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

Ben Goldys, Chunxi Jiao and Christof Melcher

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.

Keywords: stochastic PDE, transport noise, frustrated ferromagnet, topological soliton.

AMS Subject Classification: Primary 35D30; secondary 35K45, 35K55, 35Q56, 35Q60, 60H15.