Damping of spin dynamics in nanostructures:: An ab initio study -: art. no. 064450

Based on the Fermi surface breathing model of Kambersky, a phenomenological extension of the ab initio density-functional electron theory is used to derive an equation of motion for the spin dynamics in magnets. It is shown that even in the simple case of a homogeneous magnetization M the damping term (1/M)MX[alpha dM/dt] of the commonly used Gilbert equation with the damping scalar alpha has to be replaced by a term of the form (1/M)MX[(alpha) double under bar (M)center dot dM/dt] with a damping matrix (alpha) double under bar which depends on the orientation of M. Explicit calculations are performed for bulk, monolayers, and monatomic wires of Fe, Co, and Ni. The variation of (alpha) double under bar with an orientation of M is quite substantial already for the bulk materials (up to a factor of 4 in hcp Co) but most dramatic in the monolayers and monatomic wires in which for some orientations the damping is even zero. This represents an additional option for optimizing the magnetization reversal process in a magnetic nanostructure. It is shown that there is no simple relation between damping and magnetic anisotropy energy.