A drift-diffusion approach to coupled spin and charge transport has been commonly applied to determine the spin-transfer torque acting on the magnetization in metallic valves. This approach, however, is not suitable to describe the predominant tunnel transport in magnetic tunnel junctions. In this work we present a coupled Finite Element solution to the spin and charge drift–diffusion equations. We demonstrate that by introducing a magnetization dependent resistivity one can successfully reproduce the resistance dependence on the magnetization orientation in the ferromagnetic layers. We then investigate the dependence of the resulting torques on system parameters, and show that the approach is able to reproduce the torque magnitude expected in a magnetic tunnel junction. As a unique set of equations is used for the entire structure, this constitutes an efficient Finite Element based approach to describe the magnetization dynamics in emerging spin-transfer torque memories.

耦合自旋和电荷传输的漂移扩散方法已普遍应用于确定作用于金属阀中磁化的自旋转移扭矩。然而，这种方法不适合描述磁隧道结中的主要隧道传输。在这项工作中，我们提出了自旋和电荷漂移-扩散方程的耦合有限元解。我们证明，通过引入磁化相关电阻率，可以成功地重现电阻对铁磁层中磁化方向的依赖性。然后我们研究所得扭矩对系统参数的依赖性，并表明该方法能够重现磁隧道结中预期的扭矩大小。由于整个结构使用一组独特的方程，