Dynamics of complex impedance, dielectric and electric modulus for NiCuZn ferrites with theoretical justification

Ni0.80-xCu0.20ZnxFe2O4 (step size 0.05) with titular compiled chemical of various spinel ferrites have been synthesized through auto-combustion and characterized through X-ray diffraction for structural analysis which showed 43 to 46 nm distributed cubic spinel. The effect of Zn2+ substitutions to dilute the NiCuZn ferrites has been studied with electrical modulus analysis and impedance measurements within the frequency range from 20 to 5 MHz. Besides semicircular arc tendency, two-layer leaky capacitor model is indicated by the complex impedance spectroscopy at lower- and higher-frequency ranges. Non-Debye type relaxation has been revealed clearly in the electric modulus spectra. Non-Debye type dielectric nature is found in the dielectric spectrum and checked by the Non-modified Debye equation. The AC conductivity spectrum is found in increasing order and justified by theoretical Jonscher Power Law. The Cole-Cole plots confirm the single semicircles for grain boundary contribution at the lower-frequency zone, which is further justified by the theoretical model. The role of Zn in modifying nanostructure and impedance spectra of these ferrites has been explained.