Diffusion limit of the Boltzmann–Landau–Lifshitz–Gilbert system in ferromagnetic materials

Carlos J. García-Cervera (Department of Mathematics, University of California at Santa Barbara; and the BCAM Basque Center for Applied Mathematics, Bilbao, Basque Country, Spain)

Xu Yang (Department of Mathematics, University of California at Santa Barbara)

Abstract

In this paper, we continue the study initiated in our previous work on the “Semiclassical limit of the Schrödinger–Poisson–Landau–Lifshitz–Gilbert system” [Arch. for Rat. Mech. Anal., 227(3):897-928 2018]. Specifically, we consider the $s$-wave form spin dynamics coupled with the magnetization dynamics governed by the Landau–Lifshitz–Gilbert system, and rigorously obtain the diffusion limit of the coupled system.

Keywords

diffusion limit, Boltzmann–Landau–Lifshitz–Gilbert system, ferromagnetic materials

2010 Mathematics Subject Classification

35K55, 35Q20, 81S30, 82D40

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C.J.G.C. acknowledges support from NSF grant DMS 1065942 and AFORS grant FA9550-18-1-0095.

X.Y. acknowledges support from NSF grants DMS 1418936 and 1818592, and KI-Net NSF RNMS grant 1107291.

Received 27 September 2017

Accepted 27 March 2018

Published 31 October 2018