Conserved momenta of a ferromagnetic soliton

TL;DR

This paper addresses the unphysical gauge dependence of soliton momenta in ferromagnets by drawing an analogy with charged particles in magnetic fields, leading to a gauge-invariant definition of conserved momenta.

Contribution

It introduces a gauge-invariant method to define conserved momenta of ferromagnetic solitons by leveraging the analogy with magnetic translation symmetry.

Findings

Conventional momenta depend on gauge choices and are unphysical.

A new gauge-invariant momentum definition is proposed for ferromagnetic solitons.

The approach is demonstrated on domain walls and vortices.

Abstract

Linear and angular momenta of a soliton in a ferromagnet are commonly derived through the application of Noether's theorem. We show that these quantities exhibit unphysical behavior: they depend on the choice of a gauge potential in the spin Lagrangian and can be made arbitrary. To resolve this problem, we exploit a similarity between the dynamics of a ferromagnetic soliton and that of a charged particle in a magnetic field. For the latter, canonical momentum is also gauge-dependent and thus unphysical; the physical momentum is the generator of magnetic translations, a symmetry combining physical translations with gauge transformations. We use this analogy to unambiguously define conserved momenta for ferromagnetic solitons. General considerations are illustrated on simple models of a domain wall in a ferromagnetic chain and of a vortex in a thin film.