Minimal time of magnetization switching in small ferromagnetic ellipsoidal samples - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2023

Minimal time of magnetization switching in small ferromagnetic ellipsoidal samples

Abstract

In this paper, we consider a ferromagnetic material of ellipsoidal shape. The associated magnetic moment then has two asymptotically stable opposite equilibria, of the form $\pm\overline{m}$. In order to use these materials for memory storage purposes, it is necessary to know how to control the magnetic moment. We use as a control variable a spatially uniform external magnetic field and consider the question of flipping the magnetic moment, i.e., changing it from the $+\overline{m}$ configuration to the $-\overline{m}$ one, in minimal time. Of course, it is necessary to impose restrictions on the external magnetic field used. We therefore include a constraint on the $L^\infty$ norm of the controls, assumed to be less than a threshold value $U$. We show that, generically with respect to the dimensions of the ellipsoid, there is a minimal value of $U$ for this problem to have a solution. We then characterize it precisely. Finally, we investigate some particular configurations associated to geometries enjoying symmetries properties and show that in this case the magnetic moment can be controlled in minimal time without imposing a threshold condition on $U$.
Fichier principal
Vignette du fichier
min_Time_Switch_CCFP.pdf (1.81 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03931579 , version 1 (09-01-2023)

Identifiers

Cite

Raphaël Côte, Clémentine Courtès, Guillaume Ferriere, Yannick Privat. Minimal time of magnetization switching in small ferromagnetic ellipsoidal samples. 2023. ⟨hal-03931579⟩
121 View
45 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More