Magnetization Dissipation in Ferromagnets from Scattering Theory

TL;DR

This paper develops a scattering theory approach to describe magnetization dissipation in ferromagnets, linking it to the Landau-Lifshitz-Gilbert equation and providing a unified framework for various magnetization dynamics.

Contribution

It introduces a scattering theory formulation for magnetization damping, connecting it with the LLG equation and the Kubo formalism, applicable to general magnetization textures.

Findings

Dissipative magnetization dynamics described as energy pumping into electronic systems.

Gilbert damping tensor expressed via the scattering matrix derivative.

Theory validated by showing equivalence to Kubo formalism.

Abstract

The magnetization dynamics of ferromagnets are often formulated in terms of the Landau-Lifshitz-Gilbert (LLG) equation. The reactive part of this equation describes the response of the magnetization in terms of effective fields, whereas the dissipative part is parameterized by the Gilbert damping tensor. We formulate a scattering theory for the magnetization dynamics and map this description on the linearized LLG equation by attaching electric contacts to the ferromagnet. The reactive part can then be expressed in terms of the static scattering matrix. The dissipative contribution to the low-frequency magnetization dynamics can be described as an adiabatic energy pumping process to the electronic subsystem by the time-dependent magnetization. The Gilbert damping tensor depends on the time derivative of the scattering matrix as a function of the magnetization direction. By the fluctuation-dissipation theorem, the fluctuations of the effective fields can also be formulated in terms of the quasistatic scattering matrix. The theory is formulated for general magnetization textures and worked out for monodomain precessions and domain wall motions. We prove that the Gilbert damping from scattering theory is identical to the result obtained by the Kubo formalism.