Di Fratta, G., Jüngel, A., Praetorius, D., & Slastikov, V. (2023). Spin-diffusion model for micromagnetics in the limit of long times. Journal of Differential Equations, 343, 467–494. https://doi.org/10.1016/j.jde.2022.10.012
E101 - Institut für Analysis und Scientific Computing E101-02 - Forschungsbereich Numerik E101-02-2 - Forschungsgruppe Numerik von PDEs
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Journal:
Journal of Differential Equations
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ISSN:
0022-0396
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Date (published):
15-Jan-2023
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Number of Pages:
28
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Publisher:
ACADEMIC PRESS INC ELSEVIER SCIENCE
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Peer reviewed:
Yes
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Keywords:
Asymptotic analysis; Existence of solutions; Landau–Lifshitz–Gilbert equation; Micromagnetics; Spin diffusion; Weak-strong uniqueness
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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 [44] in ferromagnetic multilayers.
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Project title:
Analytische und numerische Koppelung im Mikromagnetismus: F 6509-N36 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Doktoratskolleg "Dissipation and Dispersion in Nonlinear Partial Differential Equations": W1245-N25 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
