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Micromagnetics of very thin films B y Gustavo Gioia and Richard D. James

Summary: Micromagnetics of very thin films
B y Gustavo Gioia and Richard D. James
Department of Aerospace Engineering and Mechanics, University of Minnesota,
107 Akerman Hall, Minneapolis, MN 55455, USA
We determine by a scaling calculation the limiting form of the free energy govern-
ing a ferromagnetic film of vanishing thickness. Our theory generalizes Stoner and
Wohlfarth's results for flat ellipsoids to arbitrary-shaped very thin films.
1. Introduction
In their well-known paper, Stoner & Wohlfarth (1948) made use of the idea that
if a ferromagnetic particle is small, the energy-minimizing magnetization will be
nearly constant. This becomes apparent by writing the micromagnetic energy per
unit volume of a particle of typical diameter , and uniformly rescaling the energy
onto a domain of typical diameter 1. It is found that in the rescaled energy the
exchange term is

| m|2
dy, (1.1)
where is the exchange constant. Thus, as 0, the exchange term contributes an


Source: Alouges, François - Centre de Mathématique Appliquées, École Polytechnique


Collections: Mathematics