A three-dimensional spin-diffusion model for micromagnetics
  We implement a finite-element scheme that solves the Landau-Lifshitz-Gilbert equation coupled to a diffusion equation accounting for spin-polarized currents. The latter solves for the spin accumulation not only in magnetic materials but also in nonmagnetic conductors. The presented method incorporates the model by Slonczewski for the description of spin torque in magnetic multilayers as well as the model of Zhang and Li for the description of current driven domain-wall motion. Furthermore it is able to do both resolve the time evolution of the spin accumulation or treat it in an adiabatic fashion by the choice of sufficiently large time steps. 
Claas Abert, Michele Ruggeri, Florian Bruckner, Christoph Vogler, Gino   Hrkac, Dirk Praetorius, and Dieter Suess
physics.comp-ph cond-mat.mes-hall