Investigations of the Nonlocal Exchange Energy Model on a Single Body of Ferromagnetic Material

Abstract

In this paper we do computations on a single spherical body of uniaxial ferro-magnetic material in a varying applied magnetic field. Our computations are based on a relaxed model with a nonlocal exchange energy. The model is based on Young-measures, but we will make use of recent calculations which indicate that our computations can be based on only the first and second moments. We extend the result of a single uniaxial sphere in a uniform applied magnetic field parallel to the easy direction of magnetization to uniform applied magnetic fields that are skew to the easy direction of magnetization. We show that when the exchange energy is zero, we duplicate the wide range of measured-value minimizers of De Simone's model. As the exchange energy grows, our model stabilizes at the saturated solutions of the Stoner-Wohlfarth model where the measured-valued minimizers are eliminated.