On the Landau–Lifshitz relaxation in ferromagnetic metals

Scattering of ferromagnetic band-electrons by phonons combined with the spin–orbit interaction is shown to cause magnetic relaxation of the Landau–Lifshitz–Gilbert type. Two formally distinct processes are simply analyzed: (a) spin-flip scattering of electrons and (b) ordinary scattering between spin-dependent band levels. Estimates of the magnitude of the damping constant λ are derived for both cases, which agree in orders of magnitude with the experimental values for Fe and Ni. Relations of direct and inverse proportionality between λ and the ordinary collision frequency are found in the cases (a) and (b), respectively.