Communications in Mathematical Sciences

Volume 13 (2015)

Number 7

On a model of magnetization switching driven by a spin current: A multiscale approach

Pages: 1875 – 1904

DOI: http://dx.doi.org/10.4310/CMS.2015.v13.n7.a10

Authors

Abdallah Naoufel Ben (Institut de Mathématiques de Toulouse, Université de Toulouse, France)

Elise Fouassier (Institut de Mathématiques de Toulouse, Université de Toulouse, France; and Institut Camille Jordan, Université de Lyon, Villeurbanne, France)

Clément Jourdana (Institut de Mathématiques de Toulouse, Université de Toulouse, France; Istituto di Matematica Applicata e Tecnologie Informatiche, Pavia, Italy; and Laboratoire Jean Kuntzmann, Université Grenoble Alpes, Grenoble, France)

David Sanchez (Institut de Mathématiques de Toulouse, Université de Toulouse, France)

Abstract

We study a model of magnetization switching driven by a spin current: the magnetization reversal can be induced without applying an external magnetic field. We first write our one-dimensional model in an adimensionalized form using a small parameter $\epsilon$. We then explain the various time and space scales involved in the studied phenomena. Taking into account these scales, we first construct an appropriate numerical scheme that allows us to recover numerically various results of physical experiments. We then perform a formal asymptotic study as $\epsilon$ tends to $0$ using a multiscale approach and asymptotic expansions. We thus obtain approximate limit models that we compare with the original model via numerical simulations.

Keywords

spin transfer, spintronics, micromagnetics, Landau–Lifshitz equation, numerical simulations, multiscale analysis, asymptotic expansions

2010 Mathematics Subject Classification

35B40, 35Q60, 41A60, 65Z05, 78A25

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