Dipolar and nondipolar interactions in LiTbF4

The magnetic interactions in LiTb${\mathrm{F}}_4$ have been studied in measurements of the quasielastic scattering of neutrons from the paramagnetic crystal. Scattering data have been collected at a temperature $T=18.6\mathrm{}$ K, which is 6.5 times the Curie temperature of LiTb${\mathrm{F}}_4$, and have been least-squares fitted with an expression for the scattering cross section which includes, in addition to the dominant dipolar coupling, two exchange parameters $J_1$ and $J_2$ describing the nondipolar coupling between nearest- and next-nearest-neighbor ${\mathrm{Tb}}^{3+}$ ions, respectively. The derived exchange parameters are $\frac{J_1}{k}=-0.26\mathrm{}\pm 0.09$ K and $\frac{J_2}{k}=+0.05\mathrm{}\pm 0.10$ K. Based on these parameters the total interaction energy for nearest-neighbor ions is 4/3 dipolar and -1/3 nondipolar, and the nondipolar interactions are less important for second neighbors. The interaction Hamiltonian is discussed, the wave-vector-dependent susceptibility ${\chi }_T\left(\overrightarrow{\mathrm{Q}}\right)$ is derived in the mean-field approximation, and the dipolar interactions are evaluated numerically using Ewald's technique.