Frequency dispersion model of the complex permeability of soft ferrites in the microwave frequency range

The complex permeability of Cu-doped nickel-zinc polycrystalline ferrites is strongly dependent on microstructure, particularly, on relative density () and average grain size (). In this study, a mathematical model, able to fit the measured magnetic permeability spectra from 10⁶ to 10⁹ Hz, is proposed and validated for a width range of average grain sizes (3.40–23.15 μm) and relative densities (0.83–0.96). To the authors’ knowledge, domain-wall motion and spin rotation contributions to magnetic permeability have been integrated jointly with the microstructure for the first time in the proposed model, highlighting the relative influence of each magnetizing mechanism and microstructure on the magnetic permeability at different angular frequencies.