Damping of spin waves and singularity of the longitudinal modes in the dipolar critical regime of the Heisenberg ferromagnet EuS

By inelastic scattering of polarized neutrons near the (200) Bragg reflection, the susceptibilities and linewidths of the spin waves and the longitudinal spin fluctuations, (formula presented) and (formula presented) respectively, were determined separately. By aligning the momentum transfers (formula presented) perpendicular to both (formula presented) and the spontaneous magnetization (formula presented) we explored the statics and dynamics of these modes with transverse polarizations with respect to (formula presented) In the dipolar critical regime, where the inverse correlation length (formula presented) and q are smaller than the dipolar wave number (formula presented) we observe that (i) the static susceptibility of (formula presented) displays the Goldstone divergence while for (formula presented) the Ornstein-Zernicke shape fits the data with a possible indication of a thermal (mass) renormalization at the smallest (formula presented) values; i.e., we find indications for the predicted 1/q divergence of the longitudinal susceptibility; (ii) the spin-wave dispersion as predicted by the Holstein-Primakoff theory revealing (formula presented) in good agreement with previous work in the paramagnetic and ferromagnetic regime of EuS; (iii) within experimental error, the (Lorentzian) linewidths of both modes turn out to be identical with respect to the (formula presented) variation, the temperature independence, and the absolute magnitude. Due to the linear dispersion of the spin waves, they remain underdamped for (formula presented) These central results differ significantly from the well-known exchange-dominated critical dynamics, but are quantitatively explained in terms of dynamical scaling and existing data for (formula presented) The available mode-mode coupling theory, which takes the dipolar interactions fully into account, describes the gross features of the linewidths but not all details of the T and (formula presented) dependences.