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Motivated by recent models of current driven magnetization dynamics, weexamine the coupling of the Landau-Lifshitz-Gilbert equation and classicalelectron transport governed by the Vlasov-Maxwell system. The interaction isbased on space-time gyro-coupling in the form of emergent electromagneticfields of quantized helicity that add up to the conventional Maxwell fields. Weconstruct global weak solutions of the coupled system in the framework offrustrated magnets with competing first and second order gradient interactionsknown to host topological solitons such as magnetic skyrmions and hopfions.

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