Single-Domain Particles : New Uses of Old Theorems

This article describes some applications of potential theory and classical dynamics to one field of current research, the theory of magnetization processes in “hard” magnetic materials. Many such materials owe their magnetic properties to the fact that they are composed of fine ferromagnetic particles separated by less magnetic regions. In very fine particles, the exchange forces responsible for the spontaneous magnetization keep it uniform in direction within any one particle; the magnetization curve is then determined by rotations of the particle magnetizations. The rotations are controlled by the interplay of external magnetic energy and of internal energy, also largely magnetic. A first step in the theory is therefore the derivation of a general formula for the internal magnetic energy. Simplifications can then be made because of the uniformity of magnetization of each particle; in particular, it can be shown that a particle of arbitrary shape is equivalent to an ellipsoid. Calculation of static hysteresis loops requires consideration of stability conditions ; analysis of magnetization reversals and of the behavior in microwave fields involves the dynamics of gyroscopic systems.