Properties of Haldane excitations and multiparticle states in the antiferromagnetic spin-1 chain compoundCsNiCl3

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 $T_N\hspace{0.5em}{\mathrm{CsNiCl}}_3$ 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 $\xi =4.0\mathrm{}\left(2\right)\mathrm{}$ sites at $T=6.2\mathrm{}\mathrm{K}.$ 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 $T<~12\hspace{0.5em}\mathrm{K},$ possibly caused by multiply frustrated interchain interactions.