The behaviour of ferromagnetic sheets in alternating electric and magnetic fields I. A domain theory of the skin-effect impedance and complex permeability

Abstract

Eddy current losses measured in ferromagnetic materials are generally greatly in excess of values calculated on the usual assumption that the permeability is uniform throughout the material. In reality changes of magnetization occur, for the most part, within the relatively minute volume of the Bloch walls. In this paper a domain model consisting of nearly plane domain walls normal to the surfaces of an infinite sheet is adopted as a basis for the calculation of eddy current effects. The model is basically that of Polivanov (1952) but extended to include such effects as arise from the finite surface energy and inertia of the domain walls, relaxation damping of their motion, and short-range fluctuations in both domain width and the restoring forces which localize the walls. In addition to the dispersion of the complex effective permeability, the frequency dependence of the electrical resistance and inductance of a ferromagnetic strip are also calculated. At low frequencies the losses are found to be much higher, and at high frequencies somewhat lower, than the classically computed values, the disparity increasing with increasing wall spacing from zero at zero wall spacing. The effect of short-range fluctuations of the domain width is shown to be small, but similar fluctuations in the domain wall restoring pressure constant about its mean value are found to lead to very high losses at low frequencies coupled with high-frequency losses which are not much below those predicted by the classical theory, a result in agreement with experimental observation. It is shown also that theories based on this type of simple domain model, in which the intradomain permeability is neglected entirely in comparison with that attributed to domain wall motion, must eventually break down at frequencies so high that domain wall motions are effectively damped out and the eddy current behaviour is primarily governed by the small intra-domain permeability