Transcript Holes in a Quantum Spin Liquid

Solving Impurity Structures
Using Inelastic Neutron Scattering
Collin Broholm*
Johns Hopkins University and NIST Center for Neutron Research
Quantum Magnetism
- Pure systems
- vacancies
- bond impurities
Conclusions
Y3+
Ca2+
*supported by the NSF through DMR-0074571
Collaborators
G. Aeppli
J. F. DiTusa
T. Ito
K. Oka
D. H. Reich
M. M. J. Treacy
I. A. Zaliznyak
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M. E. Bisher
C. D. Frost
T. H. Kim
R. Paul
H. Takagi
G. Xu
Inelastic Neutron Scattering
ki
2
Q
kf
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'
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SPINS Cold neutron triple axis spectrometer at NCNR
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Simple example of “Quantum” magnet
Cu(NO3)2.2.5D2O : dimerized spin-1/2 system
Only Inelastic
magnetic scattering
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Why dimerized chain is a spin liquid
A spin-1/2 pair has a singlet - triplet gap:
J
Stot  1
Stot  0
inter-dimer coupling yields dispersive mode
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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
low connectivity
interactions with fermions
Quantum
magnets can display novel coherent states
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Why study Quantum magnets ?
Coherent many body states are fascinating and useful
 Superconductivity
 Fractional Quantum Hall effect
 Bose Condensation
 Quantum magnets without static order at T=0
Each phenomenon provides different experimental info about macroscopic
quantum coherence
Only in quantum magnets are dynamic correlations directly accessible (through
neutron scattering)
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Why study impurities in quantum magnets ?
Impurities are inevitable or even necessary to produce coherence
Probing the response to impurities reveals the building blocks of
a macroscopic quantum state.
Impurities in quantum magnets can be explored at the
microscopic level.
Y3+
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Ca2+
Dynamic condensed matter: 1D antiferromag
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
Coherence in a fluctuating system
  
Probing equal time
correlation length
  
Probing spatial
coherence of
Haldane mode
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Impurities in Y2BaNiO5
• Mg2+on Ni2+ sites
• Ca2+ on Y3+ sites
finite length chains
mobile bond defects Mg
Ca2+
Ca2+
Ni
Mg
Y3+
Pure
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Kojima et al. (1995)
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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 x back into
chain
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Sub gap excitations in Ca-doped Y2BaNiO5
Pure
9.5% Ca
Y2-xCaxBaNiO5
•Ca-doping
creates states
below the gap
•sub-gap states
have doubly
peaked structure
factor
G. Xu et al. Science (2000)
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Incommensurate modulations in high TC
superconductors
YBa2Cu3O6.6 T=13 K E=25 meV
h
(rlu)
Hayden et al. (1998)
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La2-xSrxCuO4
Yamada et al. (1998)
Why is Y2-xCaxBaNiO5 incommensurate?
dq  x
dq indep. of x
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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
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G. Xu et al. Science (2000)
Bond Impurities in a spin-1 chain: Y2-xCaxBaNiO5

c
(c)
Y
(d)
Ba
(a)

b
O
Ni

a
(e)
(b)
Ca
(f)

a
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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
Conclusions
Quantum Magnets
low dimensional frustrated and/or weakly connected
Coherent low T states rather than magnetic order
Challenging to describe because fluctuations are
essential
Impurities in spin-1 chain
They create sup-gap composite spin degrees of freedom
Edge states have extended AFM wave function
Holes create AFM spin polaron with phase shift 
Probing impurities with neutrons
Spectroscopic separation yields unique sensitivity to
impurity structures (in quantum magnets) through
coherent diffuse inelastic neutron scattering
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