Spin waves in the nearly one-dimensional systems of CsNiCl3and RbNiCl3

The magnetic excitations of CsNi${\mathrm{Cl}}_3$ and RbNi${\mathrm{Cl}}_3$ in their ordered state have been studied by optical absorption in the near infrared at $T=1.7\mathrm{}$ K. Magnon sidebands associated with the ${}_{}{}^3{}_{}{}^{}A_{2g}^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}T_{2g}^{}{}_{}{}^{}$ excitons have been observed. The Hamiltonian of the spin system consists of intrachain ($J_1$) and interchain ($J_3$) interactions, both of the Heisenberg type with $\frac{J_1}{J_3}\sim 40$ for CsNi${\mathrm{Cl}}_3$ and ∼20 for RbNi${\mathrm{Cl}}_3$, and a crystal-field single-ion anisotropy. The calculated equilibrium spin orientations agree with the "triangular configuration" observed by Yelon and Cox. Spin-wave theory is applied to calculate the magnon dispersion curves and density of magnon states. The large disparity between the intrachain and the interchain interactions results in the appearance of two sets of peaks in the calculated density of states. The high-energy set corresponds to magnons propagating along the chain, while the low-energy set corresponds to magnons propagating in the basal plane. This is in agreement with the observed single-magnon sidebands.