On the Landau-Lifshitz-Bloch equation with spin torque effects

A mathematical model for current-induced magnetization dynamics in ferromagnets at elevated temperatures is considered. The model is represented by a classical Landau-Lifshitz-Bloch equation containing adiabatic and non-adiabatic torques. In the case of a ferromagnet confined to a bounded domain of...

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Bibliographic Details
Published in:Alexandria engineering journal 2021-10, Vol.60 (5), p.4433-4439
Main Authors: Ayouch, Chahid, Nisar, Kottakkaran Sooppy, Tilioua, Mouhcine, Zakarya, M.
Format: Article
Language:English
Subjects:
Asymptotic behaviour
Faedo-Galerkin method
Uniqueness
Weak solutions
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Summary:A mathematical model for current-induced magnetization dynamics in ferromagnets at elevated temperatures is considered. The model is represented by a classical Landau-Lifshitz-Bloch equation containing adiabatic and non-adiabatic torques. In the case of a ferromagnet confined to a bounded domain of R3, we prove existence of a weak solution by using Faedo-Galerkin approach and a compactness method. This paper extends the work done by Le et al. (2016) in the absence of adiabatic and non-adiabatic terms. Furthermore, uniqueness is proved in the case of dimension one and two. Finally, the limiting behaviour in large time is studied for the non-adiabatic case.
ISSN:1110-0168
DOI:10.1016/j.aej.2021.03.025