Defect-engineered charge transport and dielectric relaxation in In/Se co-substituted CoNi spinel ferrite nanoparticles by sonochemical route

This study presents a comprehensive investigation into the influence of indium and selenium co-substitution on the structural, electrical, and dielectric properties of CoNi spinel ferrite nanoparticles (SFNPs) synthesized via the sol–gel auto-combustion method. The compositional series In/Se → CoNi (x ≤ 0.10) was examined through X-ray diffraction (XRD), electron microscopy. XRD analysis confirmed the formation of a single-phase cubic spinel structure with crystallite sizes below 10 nm, consistent with earlier findings (Ref. 11). The temperature- and frequency-dependent dielectric and impedance spectra reveal pronounced modifications in charge-carrier dynamics with increasing In/Se content. AC and DC conductivity analyses demonstrate thermally activated small-polaron hopping as the dominant mechanism, with activation energies decreasing from 0.33 to 0.08 eV upon substitution, indicating enhanced charge delocalization and reduced potential barriers. The 2D conductivity (σ), permittivity (ε'), and modulus (M*) lines highlight the transition from interfacial polarization–dominated behavior to defect-assisted hopping conduction at moderate substitution levels (x ≈ 0.06–0.08). Complex impedance and Cole–Cole analyses confirm non-Debye relaxation behavior with distinct grain, grain boundary, and interfacial contributions, successfully modeled using the R(CR)(CR)(CR) equivalent circuitry. Optimal co-doping induces improved conductivity, reduced impedance, and stabilized dielectric permittivity, establishing In/Se → CoNi spinel ferrites as promising candidates for energy-storage, high-frequency, and spintronic applications.