arXiv:cond-mat/0011046 · Physical Review Letters

Multiparticle States in the S=1 Chain System CsNiCl3

M. Kenzelmann, Roger Arthur Cowley, W. J. L. Buyers, R. Coldea, J. S. Gardner, M. Enderle, MCMORROW Desmond Francis, Steve M. Bennington

Published Jun 15, 2001• 39 citations

arXiv HTML PDF

Abstract

A continuum of magnetic states has been observed by neutron scattering from the spin-1 chain compound CsNiCl3 in its disordered gapped one-dimensional phase. Results using both triple-axis and time-of-flight spectrometers show that around the antiferromagnetic point Qc = pi, the continuum lies higher in energy than the Haldane gapped excitations. At 6 K the integrated intensity of the continuum is about 12(2)% of the total spectral weight. This result is considerably larger than the 1%-3% weight predicted by the nonlinear sigma model for the three-particle continuum.

DOI: 10.1103/physrevlett.87.017201

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arXiv:cond-mat/0011046 · Physical Review Letters

Multiparticle States in the S=1 Chain System CsNiCl3

M. Kenzelmann, Roger Arthur Cowley, W. J. L. Buyers, R. Coldea, J. S. Gardner, M. Enderle, MCMORROW Desmond Francis, Steve M. Bennington

Published Jun 15, 2001• 39 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.87.017201

Related papers

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We report inelastic time-of-flight and triple-axis neutron scattering measurements of the excitation spectrum of the coupled antiferromagnetic spin-1 Heisenberg chain system

{\mathrm{CsNiCl}}_{3}.

Measurements over a wide range of wave-vector transfers along the chain confirm that above

{T}_{N} {\mathrm{CsNiCl}}_{3}

is in a quantum-disordered phase with an energy gap in the excitation spectrum. The spin correlations fall off exponentially with increasing distance with a correlation length $\ensuremath{\xi}=4.0(2)$ sites at

T=6.2\mathrm{K}.

This is shorter than the correlation length for an antiferromagnetic spin-1 Heisenberg chain at this temperature, suggesting that the correlations perpendicular to the chain direction and associated with the interchain coupling lower the single-chain correlation length. A multiparticle continuum is observed in the quantum-disordered phase in the region in reciprocal space where antiferromagnetic fluctuations are strongest, extending in energy up to twice the maximum of the dispersion of the well-defined triplet excitations. We show that the continuum satisfies the Hohenberg-Brinkman sum rule. The dependence of the multiparticle continuum on the chain wave vector resembles that of the two-spinon continuum in antiferromagnetic spin-1/2 Heisenberg chains. This suggests the presence of spin-1/2 degrees of freedom in

{\mathrm{CsNiCl}}_{3}

for

T<~12 \mathrm{K},

possibly caused by multiply frustrated interchain interactions.

For the antiferromagnetically coupled integer-spin

{\mathrm{Ni}}^{2+}

chains of

{\mathrm{CsNiCl}}_{3}

the Haldane gap is found by neutron scattering to be a singlet-to-triplet spin excitation. It has a 2\ensuremath{\pi} periodicity in momentum space with a dispersion relation that falls to a value of order twice the gap energy as Q\ensuremath{\rightarrow}2\ensuremath{\pi}. When the coupled

{\mathrm{Ni}}^{2+}

chains undergo the transition to three-dimensional order, a set of longitudinal modes is found to occur that are not present in conventional theory where the excitations are transverse spin waves. Our calculations of the intensities show that near the ordering wave vector (1/3, 1)/3 ,1) the new modes agree with the field theory of Affleck but not with spin-wave theory. At larger interchain wave vectors both field theory and spin-wave theory break down.

The spin-excitation continuum, expected to dominate the low-energy fluctuation spectrum in the Haldane spin chain around the Brillouin zone center,

q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

, is directly observed by inelastic magnetic neutron scattering in the

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

quasi-1D antiferromagnet

{\mathrm{CsNiCl}}_{3}

. We find that the single mode approximation fails, and that a finite energy width appears in the dynamic correlation function $S(q,\ensuremath{\omega})$ for $q\ensuremath{\lesssim}0.5\ensuremath{\pi}$. The width increases with decreasing

q

, while $S(q,\ensuremath{\omega})$ acquires an asymmetric shape qualitatively similar to that predicted for the two-magnon continuum in the nonlinear $\ensuremath{\sigma}$-model.

In this, and the following paper, we present the results of a detailed experimental investigation into the spin dynamics of the quasi-one-dimensional S=1/2 Heisenberg antiferromagnet

{\mathrm{KCuF}}_{3}

. In this paper we report results of inelastic neutron-scattering measurements made using the MARI time-of-flight spectrometer at the Rutherford Appleton Laboratory. Measurement of the magnetic excitation spectrum was made in both the low-temperature phase, where the chains are ordered together, and in the high-temperature phase, where the correlations between chains become unimportant. We compare our measurements with the M\"uller ansatz, which is identified with a two-spinon cross section, and find excellent agreement with this. The effect of temperature on the excitation continuum was also investigated. A series of measurements were made at temperatures ranging from 20 to 200 K. These results are compared to the predictions of field theory for the one-dimensional Heisenberg chain. Again good agreement is found with the theoretical predictions. In the following paper measurements of the low-energy scattering in the ordered phase, made on a triple-axis spectrometer, are presented.

{\mathrm{CsNiCl}}_{3}.