Topology and dynamics in ferromagnetic media

TL;DR

This paper links the topological complexity of ferromagnetic media with their dynamics by deriving conservation laws and analyzing magnetic bubble behavior under magnetic-field gradients, considering realistic conditions.

Contribution

It provides unambiguous expressions for momentum in ferromagnetic films and applies them to study magnetic bubble dynamics with realistic boundary effects.

Findings

Verification of the golden rule of bubble dynamics in gross features

Derivation of virial theorems generalizing Derrick's relation

Recalculation of the fundamental magnetic bubble

Abstract

A direct link between the topological complexity of ferromagnetic media and their dynamics has recently been established through the construction of unambiguous conservation laws as moments of a topological vorticity. In the present paper we carry out this program under completely realistic conditions, with due account of the long-range magnetostatic field and related boundary effects. In particular, we derive unambiguous expressions for the linear and angular momentum in a ferromagnetic film which are then used to study the dynamics of magnetic bubbles under the influence of an applied magnetic-field gradient. The semi-empirical golden rule of bubble dynamics is verified in its gross features but not in its finer details. A byproduct of our analysis is a set of virial theorems generalizing Derrick's scaling relation as well as a detailed recalculation of the fundamental magnetic bubble.