Spin-orbit precession damping in transition metal ferromagnets (invited)

We provide a simple explanation, based on an effective field, for the precession damping rate due to the spin-orbit interaction. Previous effective field treatments of spin-orbit damping include only variations of the state energies with respect to the magnetization direction, an effect referred to as the breathing Fermi surface. Treating the interaction of the rotating spins with the orbits as a perturbation, we include also changes in the state populations in the effective field. In order to investigate the quantitative differences between the damping rates of iron, cobalt, and nickel, we compute the dependence of the damping rate on the density of states and the spin-orbit parameter. There is a strong correlation between the density of states and the damping rate. The intraband terms of the damping rate depend on the spin-orbit parameter cubed, while the interband terms are proportional to the spin-orbit parameter squared. However, the spectrum of band spacings is also an important quantity and does not appear to depend in a simple way on material parameters.