Coupling of dynamical micromagnetism and a stationary spin drift-diffusion equation: A step towards a fully self-consistent spintronics framework

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.We consider the coupling of the Landau-Lifshitz-Gilbert equation with a quasilinear diffusion equation to describe the interplay of magnetization and spin accumulation in magnetic-nonmagnetic multilayer structures. For this problem, we propose and analyze a convergent finite element integrator, where, in contrast to prior work, we consider the stationary limit for the spin diffusion. Numerical experiments underline that the new approach is more effective, since it leads to the same experimental results as for the model with time-dependent spin diffusion, but allows for larger time-steps of the numerical integrator.The authors acknowledge support from the Vienna Science and Technology Fund (WWTF) under grant MA14-44 (GH, DP, DS), from the Austrian Science Fund (FWF) under grant W1245 (DP, MR), from TU Wien through the innovative projects initiative (DP, MR), from the Austrian Federal Ministry of Science, Research and Economy and the National Foundation for Research, Technology and Development (CA, DS), through the EPSRC grant EP/K008412/1 (GH), from the Royal Society under grant UF080837 (GH)