## G. Di Fratta - A. Jüngel - D. Praetorius - V. Slastikov

# Spin-diffusion model for micromagnetics in the limit of long times

created by difratta on 30 Apr 2021

[

BibTeX]

*preprint*

**Inserted:** 30 apr 2021

**Year:** 2020

**Abstract:**

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.