Hydrodynamic theory of coupled current and magnetization dynamics in spin-textured ferromagnets

TL;DR

This paper develops a hydrodynamical framework describing how spin currents interact with magnetization in ferromagnets, incorporating dissipative effects, thermal fluctuations, and analyzing specific magnetic textures.

Contribution

It introduces a comprehensive hydrodynamical theory linking spin currents and magnetization dynamics, including dissipative corrections and fluctuation effects, in metallic ferromagnets.

Findings

Electronic dynamics induce nonlocal Gilbert damping.

Dissipative spin-motive forces affect current and magnetization.

Analysis of magnetic vortices, helices, and spirals illustrates the theory.

Abstract

We develop the hydrodynamical theory of collinear spin currents coupled to magnetization dynamics in metallic ferromagnets. The collective spin density couples to the spin current through a U(1) Berry-phase gauge field determined by the local texture and dynamics of the magnetization. We determine phenomenologically the dissipative corrections to the equation of motion for the electronic current, which consist of a dissipative spin-motive force generated by magnetization dynamics and a magnetic texture-dependent resistivity tensor. The reciprocal dissipative, adiabatic spin torque on the magnetic texture follows from the Onsager principle. We investigate the effects of thermal fluctuations and find that electronic dynamics contribute to a nonlocal Gilbert damping tensor in the Landau-Lifshitz-Gilbert equation for the magnetization. Several simple examples, including magnetic vortices, helices, and spirals, are analyzed in detail to demonstrate general principles.