Lagrangian approach and dissipative magnetic systems

TL;DR

This paper introduces a Lagrangian framework for magnetic systems coupled to a reservoir, deriving equations of motion that describe damped or reversible magnetic precession depending on the reservoir's properties.

Contribution

It develops a Lagrangian approach that captures the coupling between magnetic moments and reservoir degrees of freedom, leading to derivations of both damped and reversible magnetic dynamics.

Findings

Derivation of a Landau-Lifshitz-Gilbert-like equation from a Lagrangian formalism.

Identification of conserved quantities via Noether's theorem for magnetic systems.

Demonstration of how reservoir coupling influences magnetic precession and damping.

Abstract

A Lagrangian is introduced which includes the coupling between magnetic moments $\mathbf{m}$ and the degrees of freedom $\boldsymbol{\sigma}$ of a reservoir. In case the system-reservoir coupling breaks the time reversal symmetry the magnetic moments perform a damped precession around an effective field which is self-organized by the mutual interaction of the moments. The resulting evolution equation has the form of the Landau-Lifshitz-Gilbert equation. In case the bath variables are constant vector fields the moments $\mathbf{m}$ fulfill the reversible Landau-Lifshitz equation. Applying Noether's theorem we find conserved quantities under rotation in space and within the configuration space of the moments.