2016 # Analysis of a coupled spin drift–diffusion Maxwell–Landau–Lifshitz system

**Abstract:** Abstract. The existence of global weak solutions to a coupled spin drift-diffusion and Maxwell-Landau-Lifshitz system is proved. The equations are considered in a two-dimensional magnetic layer structure and are supplemented with Dirichlet-Neumann boundary conditions. The spin drift-diffusion model for the charge density and spin density vector is the diffusion limit of a spinorial Boltzmann equation for a vanishing spin polarization constant. The Maxwell-Landau-Lifshitz system consists of the time-dependent M…

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“…This idea only works if the precession vector µ is constant. A non-constant vector µ (solving the Landau-Lifshitz-Gilbert equation) was considered in [41], but this spin model is simplified and no large-time asymptotics was proved.…”

confidence: 99%

“…This idea only works if the precession vector µ is constant. A non-constant vector µ (solving the Landau-Lifshitz-Gilbert equation) was considered in [41], but this spin model is simplified and no large-time asymptotics was proved.…”

confidence: 99%

“…Besides, one also discussed the so-called spin-vector drift-diffusion equations which can be derived from the spinor Boltzmann equation by assuming a moderate spin-orbit coupling [18] and the scattering rates are supposed to be scalar quantities. The existence of global weak solutions to a coupled spin drift-diffusion and Maxwell-Landau-Lifshitz system is proved in [36]. Assuming that the scattering rates are positive definite Hermitian matrices, a more general matrix drift-diffusion model was derived in [35].…”

confidence: 99%

“…Even in the case of deterministic systems, the case with time dependent Maxwell equations is not well understood and after the seminal paper [32] most of the effort was focused on the so-called quasi-static case. Recently, the interest in the full time-dependent case has been renewed, see for example [16,24,33]. In the stochastic case, the only work in this direction, we are aware of, is the paper [21] but it imposes strong simplifying assumptions on the noise and the energy functional.…”

mentioning

confidence: 99%