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

TLDR

The study investigates magnetic relaxation processes in ferromagnets by measuring ferromagnetic resonance from 1 to 70 GHz in epitaxial Fe₃Si films. Using frequency‑ and angle‑dependent FMR, the authors simultaneously identify two relaxation channels—dissipative isotropic Gilbert damping G and anisotropic two‑magnon scattering Γ—and quantitatively analyze them. They determine two‑magnon scattering rates of 0.25(2) GHz for ⟨100⟩ and 0.04(2) GHz for ⟨110⟩ spin waves, a Gilbert damping of 0.051(1) GHz, and show that film thickness (8–40 nm) and Fe concentration modify these channels, highlighting the roles of longitudinal and transverse relaxation in spin‑wave dynamics.

Abstract

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.