Angular and Linear Momentum of Excited Ferromagnets

TL;DR

This paper explores the conservation laws of angular and linear momentum in ferromagnets, demonstrating their persistence under various interactions and defining the linear momentum of magnetic textures, with implications for spin transfer torques.

Contribution

It provides a theoretical framework using Noether's theorem to analyze momentum conservation in ferromagnets with different interactions and introduces the concept of linear momentum for magnetic textures.

Findings

Angular momentum is conserved in isotropic ferromagnets.

Conservation laws persist with dipole-dipole interactions.

Non-adiabatic effective fields influence domain wall dynamics.

Abstract

The angular momentum vector of a Heisenberg ferromagnet with isotropic exchange interaction is conserved, while under uniaxial crystalline anisotropy the projection of the total spin along the easy axis is a constant of motion. Using Noether's theorem, we prove that these conservation laws persist in the presence of dipole-dipole interactions. However, spin and orbital angular momentum are not conserved separately. We also define the linear momentum of ferromagnetic textures. We illustrate the general principles with special reference to the spin transfer torques and identify the emergence of a non-adiabatic effective field acting on domain walls in ferromagnetic insulators.