SPIN-ORBIT PRECESSION DAMPING IN ITINERANT FERROMAGNETS
Keith Gilmore and Mark D. Stiles
The Landau-Lifshitz-Gilbert equation is routinely used to describe magnetization dynamics in ferromagnetic materials. However, predictive use of this phenomenological expression requires prior knowledge of the precession damping rate, which describes the relaxation of excited magnetic states. Since the rates at which nanoscale devices, such as hard drive and MRAM bits, can switch their state are strongly dependent on this damping parameter, improving these speeds through tailoring materials requires understanding the relaxation processes that contribute to damping. While magnetic alloy systems are used in most applications, we consider the simpler 3d transition metals (iron, cobalt, and nickel) in order to understand the most basic processes involved in damping before approaching the more complicated mechanisms expected in alloys.
Damping rates in these transition metal systems have non-monotonic temperature dependencies that have been empirically shown  to have one part proportional to the conductivity and one part proportional to the resistivity. It had been postulated  that both contributions result from a torque between the spin and orbital moments. We have conducted first-principles density functional calculations that validate this claim. We have further illuminated how the spin-orbit interaction produces two contributions to damping with nearly opposite temperature dependencies and quantified the influence of the spin-orbit parameter and the density of states on the damping rate. Present work focuses on improving the comparison of calculations of the damping rate to experimental results, and investigating the relevance of these damping mechanisms to alloy materials.
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