A nonlocal model for the exchange energy in ferromagnetic materials

Abstract

When the exchange energy term of micromagnetics is replaced with a nonlocal energy term, the balance laws for a ferromagnetic material change from a system of second-order partial differential equations to a system of integral equations. The new system admits "measure-valued" magnetizations which describe the oscillations of the material's domain structure. A general existence theory is established for minimizers of the new energy, and multiple solutions for specific problems are found.