Effective magnetization damping for a dynamical spin texture in metallic ferromagnet

Abstract

An additional magnetization damping for an inhomogeneous spin texture in metallic ferromagnets is calculated on the basis of the s-d exchange model. The effect of conduction electrons on the magnetization dynamics is accounted for the case of slowly varying spin texture within adiabatic approximation by using a coordinate transformation to the local quantization axis. The moving magnetic vortex in a circular nanodot made of permalloy is considered as an example. The dependence of the damping on the dot geometrical sizes is obtained. It is found that the additional damping can reach up to 50% of magnitude of the phenomenological Gilbert damping in the Landau-Lifshitz equation of magnetization motion and should be taken into account for any inhomogeneous spin texture dynamics in ferromagnetic metals.

Damping of linear spin-wave modes in magnetic nanostructures: Local, nonlocal, and coordinate-dependent damping

“…This expression has been previously derived in a more complex way, starting from the Landau-Lifshitz equation, in Ref. 22. The radius of the vortex core is almost independent of the dot radius, and increases with the increase of the dot thickness L as b ≈ λ ex 2.08 + 0.25(L/λ ex ) 0.85 , where λ ex is the material exchange length (≈ 5.5 nm for Permalloy) 44 .…”

“…In several particular cases the influence of the interlayer spin pumping and transverse spin diffusion on the damping rate of SW modes with different spatial profiles has been already discussed [18][19][20][21][22][23][24][25][26] . In this article we present a general formalism, which allows one to cal-culate the SW mode damping rate in the presence of the uniform Gilbert damping, as well as the coordinatedependent and magnetization-texture-dependent damping mechanisms.…”