Modification of the Landau-Lifshitz Equation in the Presence of a Spin-Polarized Current in CMR and GMR Materials

TL;DR

This paper derives a modified Landau-Lifshitz equation incorporating spin-polarized currents in ferromagnets, revealing topological effects, potential instabilities, and providing insights for experimental observation in CMR and GMR materials.

Contribution

It introduces a new continuum equation for magnetization that includes current effects as a topological term, advancing understanding of spin-current interactions in ferromagnetic materials.

Findings

Topological term modifies the Landau-Lifshitz equation.

Stationary magnetization maps to a charged particle in a monopole field.

Large currents induce a spin-wave instability.

Abstract

We derive a continuum equation for the magnetization of a conducting ferromagnet in the presence of a spin-polarized current. Current effects enter in the form of a topological term in the Landau-Lifshitz equation . In the stationary situation the problem maps onto the motion of a classical charged particle in the field of a magnetic monopole. The spatial dependence of the magnetization is calculated for a one-dimensional geometry and suggestions for experimental observation are made. We also consider time-dependent solutions and predict a spin-wave instability for large currents.