Some Properties of the Coercive Force in Soft Magnetic Materials

Abstract

The coercive force is the value of the magnetic field amplitude when the net magnetization in the direction of the field is zero and has a zero time rate of change. An equivalent definition of the coercive force is contained in the expression for the average instantaneous domain wall velocity; $v=k(H\ensuremath{-}{H}_{c})$, in which $k$ depends upon motional energy losses and $H$ is the applied magnetic field: ${H}_{c}$ is the coercive force. We have used this latter definition to measure the coercive force in specimens of magnetically annealed 65 Permalloy (65% Ni-Fe) tapes and a 3.25% SiFe picture frame single crystal for both low- and high-field domain configurations. The coercive force measured in this way for low applied fields is the same as that determined by other techniques. For the high-field determination, with domain walls unattached to the specimen surfaces, the coercive force is, for our samples, less than half the low-field coercive force. We call the value determined at high fields the "internal coercive force" and believe this value to be characteristic of the bulk material. The low-field coercive force includes both the "internal coercive force" and a component due to preferential "pinning" of domain walls at the specimen surfaces. The experimentally observed dependence of the coercive force upon specimen thickness may be explained using surface pinning of domain walls. This explanation was previously postulated by Dijkstra.The difference in coercive force between surface free and surface pinned domain walls may be used to make a lower limit estimate of the domain wall energy density. The results are in order-of-magnitude agreement with the values expected from theory.Considerations of the experimentally determined expression for domain wall velocity given above show that the positional free-energy variations which determine the coercive force cannot be described by conservative periodic functions.