The effective permeability of granular thin films

An extended effective medium theory for calculating the permeability spectra of 2-D, granular films is presented. In plane dipole lattice sites are summed to determine the proper relation between the applied and local fields. The Clausius-Mossotti relation is then combined with the exact scattering solution to permit calculation of the complex μ_eff spectra of polycrystalline or amorphous 2-D arrays of spherical grains excited by a magnetic field incident perpendicular or parallel to the basal plane. In calculating the effective permeability spectra it is found that there are notable differences between the bulk and thin film models. In agreement with the authors´ theoretical predictions, it is found that as the granular film changes from 2-D to 3-D the magnitude of the permeability traces decreases while the resonance frequency increases. Comparison with experimental data shows the 2-D model to predict more accurately the frequency dependent permeability of thin films than the bulk model