Semiclassical Limit of the Schrödinger–Poisson–Landau–Lifshitz–Gilbert System

The Schrödinger–Poisson–Landau–Lifshitz–Gilbert (SPLLG) system is an effective microscopic model that describes the coupling between conduction electron spins and the magnetization in ferromagnetic materials. This system has been used in connection with the study of spin transfer and magnetization reversal in ferromagnetic materials. In this paper, we rigorously prove the existence of weak solutions to SPLLG and derive the Vlasov–Poisson–Landau–Lifshitz–Glibert system as the semiclassical limit.