1. DYNAMICAL PROPERTIES OF THE ANISOTROPIC TRIANGULAR QUANTUM
ANTIFERROMAGNET WITH
DZYALOSHINSKII-MORIYA INTERACTION
Rastko Sknepnek, Denis Dalidovich, John Berlinsky, Junhua Zhang, Catherine Kallin
Department of Physics and Astronomy
McMaster University
March Meeting 2006, Baltimore
March 16, 2006
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2. March Meeting 2006, Baltimore
Outline
Motivation
1/S expansion
Renormalized spectrum
Structure factor
Summary
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3. Neutron scattering measurements on quantum magnet Cs2CuCl4.
Motivation
Neutron scattering measurements on quantum magnet Cs2CuCl4.
extended scattering continuum.
Signature of deconfined, fractionalized
spin-1/2 (spinon) excitations?
(R. Coldea, et al., PRB 68, (2003))
Can this broad scattering continuum be explained within a
conventional 1/S expansion?
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4. March Meeting 2006, Baltimore
Microscopic Hamiltonian J J’
Measurements in high magnetic field (12T):
J’’
J = 0.374(5) meV
J’ = 0.128(5) meV
J’’= 0.017(2) meV
High magnetic field experiment also observe small splitting into two magnon branches.
Indication of a weak Dzyaloshinskii-Moriya (DM) interaction.
D = 0.020(2) meV
DM interaction creates an easy plane anisotropy. D
Below TN=0.62K the interlayer coupling
J’’ stabilizes long range order.
The order is an incommensurate spin
spiral in the (bc) plane.
17.7o
e0=0.030(2)
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5. March Meeting 2006, Baltimore
Relatively large ratio J’/J≈1/3 and considerable dispersion along both b and c directions
indicate two dimensional nature of the system.
Effective Hamiltonian:
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6. A few remarks... A strong scattering continuum does not automatically
entail a spin liquid phase.
Magnon-magnon interaction can cause a broad scattering
continuum in a conventional magnetically ordered phase.
In Cs2CuCl4 strong scattering continuum is expected because:
low (S=1/2) spin and the frustration lead to a small ordered moment and strong
quantum fluctuations
the magnon interaction in non-collinear spin structures induces coupling between
transverse and longitudinal spin fluctuations  additional damping of the spin waves.
It is necessary to go beyond linear spin wave theory by taking into account magnon-magnon
interactions within a framework of 1/S expansion.
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7. Spin wave theory
Classical ground state is an incommensurate spin-spiral
along strong-bond (b) direction with the ordering wave
vector Q.
In order to find ground state energy we introduce a local reference frame:
Iowa State University
March 2, 2006
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8. March Meeting 2006, Baltimore
1/S expansion
To go beyond linear spin-wave theory we employ Holstein-Primakoff transformation:
Where a’s are bosonic spin-wave creation and annihilation operators.
The Hamiltonian for the interacting magnons becomes:
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9. March Meeting 2006, Baltimore
Energy spectrum
The renormalized magnon energy spectrum is determined by poles of the Green’s function.
Which leads to the nonlinear self-consistency equation:
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10. March Meeting 2006, Baltimore
Spin structure factor
Neutron scattering spectra is expressed in terms of Fourier-transformed real-time
dynamical correlation function:
Magnon-magnon interaction leads to the mixing of longitudinal (z) and transversal (x)
modes (detailed derivation in T. Ohyama&H. Shiba, J. Phys. Soc. Jpn. (1993))
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11. March Meeting 2006, Baltimore
G scan
Scan along a path at the edge of the Brillouin zone.
D = 0.02meV
kx = p
ky = 2p( w-0.1w2)
linear SW theory wk =0.22meV
Energy resolution DE=0.016meV
Momentum resolution Dk/2p = 0.085
linear SW theory wk+/-Q = 0.28meV
(R. Coldea, et al., PRB 68, (2003))
two-magnon continuum
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12. March Meeting 2006, Baltimore
What happens if we lower D?
J = meV
J’ = meV
D = 0.01meV
1/S theory
G scan
experiment
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13. ...to be continued Summary and conclusions Iowa State University
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