  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.
