A nonlocal model for the exchange energy in ferromagnetic materials (Q1188452)

The author proposes a new model for describing macroscopic effects in ferromagnetic materials. The \(|\nabla m|^ 2\) term in classical models is replaced by a nonlocal energy density designed to cause neighboring points to have parallel magnetization. Much of this paper is dedicated to describing measure-valued magnetizations and showing how they arise in physical situations. Then general existence results for minimization problems associated to the energy are given. In addition to the general existence theory for minimizers, some specific problems are treated and show how multiple solutions arise.