Stochastic Landau-Lifshitz-Gilbert equations for frustrated magnets under fluctuating currents

TL;DR

This paper studies a stochastic Landau-Lifshitz-Gilbert equation modeling frustrated magnets under fluctuating currents, proving solution existence and showing topological patterns persist despite noise.

Contribution

It introduces a stochastic model for frustrated ferromagnets with competing exchange interactions and establishes existence and uniqueness of solutions under random spin transfer torques.

Findings

Existence of weak martingale solutions proven

Pathwise uniqueness established

Topological patterns persist under stochastic influences

Abstract

We examine a stochastic Landau-Lifshitz-Gilbert equation for a frustrated ferromagnet with competing first and second order exchange interactions exposed to deterministic and random spin transfer torques in form of transport noise. We prove the existence and pathwise uniqueness of weak martingale solutions in the energy space. The result ensures the persistence of topological patterns, occurring in such magnetic systems, under the influence of a fluctuating spin current.