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)


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)


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


Magnetic field along a switches

polarization from +b to -b axisin TbMn2O5

Nature 429, 392 (2004)

TbMn2O5

MotivationMotivation


• 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


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

Part IPart I


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


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)


For general d-electron configurations

Microscopic Theories (mean-Microscopic Theories (mean-field)field)

M O


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


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


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


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


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


Villain’s idea of vSCVillain’s idea of vSC

Villain, JPhysC (1977)


Villain’s idea of vSCVillain’s idea of vSC


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) ?


Cinti et al. PRL 100, 057203 (2008)

vSCL found ?vSCL found ?


Quantum spin S=1/2 MultiferroicQuantum spin S=1/2 Multiferroic

Seki et al. arXiv:0801.2533

Park et al. PRL (2007)


Quantum spin S=1/2 MultiferroicQuantum spin S=1/2 Multiferroic

Enderle et al. EPL (2005)

Naito et al JPSJ (2007)


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


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


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


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?


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


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


Monte Carlo results for chiralityMonte Carlo results for chirality

Binder cumulant

Finite-SizeScaling


• 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)


Magnetic field along a switches

polarization from +b to -b axisin TbMn2O3

Nature 429, 392 (2004)

TbMn2O5

Exchange-striction-driven MultiferroicsExchange-striction-driven Multiferroics


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)


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:


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


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


R

R

RR

R

RR

R

RR

RR

LLL

LLL

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RR

RRR

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RRR

RR L R

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UD D

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D

DD

DDD

D DD

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D

DD D

DDD

D

DD

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


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.


ScalingScaling


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


Why P changes sign under H field?

Why apparent critical behavior near Hc ?

What we need to knowWhat we need to know


R

R

RR

R

RR

R

RR

RR

LLL

LLL

LLL

LLL

RR

RRR

R

RRR

RR L R

LL

L

L

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U

U

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UD D

UD

D

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


0 1 2 3 4 5

- 3

- 2

- 1

0

1

2

3

4

P

H

0 1 2 3 4 5

0

10

20

30

40

50

60

70

Su

sc

ep

tib

ility

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!


• 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)


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:


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

issp tassp workshop jun 19, 2008 multiferroic behavior in spin-chirality- and...

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