Finite element modeling of spin–orbit torques

Abstract

Using a spin drift–diffusion model for coupled spin and charge transport, including the spin Hall effect and the inverse spin Hall effect, spin–orbit torques acting on the magnetization in heavy metal/ferromagnet bilayers are evaluated employing a finite element approach. The behavior of the resulting spin accumulation and torques is analyzed for different magnetization orientations of the ferromagnetic layer and varying thicknesses of the heavy metal layer. A strong damping-like torque component, consistent with experimental results, is observed. In addition, sub-ns switching simulations based on solving the Landau–Lifshitz–Gilbert equation are demonstrated.