Micromagnetically integrated numerical model of spin pumping based on spin diffusion

We present a nanoscopic numerical model of spin pumping, complete with spin-torque effects, as an extension of a spin-diffusion solver. The model is fully integrated in a micromagnetics finite-element framework. It is shown that this model can recreate analytical solutions for standard problems. Furthermore, the Gilbert damping of a propagating magnon can be properly modeled. The model can be used to examine spin-pumping effects, and those caused by it, e.g., inverse spin Hall, on a nanoscopic scale.