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

We 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. Magnetic structures, such as mending heads, are modelled as connected sections of width, w, thickness D, resistivity p and magnetic properties: anisotropy H
_k
, saturation magnetization M, and wall coercivity H
_cw
. The easy magnetic axis is aligned perpendicular to the applied field. The model has two permeability terms: (1) from the easy-axis aligned domains, in which the bulk permeability (magnetization nitration) is radical by eddy currents and constricted by closure domains, and (2) from the hard axis regions, in which domain wall motion is described by the standard damping limited theory of wall motion solved for an oscillatory field. Saturation is handled by clipping the total moment change at 4πM, and replacing the wall phase delay with the transit time for a wall to cross the film.