Finite Temperature Spin Correlations in Quantum Magnets with a Spin Gap

Collin Broholm*Johns Hopkins University and NIST Center for Neutron Research

*supported by the NSF through DMR-0074571

Ca2+

Y3+

Quantum Magnets at T=0From coherent singlet to paramagnet - Large gap : Coupled spin-1/2 dimers - Small gap : Haldane spin-1 chain Conclusions

Guangyong Xu and D. H. ReichPhysics and Astronomy, Johns Hopkins University

G. Aeppli, M. E. Bisher, and M. M. J. Treacy

NEC Research Institute

J. F. DiTusaPhysics and Astronomy, Lousiana State University

C. D. Frost and M. A. AdamsISIS Facility Rutherford Appleton Laboratory

T. Ito K. OkaElectrotechnical Laboratory, Japan

H. TakagiISSP, University of Tokyo

A. Tennant, G. Granroth, and S. NaglerOak Ridge National Laboratory

Colla

bora

tors

Colla

bora

tors

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Magnetic Neutron Scattering

fi kkQ

fi EE

ikfk

Q

2

RR'RR

RRQQ )(S)0(1

2

1),( '

' tSeN

edt iti

S

ICM2000 8/11/00SPINS Cold neutron triple axis spectrometer at NCNR

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Focusing analyzer system on SPINS

Y2BaNiO5 Ito, Oka, and Takagi

Cu(NO3)2.2.5 D2O

Guangyong Xu

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Simple example of “Quantum” magnet

Cu(NO3)2.2.5D2O : dimerized spin-1/2 system

Only Inelastic magnetic scatteringOnly Inelastic magnetic scattering

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Dispersion relation for triplet waves

Dimerized spin-1/2 system: copper nitrate

JTkB

Xu et al PRL May 2000

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A spin-1/2 pair with AFM exchange has a singlet - triplet gap:

Qualitative description of excited states

J0totS

1totS

Inter-dimer coupling allows coherent triplet propagation and

produces well defined dispersion relation

Triplets can also be produced in pairs with total Stot=1

Creating two triplets with one neutron

One magnonOne magnon

Two magnonTwo magnon

Tennant et al (2000)

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Heating coupled dimers

q~

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SMA fit to scattering data

T-Parameters extracted from fit

qJ

TnJq ~cos2

~ 21

TdSS0

qq ~cos2

~ 10

More than 1000 data points per parameter!

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T-dependence of singlet-triplet mode

100 10

SSTd

SS SS

10 SSTn

)exp()( 11 TkJTk

JT B

B

meV)2(10.0

)2(0.1

meV)4(13.0

)2(6.0

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Types of Quantum magnets

Definition: small or vanishing frozen moment at low T:

Conditions that yield quantum magnetism Low effective dimensionality Low spin quantum number geometrical frustration dimerization weak connectivity interactions with fermions

Novel coherent states

JTkS B S for

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2

Y2BaNiO5 : spin 1 AFM

One dimensional spin-1 antiferromagnet Y2BaNiO5

Ni 2+

Impure

Pure

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Macroscopic singlet ground state of S=1 chain

• This is exact ground state for spin projection Hamiltonian

• Magnets with 2S=nz have a nearest neighbor singlet covering with full lattice symmetry.

• Excited states are propagating bond triplets separated from the ground state by an energy gap .J

Haldane PRL 1983Affleck, Kennedy, Lieb, and Tasaki PRL 1987

i

iii

iiiii

toti SP 12

131

12 SSSSSSH

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Two length scales in a quantum magnet

q~2

Y2BaNiO5 : spin 1 AFMEqual time correlation length

ll

SS

llqiSSN

qS

qSqS

l

llll

exp1

~exp1~

,~~

0

d

Triplet Coherence length :length of coherent triplet wave packet

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Coherence in a fluctuating system

Coherent tripletpropagation

Short range G.S.spin correlations

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Mix in thermally excited triplets

Coherence length

approaches

Correlation length

for

Coherence length

approaches

Correlation length

for BkT

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Coherence and correlation lengths versus T

Damle and Sachdev semi-classical theory of triplet scattering

Damle and Sachdev semi-classical theory of triplet scattering

Jolicoeur and GolinellyQuantum non-linear model

Jolicoeur and GolinellyQuantum non-linear model

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q=Triplet creation spectrum versus T

Triplet relaxes due to interaction with thermal triplet ensemble

Triplet relaxes due to interaction with thermal triplet ensemble

There is slight “blue shift”with increasing TThere is slight “blue shift”with increasing T

Anisotropy fine structure

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Resonance energy and relaxation rate versus T

Jolicoeur and GolinelliQuantum non-linear modelJolicoeur and GolinelliQuantum non-linear model

Tk

Tk

vT

B

B

TS

exp3

21

Damle and Sachdev

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ConclusionsStrong coupling : Alternating spin chain

Thermally activated triplet relaxation Wave-vector dependent relaxation Thermally activated band narrowing

Weak coupling : Haldane spin-1 chain Coherence length decreases with mean triplet spacing model accounts for T-dependent equal-t correlation length Triplet relaxation due to semi classical triplet scattering -model over estimates thermally activated blue shift

Notable strong/weak coupling differences Different power-law pre-factor to T-dependent

relaxation rate Theory not yet in place for strong coupling case