Control of travelling walls in a ferromagnetic nanowire

Gilles Carbou (1) , Stéphane Labbé (2) , Emmanuel Trélat (3)

1 MAB - Laboratoire de Mathématiques Appliquées de Bordeaux
2 EDP
3 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Mots clés: Exact controllability; Partial Differential Equations; Robustness; micromagnetism

Domaines: Optimisation et contrôle [math.OC]

Gilles Carbou, Stéphane Labbé, Emmanuel Trélat. Control of travelling walls in a ferromagnetic nanowire. 2006. ⟨hal-00092133v1⟩