Neutron scattering study of spin waves and exchange interactions in ferromagnetic EuS

From inelastic neutron scattering the strongly anisotropic spin-wave dispersion curves of a ${}_{}{}^{153}{}_{}{}^{}\mathrm{EuS}$ single crystalline sample have been measured at 1.3 K for the main symmetry directions $〈100〉$, $〈110〉$, and $〈111〉$ over the entire first Brillouin zone. Least-squares fits to the Holstein-Primakoff spin-wave theory yield the isotropic exchange energy constants, $J_i$, up to fifth nearest neighbors ($i=5\mathrm{}$) as follows: $\frac{J_1}{k_B}=0.221\mathrm{}\pm 0.003$ K, $\frac{J_2}{k_B}=-0.100\mathrm{}\pm 0.004$ K, $\frac{J_3}{k_B}=0.006\mathrm{}\pm 0.002$ K, $\frac{J_4}{k_B}=-0.007\mathrm{}\pm 0.002$ K, $\frac{J_5}{k_B}=-0.004\mathrm{}\pm 0.002$ K which correspond to a paramagnetic Curie temperature of ${\Theta }_P=21.1\mathrm{}\pm 0.2$ K. The results confirm previous assumptions that the range of the $J_i$ is essentially limited to next nearest neighbors, and thus agree fairly well with most of the previous experimental results on $J_1$ and $J_2$. The temperature dependence of the $J_i$ disagrees with the predictions of the spin-wave renormalization theory.