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

Abstract

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 $\ensuremath{-}2{J}_{\mathrm{nm}}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{n}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{m}$, we obtained for EuO, $\frac{{J}_{1}}{{k}_{B}}=0.606\ifmmode\pm\else\textpm\fi{}0.008$ \ifmmode^\circ\else\textdegree\fi{}K and $\frac{{J}_{2}}{{k}_{B}}=0.119\ifmmode\pm\else\textpm\fi{}0.015$ \ifmmode^\circ\else\textdegree\fi{}K; for EuS, $\frac{{J}_{1}}{{k}_{B}}=0.236\ifmmode\pm\else\textpm\fi{}0.009$ \ifmmode^\circ\else\textdegree\fi{}K and $\frac{{J}_{2}}{{k}_{B}}=\ensuremath{-}0.118\ifmmode\pm\else\textpm\fi{}0.011$ \ifmmode^\circ\else\textdegree\fi{}K. The measured Curie temperatures for EuO, 69.15 \ifmmode\pm\else\textpm\fi{} 0.05\ifmmode^\circ\else\textdegree\fi{}K, and for EuS, 16.57 \ifmmode\pm\else\textpm\fi{} 0.01 \ifmmode^\circ\else\textdegree\fi{}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.