Spin-polarized currents in ferromagnetic multilayers

We present a semi-implicit numerical method for micromagnetics simulations, in the presence of spin-currents. The dynamics of the magnetization are described by the Landau–Lifshitz–Gilbert equation, while the dynamics of the spin are described by a diffusion equation with discontinuous coefficients. The complexity of the method presented is comparable to that of solving the linear heat equation with the Backward Euler method. To illustrate the procedure, we carry out three dimensional simulations of the magnetization reversal process in a magnetic multilayer when a current flows perpendicular to the layers. Spin-polarized currents are shown to decrease the coercive field, and to induce magnetization reversal even in the absence of external magnetic fields.