We consider the magnetization of ferromagnetic samples in form of a thin film under an in-plane exterior field. Bryant and Suhl have proposed an model which predicts the equilibrium magnetization given the exterior field. Hubert and coworkers have shown that the predictions of this ad hoc model are in good agreement with the experimental observations. We rigorously derive the ad hoc model from the well-accepted micromagnetic model in a broad regime of the physical parameters. Moreover, our derivation extends the original model.
Mathematically speaking, the micromagnetic model comes in form
of a variational problem: The equilibrium magnetization is
the minimizer (groundstate) of the micromagnetic energy.
This variational problem is NON CONVEX and non local, which
makes numerical simulations extremely delicate
and expensive. We prove that in the above mentioned parameter
regime we have a nice separation of
energy scales, so that the major part of the variational
problem reduces to a CONVEX (but still non local) problem.
We also present numerical simulations of the simplified problem.
This is joint work with R. V. Kohn (Courant Institute, New York)
and S. Mueller and A. DeSimone (both Max-Planck Institute,
Leipzig, Germany).
Friday, October 23rd
11:00 - 12:00 am
South Hall 6623