Magnetic Interactions andOrder-out-of-disorderin Insulating Oxides

Ora Entin-Wohlman, A. Brooks Harris, Taner Yildirim

Robert J. Birgeneau, Marc A. Kastner, Koichi Katsumata

R. Ramirez, C. Broholm, J. W. Lynn

TAU, BGU, U Penn, NIST, MIT, RIKEN, Lucent, JHU

Les Houches summer school on Quantum Magnetism, June 2006

Amnon Aharony

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Lecture 3:

Vanadates:

Competing nn and nnn interactions yieldIncommensurate order

Competing anisotropies yield complex field dependent phase diagrams

Ni and Co have very different magnetic structures

Theoretical tools introduced in pervious lectures suffice to explain most features

3

General outline:

Cuprates

VanadatesLecture 3

4

823 OVCoBuckled Kagome

823 OVNiS=1 S=3/2

5

823 OVCo

Buckled Kagome

823 OVNi

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Crystal Structure of Ni3V2O8

c

a

b

Cross-tie Spine

Only magnetic (S=1) Ni ions are shown

Cross-tie is

FRUSTRATED

?

7

823 OVNi

8

0

5

0

5

0

5

Ma

gn

etic

Fie

ld (

T)

0 2 4 6 8 10

Temperature (K)

H || a

H || b

H || c

9

10

Specific heat

Neutron scattering intensities in C, LTI and HTI

Incommensurate wave vector

Weak ferromagnetism in C phase

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CAF’ = Incommensurate?

Paramagnetic

HTI = High TemperatureIncommensurate Phase

LTI = Low TemperatureIncommensurate Phase

CAF = Antiferromagnetic + weakly ferromagnetic

MAGNETIC PHASE DIAGRAM OF Ni3V2O8

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MAGNETIC PHASE DIAGRAM OF Ni3V2O8

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Theory

Step I: Main interactions along spines:

Superexchange, Ni—O—Ni and Ni—O—O--Ni

AHSSJSSJH )()( 312211

O

Ni Ni

O O

Ni Ni

Explain HTI, LTI, CAF

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Incommensurability? -- simplest model:

AHSSJSSJH )()( 312211

)0),sin(),cos(cos((

)0,0),cos((

21

qnaSqnaSS

qnaSS

n

nHTI

LTI

)4/()cos( 21 JJqa

At low T, anisotropy wins again CAF

(q locked in)

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Step II: Anisotropy comes from spin orbit interactions

Spin-orbit interaction generates Antiferromagnetic bond-dependent

spin anisotropy

Also Dzyaloshinskii-Moria antisymmetric exchange

Ni Ni

O

Oxygen tilted along z D along y, AFM along x FM along z

Bilinear coupling between staggered Moment along a and ferromagneticMoment along c

16

xy

I1 I2

II

xy

I1 I2

II

Step III: spin on cross-tie NI? Pseudodipolar interactions

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More recent results: Multiferroic behavior

Ferroelectric moment alongb, only in LTI phase!

Can switch ferroelectric moment with magnetic field!

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PHASE DIAGRAM SPONTANEOUS POLARIZATION

Ma

gn

etic

Fie

ld (

T)

0

5

0

5

0

5

0 2 4 6 8 10Temperature (K)

ab

P( C

/m2 )

T=5K

P || b

H || c

T=4K

H || a

H || c

0 0.5 1 1.5 2 2.5 3 3.5

Magnetic Field (T)

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LANDAU THEORY WITH TWO ORDER PARAMETERS

4242)()( PdPTTcMbMTTaF PM

THIS DOES NOT WORK!!

WE DO NOT BELIEVE IN ACCIDENTALDEGENERACY (TP = TM). ALSO BOTHM AND P DEPEND STRONGLY ON H, SO

xMPPbMTTaF M

22)(

THEN, WHEN WE MINIMIZE WITH RESPECT TO P, P APPEARS ONLY WHEN M IS NONZERO:

xMP const

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MAGNETOELECTRIC COUPLING

PqqaH yxxy

yx

)()(,,

where x,y are LTI or HTI and = x,y,z

In the HTI phase we have a single order parameterwhich has a node at some lattice site. About thissite there will be inversion symmetry. So

I )q( = )-q( = )q(* I = inversion operator

q) = (-q)* is an order parameter

PqaH |)(| 2 = 0 ) IH = H(

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MANETOELECTRIC INTERACTION

Thus the trilinear magnetoelectricinteraction is of the form

H = HTI LTI P + d P2

So, after we minimize with respect to P:

P = const HTI LTI = const LTI

This qualitatively explains the dependence of P on T and H

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Confirm mean field trilinear term from microscopic Hamiltonian

Can arise from DM and PD interactions

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B2u-phononsMode Number: 64Mode Energy: 69.24 meV (experimental value is about 80 meV!)

Mode Description: Two oxygen atoms connected to cross-tie Ni moves along b-axis, significantly effecting the Ni-O-Ni bond angle for the spine spins (see the animations; side and top views).

Dipole Moment: 0.4612 (One of the largest dipole moment!)

b-axis

Spine-spins (a-axis)

Cross-tieConnected to V

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25 Phys. Rev. B, in press

26 (Spins along spine parallel to each other)

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FM, =0

AFM, =1/2

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Theory

x(J3)

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Quartic terms

Higher harmonics

Lock-in

Lock-in

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Dielecric constant

Ferroelectricity???

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Conclusions:

Vanadates are almost frustrated; interesting phase diagrams

Can explain incommensurate phases by competing interactions

Multiferroics!

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THE END