Spindiffusion model for micromagnetics in the limit of long times
Abstract
In this paper, we consider spindiffusion LandauLifshitzGilbert equations (SDLLG), which consist of the timedependent LandauLifshitzGilbert (LLG) equation coupled with a timedependent 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 steadystate equation, referred to as SLLG. As a byproduct, the existence of global weak solutions to the SLLG equation is obtained. Moreover, we prove weakstrong 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 [44] in ferromagnetic multilayers.
 Publication:

Journal of Differential Equations
 Pub Date:
 January 2023
 DOI:
 10.1016/j.jde.2022.10.012
 arXiv:
 arXiv:2009.14534
 Bibcode:
 2023JDE...343..467D
 Keywords:

 35C20;
 35D30;
 35G20;
 35G25;
 49S05;
 Mathematics  Analysis of PDEs;
 35C20;
 35D30;
 35G20;
 35G25;
 49S05