Spin dynamics and the Haldane gap in the spin-1 quasi-one-dimensional antiferromagnetCsNiCl3

A full description of a series of spin-wave measurements in ${\mathrm{CsNiCl}}_3$ in the three-dimensional (3D) and one-dimensional (1D) phases and their analysis to provide the first experimental evidence for the Haldane gap is presented. Neutron scattering experiments were performed on a single crystal of ${\mathrm{CsNiCl}}_3$ with both (h,0,l) and (h,h,l) as the scattering plane. The order parameter in both 3D phases was measured and the spin-wave dispersion determined in the lower phase. The spin-wave spectrum calculated from a dynamic susceptibility method was compared with the experimental response in the lower 3D phase to obtain the following values for the exchange and anisotropy constants: J=0.345±0.008 THz, J’=0.0060±0.005 THz, and D=-0.0130±0.0015 THz. These parameters confirm that ${\mathrm{CsNiCl}}_3$ in its disordered phase is a good approximation to a one-dimensional Heisenberg antiferromagnet. In the 1D phase the gap frequency for an isolated chain of ${\mathrm{Ni}}^{2+}$ ions is found to be 0.32 THz close to the gap estimated in finite-chain calculations. The results constitute experimental support for the Haldane conjecture that the excitations of integer-spin chains, unlike half-integer–spin chains, exhibit an apparent anisotropy that arises not from the underlying isotropic Hamiltonian, but from many-body effects.