Transcript Holes in a Quantum Spin Liquid

Holes in a Quantum Spin
Liquid
Collin Broholm*
Johns Hopkins University and NIST Center for Neutron Research
Strongly Fluctuating Condensed Matter
Magnetism in one dimension
Y2-xCaxBaNiO5
Pure systems versus T
alternating spin-1/2 chain
Uniform spin-1 chain
Doped systems
Edge states in Mg-doped Y2BaNiO5
Spin polarons in Ca-doped Y2BaNiO5
Conclusions
*supported by NSF DMR-0074571
Ying Chen
Guangyong Xu
G. Aeppli
J. F. DiTusa
I. A. Zaliznyak
C. D. Frost
T. Ito
K. Oka
H. Takagi
M. E. Bisher
M. M. J. Treacy
R. Paul
JHU
LSU
ISIS
JHU -> University of Chicago
NEC
JHU -> BNL
Electro-Technical Lab Japan
Electro-Technical Lab Japan
ISSP and CREST-JST
NEC
NEC
NIST Center for Neutron Research
Science 289, 419 (2000)
Alternating spin-1/2 chain Cu(NO3)2.2.5D2O
Guangyong Xu
Daniel Reich
M. A. Adams
PRL 84, 4465 (2000)
JHU -> University of Chicago
JHU
ISIS facility
Collaborators
Collaborators
Uniform spin-1 chain Y2BaNiO5
Dynamic condensed matter: Phonons
ZrW2O8
Weak connectivity
Low energy
“twist” modes
Al2O3
Strong connectivity
“Hard” spectrum
Princeton 3/2/1
Ernst el al (1998)
Dynamic Condensed matter: Magnetic Frustration
ZnCr2O
SQ,  
T  CW
4
  k B CW
S.-H. Lee et al
Weak connectivity
triangular motif
Princeton 3/2/1
Interactions specify local
order, not a critical Q vector
Dynamic condensed matter: 1D antiferromag.
KCuF3
NDMAP
I.R. divergence destabilizes Neel order
Princeton 3/2/1
Cooperative singlet ground state
Consequences of strong fluctuations
Phonons : Thermal contraction
Frustration : cooperative paramagnet
c-1
Ernst et al (1998)
CW  TN
0
0
200
1D magnons : macroscopic singlet
Ajiro et al. (1989)
400
600
800
T (K)
1000
Inelastic Neutron Scattering
ki
2
kf
Q
Q  ki - k f
  Ei - E f
Nuclear scattering
1
- i t 1
S(Q,  ) 
 Q 0 -Q t 
 dt e
2
N
Magnetic scattering
1
- i t 1
iQ R - R ' 


S (Q,  ) 
dt
e
e

S
(
0
)
S


R
R ' (t ) 
2
N RR'

Princeton 3/2/1
NIST Center for Neutron
Research
Princeton 3/2/1
SPINS Cold neutron triple axis spectrometer at NCNR
Princeton 3/2/1
Focusing analyzer system on SPINS
Princeton 3/2/1
MAPS Spectrometer at ISIS in UK
Princeton 3/2/1
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
Princeton 3/2/1
Dispersion relation for triplet waves
Dimerized spin-1/2 system: copper nitrate
kBT  J
Princeton 3/2/1
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
Princeton 3/2/1
Creating two triplets with one neutron
Two magnon
One magnon
Tennant et al (2000)
Heating coupled dimers
Princeton 3/2/1
q~  
SMA fit to scattering data
T-Parameters
extracted from fit
S0 Sd
T
J2
~
 q   J1  nT  cos q~
2
1
~
q   0  cos q~
2
More than 1000 data
points per parameter!
Princeton 3/2/1
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
Princeton 3/2/1

 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
Princeton 3/2/1
One dimensional spin-1 antiferromagnet
Y2BaNiO5
Ni
2+
Y2BaNiO5
Impure
Nuclear Elastic Scattering
Pure
Princeton 3/2/1
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 .
Princeton 3/2/1
Haldane PRL 1983
Affleck, Kennedy, Lieb, and Tasaki PRL 1987
Single mode approximation for spin-1 chain
Dispersion relation
Equal time
correlation function
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Two length scales in a quantum magnet
Y2BaNiO5
Equal time correlation length
S q~    S q~,   d

1
~
S q  
N

ll 
Sl Sl expiq~ l - l 
1
S 0 Sl 
exp - l 


l
Triplet Coherence length :
Nuclear Elastic Scattering
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length of coherent triplet
wave packet
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
Princeton 3/2/1
B
Coherence and correlation lengths versus
T
Damle and Sachdev
semi-classical theory of triplet scattering
1
~

1
2
 SD
 2
 
 lchain




2
Jolicoeur and Golinelly
Quantum non-linear s model
Princeton 3/2/1
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
Princeton 3/2/1
Resonance energy and relaxation rate versus T
Jolicoeur and Golinelli
Quantum non-linear s model
Damle and Sachdev
    S 1 T 

Princeton 3/2/1
v2
T
  

exp 
 k BT 
3k BT
Pure quantum spin chains
- at zero and finite T
Gap is possible when n(S-m) is integer
gapped systems: alternating spin-1/2 chain, integer chain,…
gapless systems: uniform spin-1/2 chain
gapped spin systems have coherent collective mode
For appreciable gap SMA applies: S(q) ~ 1/(q)
Thermally activated relaxation due to triplet interactions
Thermally activated increase in resonance energy
Coherence length exceeds correlation length for T<
/kB
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Impurities in Y2BaNiO5
• Mg2+on Ni2+ sites
• Ca2+ on Y3+ sites
finite length chains
mobile bond defects
Mg
Ca2+
Ni
Mg
Y3+
Pure
Princeton 3/2/1
Kojima et al. (1995)
Princeton 3/2/1
20
15
h (meV)
I(H=9 T)-I(H=0 T) (cts. per min.)
Zeeman resonance of chain-end
spins
g=2.16
0
2
4
6
g B H
8
H (Tesla)
10
0
g B H
-5
0
0.5

1
1.5
(meV)
2
Form factor of chain-end spins
Y2BaNi1-xMgxO5 x=4%
  g B H
Q-dependence reveals
that resonating object
is AFM.
The peak resembles
S(Q) for pure system.
Chain end spin carry
AFM spin polarization
of length  back into
chain
Princeton 3/2/1
Impurities in Y2BaNiO5
• Mg2+on Ni2+ sites
• Ca2+ on Y3+ sites
finite length chains
mobile bond defects
Mg
Ca2+
Ca2+
Ni
Mg
Y3+
Pure
Princeton 3/2/1
Kojima et al. (1995)
Transport in Ca doped Y2BaNiO5
1D conductivity, no Charge ordering
Charge Transfer excitation
Charge polaron
T. Ito et al. Submitted to PRL (2001)
Princeton 3/2/1
Gap modes in Ca-doped Y2BaNiO5
4% Ca
10% Ca
Energy (meV)
Pure
q (2)
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q (2)
q (2)
Why is Y2-xCaxBaNiO5 incommensurate?
dq  x
dq indep. of x
Princeton 3/2/1
Charge ordering yields incommensurate spin
order
Quasi-particle Quasi-hole pair excitations in
Luttinger liquid
Single impurity effect
Does d q vary with calcium concentration?
dq not strongly
dependent on x
single impurity effect
Princeton 3/2/1
G. Xu et al. Science (2000)
Bond Impurities in a spin-1 chain: Y2-xCaxBaNiO5
Ni
AFM
FM
Ca2+
Y3+
O
Princeton 3/2/1
Form-factor for FM-coupled chain-end spins
A symmetric AFM droplet

S (q)  2 Re M  (q)eiq / 2

Ensemble of independent
randomly truncated AFM droplets
S (q)   Pll  M l (q )e
ll 
iq / 2
 M ( q )e
*
l
-iq / 2 2
Measuring Magnetic DOS for Gap modes
4% Ca
10% Ca
Energy (meV)
Pure
q (2)
Princeton 3/2/1
q (2)
q (2)
Spin polaron in Ca-doped Y2BaNiO5
Clean gap in pure sample
Anisotropy split triplet?
Triplet-singlet transition?
Impurity interactions
sub gap continuum
0
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5
10
Conclusions:
 Dilute impurities in the Haldane spin chain create sub-gap
composite spin degrees of freedom.
 Edge states have an AFM wave function that extends into
the bulk over distances of order the Haldane length.
 Ca doping yields charge polarons with 1 eV binding energy
 Holes in Y2-xCaxBaNiO5 are surrounded by AFM spin
polaron with central phase shift of 
 Spin polaron has fine structure possibly from spin space
anisotropy
 Neutron scattering can detect the structure of composite
impurity spins in gapped quantum magnets.
 The technique may be applicable to probe impurities in
other gapped systems eg. high TC superconductors.
Princeton 3/2/1