Christian Doppler Laboratory of Advanced Magnetic Sensing and Materials, Institute of Solid State, Physics, TU Wien, Austria.
Institute for Analysis and Scientific Computing, TU Wien, Austria.
Sci Rep. 2016 Dec 21;6(1):16. doi: 10.1038/s41598-016-0019-y.
We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the electric potential in a self-consistent fashion. This treatment allows for an accurate description of magnetization dependent resistance changes. Moreover, the presented algorithm describes both spin accumulation due to smooth magnetization transitions and due to material interfaces as in multilayer structures. The model and its finite-element implementation are validated by current driven motion of a magnetic vortex structure. In a second experiment, the resistivity of a magnetic multilayer structure in dependence of the tilting angle of the magnetization in the different layers is investigated. Both examples show good agreement with reference simulations and experiments respectively.
我们提出了一个三维的微磁模型,该模型可以动态求解与全自旋扩散方程耦合的 Landau-Lifshitz-Gilbert 方程。与之前的方法不同,我们以自洽的方式求解磁化动力学和电势。这种处理方式可以准确地描述磁化相关的电阻变化。此外,所提出的算法既描述了由于平滑磁化跃迁引起的自旋积累,也描述了多层结构中由于材料界面引起的自旋积累。该模型及其有限元实现通过对磁性涡旋结构的电流驱动运动进行了验证。在第二个实验中,研究了不同层中磁化倾斜角度对磁性多层结构电阻率的影响。这两个例子都与参考模拟和实验结果吻合得很好。