Neutron scattering from the Heisenberg ferromagnets EuO and EuS. I. The exchange interactions

Inelastic-neutron-scattering methods have been used to measure the spin-wave spectrum in EuO and EuS over the entire Brillouin zone. The samples were polycrystalline powders enriched in ${}_{}{}^{153}{}_{}{}^{}\mathrm{Eu}$. Defining the interaction between pairs of spins to be $-2\mathrm{}{J}_{\mathrm{nm}}{\overrightarrow{\mathrm{S}}}_n·{\overrightarrow{\mathrm{S}}}_m$, we obtained for EuO, $\frac{J_1}{k_B}=0.606\mathrm{}\pm 0.008$ °K and $\frac{J_2}{k_B}=0.119\mathrm{}\pm 0.015$ °K; for EuS, $\frac{J_1}{k_B}=0.236\mathrm{}\pm 0.009$ °K and $\frac{J_2}{k_B}=-0.118\mathrm{}\pm 0.011$ °K. The measured Curie temperatures for EuO, 69.15 ± 0.05°K, and for EuS, 16.57 ± 0.01 °K, are in excellent agreement with calculated values obtained from series expansions relating $T_c$ to the exchange constants. In EuO, the neutron scattering measurements determine $J_1$ and $J_2$ separately. Although separate values for the exchange constants were reported in earlier experiments, we show that in fact only the spin-wave stiffness constant of EuO, which is proportional to $J_1+J_2$, was actually determined. In EuS, our values of $J_1$ and $J_2$ agree with a reanalysis of the specific-heat data.