Experimental Investigations on the Electrical Conductivity and Complex Dielectric Permittivity of Zn x Mn 1−x Fe 2 O 4 (x = 0 and 0.4) Ferrites in a Low-Frequency Field.

Two samples of Zn_xMn_1−xFe₂O₄ (x = 0, sample A; and x = 0.4, sample B) were synthesized by the hydrothermal method. From complex impedance measurements in the range 100 Hz–2 MHz and for temperatures T between 30 and 130 °C, the barrier energy between localized states ΔE_relax was determined for the first time in these samples. For sample B, a single value of ΔE_relax was highlighted (0.221 eV), whilst, for sample A, two values were obtained (0.012 eV and 0.283 eV, below 85 °C and above 85 °C, respectively), associated with two zones of different conductivities. Using the Mott's VRH model and the CBH model, we determined for the first time both the bandgap energy barrier (W_m) and the hopping (crossover) frequency (ω_h), at various temperatures. The results show that, for sample A, W_m has a maximum equal to 0.72 eV at a temperature between 70 and 80 °C, whilst, for sample B, W_m has a minimum equal to 0.28 eV at a temperature of 60 °C, the results being in good agreement with the temperature dependence of the static conductivity σ_DC(T) of the samples. By evaluating σ_DC and eliminating the conduction losses, we identified, using a novel approach, a dielectric relaxation phenomenon in the samples, characterized by the activation energy E_A,rel. At various temperatures, we determined E_A,rel, which ranged from 0.195 eV to 0.77 eV. These results are important, as understanding these electrical properties is crucial to various applications, especially in technologies where temperature variation is significant. [ABSTRACT FROM AUTHOR]