Simple model of the high frequency permeability of narrow thin-film structures with eddy currents, walls, and saturation

The authors report the derivation and experimental verification of a simple model of the high-frequency permeability of narrow soft-magnetic thin-film structures which includes eddy currents and magnetization rotation, wall motion, and saturation. Data are presented for long narrow magnetic rectangles with the idea that common thin-film magnetic structures, such as recording heads, can be modeled as connected stripes of different widths. The easy magnetic axis is aligned perpendicular to the applied field and to the long axis of the stripes. The model has two terms: from the easy-axis aligned domains, the bulk permeability (magnetization rotation) reduced by eddy currents and and constriction due to closure domains, and from the hard axis regions, domain wall motion described by the standard damping limited theory of wall motion solved for an oscillatory field. Saturation is handled by clipping the total moment change of 4 πM, and replacing the wall phase delay with the transit time for a wall to cross the film