
Co2+ : d7 (e)4 (t2)3
Cr3+ : d3 (t2g)32; [qq0] q~0.63 ferrimagnetic
MnWO4
(Taniguchi et al. PRL 2006)d5 (t2g)3 (eg)2
50; q=(-.214, .5, .45
7)N/A
CuFeO2
(Kimura et al PRB 2006)
d5 (t2g)3 (eg)2 400 (B>10T); 1/5<q<1/4
2D triangular;
Field-driven
LiCuVO4
(Naito et al JPSJ 2007)d9 (t2g)6 (eg)3 N/A; q~0.532 1D chain
LiCu2O2 (Park et al PRL 2007)
d9 (t2g)6 (eg)3 <10; q~0.174 1D chainRED = magnetic ions
vSC-driven multiferroicsvSC-driven multiferroics
ISSP TASSP workshop Jun 19, 2008
Microscopic Theories Microscopic Theories (LDA)(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
ISSP TASSP workshop Jun 19, 2008
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
Existing Existing ExperimentsExperiments
T, frustrationSpiralMagnetic
CollinearMagnetic
Paramagnetic
Ferro-electric
ISSP TASSP workshop Jun 19, 2008
T, frustrationMagnetic Chiral Paramgnetic
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)
Ferroelectric
Chiral spin states !
What’s possibleWhat’s possible
ISSP TASSP workshop Jun 19, 2008
Villain’s idea of vSCVillain’s idea of vSC
Villain, JPhysC (1977)
ISSP TASSP workshop Jun 19, 2008
Villain’s idea of vSCVillain’s idea of vSC
ISSP TASSP workshop Jun 19, 2008
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
vSC liquid (vSCL) ?vSC liquid (vSCL) ?
ISSP TASSP workshop Jun 19, 2008
Cinti et al. PRL 100, 057203 (2008)
vSCL found ?vSCL found ?
ISSP TASSP workshop Jun 19, 2008
Quantum spin S=1/2 MultiferroicQuantum spin S=1/2 Multiferroic
Seki et al. arXiv:0801.2533
Park et al. PRL (2007)
ISSP TASSP workshop Jun 19, 2008
Quantum spin S=1/2 MultiferroicQuantum spin S=1/2 Multiferroic
Enderle et al. EPL (2005)
Naito et al JPSJ (2007)
ISSP TASSP workshop Jun 19, 2008
Search for models of vSCLSearch 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
ISSP TASSP workshop Jun 19, 2008
XXZ spin chain (S=1) with nearest and next-nearest neighbor exchange
,1J
,2J
1D model of vSCL (quantum)1D model of vSCL (quantum)
vSC correlation is long-ranged
vSCL found for XY-like, J2-dominant regime of the model
Hikihara et al. JPSJ 69, 259 (2000)
=J2/J1
ISSP TASSP workshop Jun 19, 2008
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)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?
ISSP TASSP workshop Jun 19, 2008
JJ11-J-J22 model on triangular lattice model on triangular lattice
PM = paramagneticaM = (algebraic ordered) magneticaN = (algebraic ordered) nematicC = chirality-ordered
PONH, arXiv:0804.4034
ISSP TASSP workshop Jun 19, 2008
Chirality for JChirality for J11-J-J22 model model
Introduce a vector potential
From the corresponding free energy define the spin current
Staggered sum of the spin current is the vSC
ISSP TASSP workshop Jun 19, 2008
Monte Carlo results for chiralityMonte Carlo results for chirality
Binder cumulant
Finite-SizeScaling
ISSP TASSP workshop Jun 19, 2008
• 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
Summary (Part Summary (Part I)I)
ISSP TASSP workshop Jun 19, 2008
Magnetic field along a switches
polarization from +b to -b axisin TbMn2O3
Nature 429, 392 (2004)
TbMn2O5
Exchange-striction-driven MultiferroicsExchange-striction-driven Multiferroics
ISSP TASSP workshop Jun 19, 2008
Two types of Mn ions:
Mn3+ (oxygen tetrahedron) Mn4+ (oxygen octahedron)
Exchange-striction-driven MultiferroicsExchange-striction-driven Multiferroics
Radaelli et al. PRB (2005); PRL (2004,2006)
ISSP TASSP workshop Jun 19, 2008
Mn3+ (RED) Mn4+ (BLUE)
Interactions along c-axiseither FM or AFM (no frustration)
Project down to 2D (ab plane)without loss of generality
Looking at the Mn Lattice:Looking at the Mn Lattice:
ISSP TASSP workshop Jun 19, 2008
Intra-chain interaction is AFM (no frustration)Inter-chain is also AFM, every other bond is frustratedShifting the spin orientation by one lattice does not lower
energy -> 2-fold degeneracy between every chains -> macroscopic degeneracy
Frustrated Mn spin interactionsFrustrated Mn spin interactions
ISSP TASSP workshop Jun 19, 2008
According to pure Heisenberg exchange, the middle spin is frustrated
It can choose one spin orientation and move toward atoms of opposite
spins, lowering the overall exchange energy
J J
J-J J+J
Exchange-striction PrimerExchange-striction Primer
ISSP TASSP workshop Jun 19, 2008
R
R
RR
R
RR
R
RR
RR
LLL
LLL
LLL
LLL
RR
RRR
R
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RR L R
LL
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DDD
D
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DD(c)(a)
(d)(b)
B
B
Exchange striction causesdisplacement of Mn3+ resulting in net polarization along b axis (consistent with exp.)
Lifts macroscopicdegeneracy
All this well known (S.-W. Cheong, Radaelli, etc.) before I got interested…
OR
Lifting of Degeneracy by Exchange-strictionLifting of Degeneracy by Exchange-striction
ISSP TASSP workshop Jun 19, 2008
Electric polarization, initially along +b, reverses direction due to magnetic field (magneto-electric coupling)
Effects of B field along a-axis on Effects of B field along a-axis on BiMnBiMn22OO55
Kee Hoon Kim et al. Submitted
Dielectric constant along b-axis shows pronounced increases where P=0.
ISSP TASSP workshop Jun 19, 2008
ScalingScaling
ISSP TASSP workshop Jun 19, 2008
P>0 and P<0 regions are separated by a line as if by a phase transition
Genuine 2nd order PT is impossible
Phase diagram of BiMnPhase diagram of BiMn22OO55
First-order PT
ISSP TASSP workshop Jun 19, 2008
Why P changes sign under H field?
Why apparent critical behavior near Hc ?
What we need to knowWhat we need to know
ISSP TASSP workshop Jun 19, 2008
R
R
RR
R
RR
R
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RR
LLL
LLL
LLL
LLL
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RRR
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RR L R
LL
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LLL
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UD D
UD
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DD
DDD
D DD
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DD D
DDD
D
DD
DD(c)(a)
(d)(b)
B
B
In an ordinary AFM, H field will causespin flop. All spins will rotate either CWor CCW as to be orthogonal to B field
The relative spin orientations will be thesame after spin flop, hence no changein exchange striction force (~Si * Sj)
-> Can’t explain experiment
Suggestion: Perhaps each spin chainundergoes spin flop with different senseof rotations… (possible since inter-chaincoupling is weak)
Understanding Polarization ReversalUnderstanding Polarization Reversal
ISSP TASSP workshop Jun 19, 2008
0 1 2 3 4 5
- 3
- 2
- 1
0
1
2
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P
H
0 1 2 3 4 5
0
10
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Su
sc
ep
tib
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H
Preliminary MC dataPreliminary MC data
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
• 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
Summary (Part Summary (Part II)II)
ISSP TASSP workshop Jun 19, 2008
2D model of vSCL (quantum) ??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:
ISSP TASSP workshop Jun 19, 2008
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 vSC-ordered state in the spin picture (Dillenschneider et al. arXiv:0705.3993)
Analogy with persistent Analogy with persistent currentcurrent