论文标题
长时间极限的微磁旋转扩散模型
Spin-diffusion model for micromagnetics in the limit of long times
论文作者
论文摘要
在本文中，我们考虑了自旋扩散Landau-lifshitz-gilbert方程（SDLLG），该方程由时间依赖性的Landau-Lifshitz-Gilbert（LLG）方程组成，并与电子自旋积累的时间相关扩散方程相连。该模型考虑了铁磁多层的磁化动力学中自旋积累的扩散过程。我们证明，在长时间的限制中，系统还原为更简单的方程式，其中llg方程与非线性和非局部稳态方程（称为SLLG）耦合。作为副产品，获得了SLLG方程的全球弱解的存在。此外，我们证明了SLLG解决方案的弱唯一性，即，只要后者及时存在，所有弱解决方案就与（独特的）强溶液一致。该结果为张，征税和Fert在[物理评论信88（2002）]中最初预测的定性行为提供了坚实的数学基础。
In this paper, we consider spin-diffusion Landau-Lifshitz-Gilbert equations (SDLLG), which consist of the time-dependent Landau-Lifshitz-Gilbert (LLG) equation coupled with a time-dependent diffusion equation for the electron spin accumulation. The model takes into account the diffusion process of the spin accumulation in the magnetization dynamics of ferromagnetic multilayers. We prove that in the limit of long times, the system reduces to simpler equations in which the LLG equation is coupled to a nonlinear and nonlocal steady-state equation, referred to as SLLG. As a by-product, the existence of global weak solutions to the SLLG equation is obtained. Moreover, we prove weak-strong uniqueness of solutions of SLLG, i.e., all weak solutions coincide with the (unique) strong solution as long as the latter exists in time. The results provide a solid mathematical ground to the qualitative behavior originally predicted by Zhang, Levy, and Fert in [Physical Review Letters 88 (2002)] in ferromagnetic multilayers.
