Finite Temperature Spin Correlations in Quantum Magnets with a Spin Gap Collin Broholm* Johns...
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Transcript of Finite Temperature Spin Correlations in Quantum Magnets with a Spin Gap Collin Broholm* Johns...
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
ICM2000 8/11/00
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
ICM2000 8/11/00
Focusing analyzer system on SPINS
Y2BaNiO5 Ito, Oka, and Takagi
Cu(NO3)2.2.5 D2O
Guangyong Xu
ICM2000 8/11/00
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!
ICM2000 8/11/00
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
ICM2000 8/11/00
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
ICM2000 8/11/00 q~
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
ICM2000 8/11/00
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
ICM2000 8/11/00
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
ICM2000 8/11/00
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