Analysis of conductivity and dielectric spectra of Mn_0.5Zn_0.5Fe₂O₄ with coupled Cole-Cole type anomalous relaxations

Most of the crystalline materials seldom show a well-defined dielectric loss peak due to domination of dc conductivity contribution, but effects of loss peaks are seen at high frequencies. Ac electrical data of nano-crystalline Mn_0.5Zn_0.5Fe₂O₄ synthesised by chemical co-precipitation method show such behaviour. Properly combined and formulated conduction and dielectric relaxation functions are required for such materials. Cole-Cole type relaxation function in the combined conduction and dielectric process is formulated for complex resistivity ρ(ω), complex permittivity ε(ω), complex conductivity ^σ(ω) and complex electric modulus M(ω). Conduction and dielectric relaxation are linked to Jonscher's idea of 'pinned dipole' and 'free dipole' to understand the relaxation dynamics. The physical parameters of 'pinned dipole' and 'free dipole' formalism are unique for all representations like ^ρ(ω), ^ε(ω), ^σ(ω) and M(ω). 'Pinned dipole' relaxation time τ_c related to conduction process and 'free dipole' relaxation time τ_d related to dielectric process show Arrhenius behaviour with the same activation energy. Correlation of dc conductivity σ_c with τ_c and τ_d indicates the coupled dynamics of 'pinned dipole' and 'free dipole'. Time-temperature scaling of conduction and dielectric relaxation reveals that the mechanism of coupled dynamics of 'pinned dipole' and 'free dipole' is temperature independent. Hopping of charge carriers with dynamics of disordered cation distribution of host matrix generates a coupled conduction and dielectric relaxation in Mn_0.5Zn_0.5Fe₂O₄.