Impact of skin effect on permeability of Permalloy films

We investigated the impact of skin effect on permeability of Permalloy films with different thicknesses. With eliminating multi domain structure by measuring field permeability spectrum, the picture of permeability determined by natural resonance and modulated by skin effect was demonstrated. It is found that both the value of permeability and line shape of the field permeability spectrum depend on thickness significantly due to skin effect. The real part of field permeability spectrum decreases from 974 (0.04 mu m) to 14 (4 mu m) at 3.2 GHz, and two loss peaks appear in the imaginary part in films thicker than 2 mu m, which can't be explained by previous work. We established a skin effect-related model of permeability with which the experimental permeability spectra can be well fitted. The calculated cut-off frequency is significantly reduced by skin effect from 3.5 GHz (0.02 mu m) to 0.3 GHz (4 mu m), which is dominated by the natural resonance frequency (t = 1.46 mu m) and the additional loss peak frequency caused by skin effect (t > 1.46 mu m) successively.