Evolution of spin excitations in a gapped antiferromagnet from the quantum to the high-temperature limit

We have mapped from the quantum to the classical limit the spin excitation spectrum of the antiferromagnetic spin-1 Heisenberg chain system CsNiCl3 in its paramagnetic phase from T55 to 200 K. Neutron scattering shows that the excitations are resonant and dispersive up to at least T570 K.2.7J, but broaden considerably with increasing temperature. The dispersion flattens out with increasing temperature as the resonance energy D at the antiferromagnetic wave vector increases and the maximum in the dispersion decreases. The correlation length j between T512 and 50 K is in agreement with quantum Monte Carlo calculations for the spin-1 chain. j is also consistent with the single mode approximation, suggesting that the excitations are short-lived single particle excitations. Below T512 K where three-dimensional spin correlations are important, j is shorter than predicted and the experiment is not consistent with the random phase approximation for coupled quantum chains. At T5200 K, the structure factor and second energy moment of the excitation spectrum are in excellent agreement with the high-temperature series expansion.