Neutron scattering from the Heisenberg ferromagnets EuO and EuS. III. Spin dynamics of EuO

Abstract

Inelastic neutron scattering has been used to investigate the spin dynamics of the isotropic Heisenberg ferromagnet EuO over a wide range of wave vectors and over a temperature range extending from 0.14 to $1.9T_C$. Below the ordering temperature spin-wave renormalization is found to agree well with the predictions of Dyson-Maleev theory (including the dynamical but not the kinematical interaction) when both exchange and dipolar couplings between the ${\mathrm{Eu}}^{2+}$ ions are taken into account. At temperatures near $T_C$ broadening of the spin-wave lines was observed. For hydrodynamic spin waves, the wave-vector dependence of the linewidths is found to be consistent with the expectations of microscopic spin-wave theory and the temperature dependence with predictions based on dynamical scaling. At $T_C$, linewidths were found to deviate from the $q^{\frac{5}{2}}$ wave-vector dependence expected on the basis of dynamical scaling arguments when only exchange couplings are taken into consideration. But when dynamical scaling theory is modified by including dipolar interactions, it satisfactorily accounts for the weaker $q$ dependence observed experimentally. Current microscopic theories appear to overestimate the magnitudes of the linewidths at $T_C$ although above $T_C$ theory properly predicts the temperature dependence of the spin diffusion coefficient in the hydrodynamic regime and also provides a good estimate of its magnitude.