# A three-dimensional spin-diffusion model for micromagnetics

## TL;DR

The paper introduces a 3D model that simulates spin-diffusion in magnetic materials and validates it against existing theories.

## Contribution

A new three-dimensional spin-diffusion model is proposed and validated against two established spin-torque models.

## Key findings

- The model captures nonlocal effects from the Slonzewski model.
- It also accounts for spin-accumulation effects from the Zhang and Li model.
- The model resolves the time dependency of spin-accumulation.

## Abstract

We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation.