Structural and complex impedance spectroscopic studies of Ni_0.5Mg_0.3Cu_0.2Fe₂O₄ ferrite nanoparticle

Spinel ferrite having composition Ni_0.5Mg_0.3Cu_0.2Fe₂O₄ was prepared by the sol–gel technique at 1473 K. The X-ray diffraction results indicate that the ferrite sample has a cubic spinel-type structure with Fd3 ¯ m space group. The electrical properties of the studied sample using complex impedance spectroscopy technique have been investigated in the frequency range 10²–10⁷ Hz and in the temperature range 300–500 K. The total conductivity curves for sample are found to obey Jonscher power law (σ(ω) = σ_dc + Aωⁿ) with an increase in the frequency exponent (n) as temperature increases. The activation energy deduced from the analysis of the conductivity curves matches very well with the value estimated from the relaxation time, indicating that relaxation process and electrical conductivity are attributed to the same defect. Nyquist plots of impedance show semicircle arcs for sample, and an electrical equivalent circuit has been proposed to explain the impedance results. The effect of frequency and temperature on dielectric constant (ε″) and dielectric loss (tanδ) has also been discussed in terms of hopping of charge carriers between Fe²⁺ and Fe³⁺ ions.