2015/08/11 by Nicola Zamponi, Ansgar Jüngel, Zamponi, Nicola +1
Mathematics · #35K51 #35Q60 #35Q61 #82D40 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35K51 #msc:35Q60 #msc:35Q61 #msc:82D40
paper · pdf · doi:10.48550/arxiv.1508.02660
arxiv created 2015/08/11 · arxiv updated 2015/08/12
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 Maxwell equations for the electric and magnetic fields and of the Landau-Lifshitz-Gilbert equation for the local magnetization, involving the interaction between magnetization and spin density vector. The existence proof is based on a regularization procedure, L2-type estimates, and Moser-type iterations which yield the boundedness of the charge and spin densities. Furthermore, the free energy is shown to be nonincreasing in time if the magnetization-spin interaction constant in the Landau-Lifshitz equation is sufficiently small.