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By inelastic scattering of polarized neutrons near the (200)-Braggreflection, the susceptibilities and linewidths of the spin waves and thelongitudinal spin fluctuations were determined separately. By aligning themomentum transfers q perpendicular to both \delta S_sw and the spontaneousmagnetization M_s, we explored the statics and dynamics of these modes withtransverse polarizations with respect to q. In the dipolar critical regime,where the inverse correlation length kappa_z(T) and q are smaller than thedipolar wavenumber q_d, we observe:(i) the static susceptibility of \deltaS_sw^T(q) displays the Goldstone divergence while for \delta S_z^T(q) theOrnstein-Zernicke shape fits the data with a possible indication of athermal(mass-)renormalization at the smallest q-values, i.e. we findindications for the predicted 1/q divergence of the longitudinalsusceptibility; (ii) the spin wave dispersion as predicted by theHolstein-Primakoff theory revealing q_d=0.23(1)\AA^{-1}in good agreement withprevious work in the paramagnetic and ferromagnetic regime of EuS; (iii) withinexperimental error, the (Lorentzian) linewidths of both modes turn out to beidentical with respect to the q^2-variation, the temperature independence andthe absolute magnitude. Due to the linear dispersion of the spin waves theyremain underdamped for q<q_d. These central results differ significantly fromthe well known exchange dominated critical dynamics, but are quantitativelyexplained in terms of dynamical scaling and existing data for T>=T_C. Theavailable mode-mode coupling theory, which takes the dipolar interactions fullyinto account, describes the gross features of the linewidths but not alldetails of the T- and q-dependencies. PACS: 68.35.Rh, 75.40.GbComment: 10 pages, 7 figure

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