A finite element approximation of a current-induced magnetization dynamics model

Micromagnetics is a continuum theory describing magnetization patterns inside ferromagnetic media. the dynamics of a ferromagnetic material are governed by the landau-lifshitz equation. this equation is highly nonlinear and has a non-convex constraint. in this work, a finite element approximation of a current-induced magnetization dynamics model is proposed. the model consists of a modified landau-lifshitz-gilbert (llg) equation incorporating spin transfer torque. the scheme preserves a non-convex constraint, requires only a linear solver at each time step and is easily applicable to the limiting cases. as the time and space steps tend to zero, a proof of convergence of the numerical solution to a (weak) solution of the modified llg equation is given. numerical results are presented to show the effect of the injected current on magnetization switching.