Control of travelling walls in a ferromagnetic nanowire

Gilles Carbou; Stéphane Labbé; Emmanuel Trélat

doi:10.3934/dcdss.2008.1.51

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2008, Volume 1, Issue 1: 51-59. Doi: 10.3934/dcdss.2008.1.51

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Control of travelling walls in a ferromagnetic nanowire

1.
MAB, UMR 5466, CNRS, Université Bordeaux 1, 351, cours de la Libération, 33405 Talence cedex
2.
Université Paris-Sud, Labo. Math., Bat. 425, 91405 Orsay Cedex
3.
Université d’Orléans, UFR Sciences, Fédération Denis Poisson Mathématiques, Laboratoire MAPMO, UMR 6628, Route de Chartres, BP 6759, 45067 Orléans Cedex 2

Received: June 30, 2006

Revised: August 31, 2007

Published: February 2008

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Abstract

We investigate the problem of controlling the magnetic moment in a ferromagnetic nanowire submitted to an external magnetic field in the direction of the nanowire. The system is modeled with the one dimensional Landau-Lifschitz equation. In the absence of control, there exist particular solutions, which happen to be relevant for practical issues, called travelling walls. In this paper, we prove that it is possible to move from a given travelling wall profile to any other one, by acting on the external magnetic field. The control laws are simple and explicit, and the resulting trajectories are shown to be stable.

Keywords:

Landau-Lifschitz equation,
control.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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