Ferromagnetic resonance relaxation in ultrathin metal films: The role of the conduction electrons

We explore the contribution to the damping term in the equation for spin dynamics in ferromagnetic films with the origin in the transfer of angular momentum from precessing moments, modeled here as localized spins, to conduction electrons. Our starting point views the origin of the damping as a time lag in the RRKY oscillations, following the approach of Simanek and Heinrich. We show this results in a damping term distinctly different from that which appears in the classical Landau-Lifschitz equation, but in agreement with a more general form derived by Mills and Rezende. It is the case that the dominant term can be absorbed into an effective Gilbert damping constant. Our analysis shows that while an overall factor inversely proportional to the film thickness appears in the final form, as argued by others, this is multiplied by a factor which displays strong quantum oscillations as a function of film thickness. There is a short-period and long-period oscillation, with physical origin in the fact that the transfer of angular momentum takes place in a finite quantum well. We comment on the relation of our work to that of others.