Global weak solutions for the Landau-Lifshitz-Gilbert-Vlasov-Maxwell system coupled via emergent electromagnetic fields

TL;DR

This paper develops a mathematical framework for global weak solutions to a coupled system modeling magnetization dynamics and electron transport, incorporating emergent electromagnetic fields in complex magnetic materials.

Contribution

It introduces a novel coupling of Landau-Lifshitz-Gilbert and Vlasov-Maxwell equations via emergent fields, addressing topological solitons in frustrated magnets.

Findings

Constructed global weak solutions for the coupled system.

Incorporated emergent electromagnetic fields based on helicity.

Applicable to models with topological solitons like skyrmions.

Abstract

Motivated by recent models of current driven magnetization dynamics, we examine the coupling of the Landau-Lifshitz-Gilbert equation and classical electron transport governed by the Vlasov-Maxwell system. The interaction is based on space-time gyro-coupling in the form of emergent electromagnetic fields of quantized helicity that add up to the conventional Maxwell fields. We construct global weak solutions of the coupled system in the framework of frustrated magnets with competing first and second order gradient interactions known to host topological solitons such as magnetic skyrmions and hopfions.