Holes in a Quantum Spin Liquid

1
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
• 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

Y2-xCaxBaNiO5
supported by NSF DMR-0074571
2
Uniform spin-1 chain Y2BaNiO5 Ying Chen
JHU Guangyong Xu JHU -gt University of
Chicago G. Aeppli NEC J. F. DiTusa LSU I. A.
Zaliznyak JHU -gt BNL C. D. Frost ISIS T.
Ito Electro-Technical Lab Japan K. Oka
Electro-Technical Lab Japan H. Takagi ISSP and
CREST-JST M. E. Bisher NEC M. M. J. Treacy
NEC R. Paul NIST Center for Neutron
Research Science 289, 419 (2000) Alternating
spin-1/2 chain Cu(NO3)2.2.5D2O Guangyong Xu
JHU -gt University of Chicago Daniel
Reich JHU M. A. Adams ISIS facility PRL 84,
4465 (2000)
Collaborators
Collaborators
3
Dynamic condensed matter Phonons
Weak connectivity
Low energy twist modes
Strong connectivity
Hard spectrum
Ernst el al (1998)
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Dynamic Condensed matter Magnetic Frustration
ZnCr2O4
S.-H. Lee et al
Weak connectivity triangular motif
Interactions specify local order, not a critical
Q vector
5
Dynamic condensed matter 1D antiferromag.
KCuF3
Chain direction
NDMAP
I.R. divergence destabilizes Neel order
Cooperative singlet ground state
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Consequences of strong fluctuations
Phonons Thermal contraction
Frustration cooperative paramagnet
c-1
Ernst et al (1998)
0
0 200 400 600 800
1000
T (K)
1D magnons macroscopic singlet
Ajiro et al. (1989)
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Inelastic Neutron Scattering
8
NIST Center for Neutron Research
9
SPINS Cold neutron triple axis spectrometer at
NCNR
10
Focusing analyzer system on SPINS
11
MAPS Spectrometer at ISIS in UK
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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 scattering
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Dispersion relation for triplet waves
Dimerized spin-1/2 system copper nitrate
Xu et al PRL May 2000
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Qualitative description of excited states

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

• Inter-dimer coupling allows coherent triplet
  propagation and
• produces well defined dispersion relation

• Triplets can also be produced in pairs with total
  Stot1

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Creating two triplets with one neutron
Two magnon
One magnon
Tennant et al (2000)
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Heating coupled dimers
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SMA fit to scattering data
T-Parameters extracted from fit
More than 1000 data points per parameter!
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T-dependence of singlet-triplet mode
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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

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One dimensional spin-1 antiferromagnet Y2BaNiO5
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Macroscopic singlet ground state of S1 chain

• Magnets with 2Snz have a nearest neighbor
  singlet covering
• with full lattice symmetry.

• This is exact ground state for spin projection
  Hamiltonian

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

Haldane PRL 1983 Affleck, Kennedy, Lieb, and
Tasaki PRL 1987
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Single mode approximation for spin-1 chain
Dispersion relation
Equal time correlation function
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Two length scales in a quantum magnet
Triplet Coherence length length of coherent
triplet wave packet
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Coherence in a fluctuating system
Short range G.S. spin correlations
Coherent triplet propagation
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Mix in thermally excited triplets
Coherence length approaches Correlation
length for
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Coherence and correlation lengths versus T
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qp 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
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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/e(q)
• Thermally activated relaxation due to triplet
  interactions
• Thermally activated increase in resonance energy
• Coherence length exceeds correlation length for
  Tlt D/kB

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Impurities in Y2BaNiO5

• Mg2on Ni2 sites finite length
  chains
• Ca2 on Y3 sites mobile bond defects

Mg
Ca2
Ni
Y3
Kojima et al. (1995)
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Zeeman resonance of chain-end spins
g2.16
20
hw (meV)
15
0 2 4 6 8
H (Tesla)
10
I(H9 T)-I(H0 T) (cts. per min.)
0
-5
0 0.5 1 1.5
2
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Form factor of chain-end spins
Y2BaNi1-xMgxO5 x4
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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Impurities in Y2BaNiO5

• Mg2on Ni2 sites finite length
  chains
• Ca2 on Y3 sites mobile bond defects

Mg
Ca2
Ni
Y3
Kojima et al. (1995)
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Transport in Ca doped Y2BaNiO5
1D conductivity, no Charge ordering
T. Ito et al. Submitted to PRL (2001)
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Gap modes in Ca-doped Y2BaNiO5
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Why is Y2-xCaxBaNiO5 incommensurate?

• Charge ordering yields incommensurate spin order
• Quasi-particle Quasi-hole pair excitations in
  Luttinger liquid
• Single impurity effect

dq indep. of x
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Does d q vary with calcium concentration?
dq not strongly dependent on x
single impurity effect
G. Xu et al. Science (2000)
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Bond Impurities in a spin-1 chain Y2-xCaxBaNiO5
Ni
Ca2
Y3
O
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Form-factor for FM-coupled chain-end spins
A symmetric AFM droplet
Ensemble of independent randomly truncated AFM
droplets
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Measuring Magnetic DOS for Gap modes
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Spin polaron in Ca-doped Y2BaNiO5
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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 p
• 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.