Transcript Holes in a Quantum Spin Liquid

Finite Temperature Spin Correlations
in Quantum Magnets with a Spin Gap
Collin Broholm*
Johns Hopkins University and NIST Center for Neutron Research
Quantum Magnets at T=0
From coherent singlet to paramagnet
Y3+
- Large gap : Coupled spin-1/2 dimers
- Small gap : Haldane spin-1 chain
Ca2+
Conclusions
*supported by the NSF through DMR-0074571
G. Aeppli, M. E. Bisher, and M. M. J. Treacy
NEC Research Institute
J. F. DiTusa
Physics and Astronomy, Lousiana State University
C. D. Frost and M. A. Adams
ISIS Facility Rutherford Appleton Laboratory
T. Ito K. Oka
Electrotechnical Laboratory, Japan
H. Takagi
ISSP, University of Tokyo
A. Tennant, G. Granroth, and S. Nagler
Oak Ridge National Laboratory
Collaborators
Collaborators
Guangyong Xu and D. H. Reich
Physics and Astronomy, Johns Hopkins University
Magnetic Neutron Scattering
ki
2
Q
kf
Q  ki  k f
  E i  E f
1
it 1
iQ R  R ' 


S (Q,  ) 
dt
e
e

S
(
0
)
S


R
R ' (t ) 
2
N RR'

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SPINS Cold neutron triple axis spectrometer at NCNR
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Focusing analyzer system on SPINS
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Y2BaNiO5
Ito, Oka, and Takagi
Cu(NO3)2.2.5 D2O
Guangyong Xu
Simple example of “Quantum” magnet
Cu(NO3)2.2.5D2O : dimerized spin-1/2 system
Only Inelastic
magnetic scattering
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Dispersion relation for triplet waves
Dimerized spin-1/2 system: copper nitrate
kBT  J
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Xu et al PRL May 2000
Qualitative description of excited states
 A spin-1/2 pair with AFM exchange has a singlet - triplet
gap:
J
Stot  1
Stot  0
 Inter-dimer coupling allows coherent triplet propagation
and
produces well defined dispersion relation
 Triplets can also be produced in pairs with total Stot=1
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Creating two triplets with one neutron
Two magnon
One magnon
Tennant et al (2000)
Heating coupled dimers
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q~  
SMA fit to scattering data
T-Parameters
extracted from fit
S0 S d
T
J2
~
 q   J1  nT  cos q~
2
1
~
q   0  cos q~
2
More than 1000 data
points per parameter!
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T-dependence of singlet-triplet mode
 S0  S d
0
T
 S S  1 S 0   S 1 
nT    S 0   S 1
  1.0(2)
  0.10(2) meV
  0 . 6 ( 2)
  0.13(4) meV
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
 J1 
 exp(  J1 k BT )
(T )   
 k BT 
Types of Quantum magnets
Definition: small or vanishing frozen moment at low T:
S  S for k BT  J
Conditions that yield quantum magnetism
Low effective dimensionality
Low spin quantum number
geometrical frustration
dimerization
weak connectivity
interactions with fermions
Novel coherent states
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One dimensional spin-1 antiferromagnet
Y2BaNiO5
Y2BaNiO5 : spin 1 AFM
Ni 2+
Impure
Pure
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q~  
2
Macroscopic singlet ground state of S=1
chain
• Magnets with 2S=nz have a nearest neighbor singlet covering
with full lattice symmetry.
• This is exact ground state for spin projection Hamiltonian


H   Pi Stot  2   Si  Si 1  Si  Si 1    Si  Si 1
i
i
1
3
2
i
• Excited states are propagating bond triplets separated from the
ground state by an energy gap   J .
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Haldane PRL 1983
Affleck, Kennedy, Lieb, and Tasaki PRL 1987
Two length scales in a quantum magnet
Equal time correlation length
S q~    S q~,   d
Y2BaNiO5 : spin 1 AFM

1
~
S q  
N

ll 
Sl Sl exp iq~ l  l 
1
S 0 Sl 
exp   l 


l
Triplet Coherence length :
length of coherent triplet
wave packet
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q~  
2
Coherence in a fluctuating system
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  
Short range G.S.
spin correlations
  
Coherent triplet
propagation
Mix in thermally excited triplets
Coherence length
approaches
Correlation length

T

for
k
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B
Coherence and correlation lengths versus
T
Damle and Sachdev
semi-classical theory of triplet scattering
Jolicoeur and Golinelly
Quantum non-linear s model
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q= Triplet creation spectrum versus T
Anisotropy fine structure
Triplet relaxes due to
interaction with thermal
triplet ensemble
There is slight “blue shift”
with increasing T
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Resonance energy and relaxation rate versus T
Jolicoeur and Golinelli
Quantum non-linear s model
Damle and Sachdev
    S 1 T 

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v2
T
 
exp  

 k BT
3k BT



Conclusions
Strong 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
s model accounts for T-dependent equal-t correlation length
Triplet relaxation due to semi classical triplet scattering
s-model over estimates thermally activated blue shift
Notable strong/weak coupling differences
Different power-law pre-factor to T-dependent relaxation
rate
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