# HM-MAG : Hytérésis et Modélisation des micro-objets MAGnétiques

## Essential

Magnetic micro ob jects take an important place in domains such as nano-
electronic, magnetic recording or characterization. The aim of the study is
to model the behavior of the magnetization in small magnetic ob jects in order
optimize their performances in complex systems. In this study we will focus on
two main themes: the development of a mesoscopic model from the atomistic
description of the material and the understanding of the hysteresis which is a
strong characterization tool.
The micro-scale modeling has two main aims: to understand the Landau-Lifchitz
equation of the micromagnetism theory and particularly the dissipation coe?-
cient and to introduce the heat inßuence in the dynamic micromagnetic model.
In the hysteresis part of the pro ject, we are interested in demonstrating the exis-
tence of hysteresis and characterizing the cycle, for the dynamic micromagnetic
model. The main challenges are the understanding of the Barkhausen noise
phenomenon, in particular we would like to investigate if this phenomena is at
least partially modeled by the micromagnetism theory.

## International position

The transition between atomic and mesoscopic scales has not been studied math-
ematically yet, but physicist are very interested in understanding the real link
between the micromagnetic model and the ab-initio model of magnetic materi-
als. This understanding is of great importance in building a mesoscopic model
for nano-electronic purpose, in particular, in taking into account the caloriÞc
phenomenon. Nowadays, many physical laboratories are developing research
programs on this subject.
Hysteresis has been mathematically studied, for example, by A. Visintin for
simpliÞed magnetic systems using additional contribution in order to obtain
the hysteresis behavior forecasted by physicists. In the physical point of view,
hysteresis is particularly useful in order to study ferromagnetic materials and
try to characterize the presence of defects in the crystalline structure.

# Financement

Le projet HM-MAG est financé par le RTRA Nano-sciences de Grenoble.

# Les personnes investies dans le projet

Labbé Stéphane (Enseignant-chercheur, responsable),

Bidegaray Brigitte (Chercheur, collaborateur),

Dumas Eric (Enseignant-chercheur, collaborateur),

Bokoch Serguiy (Post-doctorant fondation Nano-Sciences, collaborateur),

Jouet Quentin (Doctorant UJF, collaborateur),

# Les publications

**[1]** Eric Dumas et Stéphane Labbé, *Hysteresis for ferromagnetism: asymptotics of some 2-scale Landau-Lifshitz model*, Journal of Evolution Equations, 12, 3, 621-645, 2012 .
**[2]** Brigitte Bidégaray, Quentin Jouet et Stéphane Labbé, *Static ferromagnetic materials: from the microscopic to the mesoscopic scale*, Communications in Contemporary Mathematics, A paraître, 2013 .
**[3]** Pierre Etoré, Stéphane Labbé et Jérôme Lelong, *Long time behaviour of a stochastic nano particle*, Jounal of Differential Equations, 257, 6, 2115-2135, 2014 .

# Nouvelles