Gyroscopic tensor of a magnetic soliton

TL;DR

This paper reviews the gyroscopic tensor of magnetic solitons, emphasizing its fundamental mathematical importance and historical development beyond its initial auxiliary role.

Contribution

It provides a comprehensive review of the gyroscopic tensor's applications and historical background in the context of magnetic solitons.

Findings

The gyroscopic tensor generalizes Thiele's gyrovector.

It is crucial for understanding the dynamics of magnetic solitons.

The tensor has deep mathematical and physical significance.

Abstract

The gyroscopic force acting on a ferromagnetic soliton reflects the tendency of spins to precess. Its components increase linearly with (generalized) velocities of the soliton. The proportionality coefficients form the gyroscopic tensor, a generalization of Thiele's gyrovector. Originally introduced as an auxiliary quantity, the gyroscopic tensor turns out to be a mathematical object of fundamental importance with a long history going back to Lagrange. We review the applications of the gyroscopic tensor and its historical roots.