Magnetic thin-film media response in presence of displacement eddy currents

Experimental tests have shown that macroscopic multilayer thin films excited by high-frequency magnetic field present permeance resonances. This unexpected behavior exists, even if the thickness of the magnetic films is smaller than the skin depth: in fact, for this condition, eddy currents within laminated magnetic sample should be inhibited. This phenomenon can be justified, observing that, for small thickness of the insulating interlayer, capacitive eddy currents across the dielectric layers begin to circulate between magnetic films. To predict the displacement eddy currents in macroscopic magnetic laminates some authors have provided various computational models based on different theoretical approaches. In particular, the computation of the effective complex permeability has been pointed out by means of coupled Maxwell's equations, both in differential form and in an integral one. In a previous work we have proposed and validated a circuit model able to simulate the behavior of magnetic samples in the frequency domain. In this paper we present an extensive comparative analysis between our model and the previous ones. The calculations provide the magnitude and the phase of the effective permeability of a laminate with 30 permalloy-ZrO2 film pairs. The simulations have been performed over the frequency range of 1-100 MHz and for different geometries. The results of the simulations have been also compared with those provided by experimental tests available in literature. The main goal of this study is to evaluate the performance and reliability of each model.