Spin dynamics in ferromagnets : Gilbert damping and two-magnon scattering

The magnetic relaxation processes following the dynamical excitation of the spin system of ferromagnets are investigated by ferromagnetic resonance (FMR) between 1 and $70\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ using epitaxial ${\mathrm{Fe}}_{3}\mathrm{Si}$ films as a prototype system. Two relaxation channels, i.e., dissipative, isotropic Gilbert damping $G$ as well as anisotropic two-magnon scattering $\ensuremath{\Gamma}$, are simultaneously identified by frequency and angle dependent FMR and quantitatively analyzed. The scattering rates due to two-magnon scattering at crystallographic defects for spin waves propagating in ⟨100⟩ and ⟨110⟩ directions, $\ensuremath{\gamma}{\ensuremath{\Gamma}}_{⟨100⟩}=0.25(2)\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ and $\ensuremath{\gamma}{\ensuremath{\Gamma}}_{⟨110⟩}=0.04(2)\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$, and the Gilbert damping term $G=0.051(1)\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ are determined. We show that changing the film thickness from $8\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}40\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and slightly modifying the Fe concentration influence the relaxation channels. Our results, which reveal the contributions of longitudinal and transverse relaxation processes may be of general importance for the understanding of spin-wave dynamics in magnetic structures.