Enhancement of dielectric permittivity and Havriliak-Negami relaxation mechanism in MnFe₂O₄ through Dy substitution

Pristine and Dy substituted MnFe₂O_4,MnFe_2-<i>x</i>Dy<i>_x</i>O₄(<i>x</i>= 0.00, 0.02, 0.04, 0.06, 0.08 & 0.10) were successfully synthesized by sol-gel method to investigate the dielectric properties of the system. MnFe₂O₄exhibits a high dielectric permittivity of order 10⁴which is further augmented by 60% through Dy substitution. This is owing to the rise in interfacial polarization resulting from localized states, dipolar polarization arising from the multiple valence states of Fe and Mn ions, atomic polarization due to structural distortion induced by strain, and electronic polarization stemming from the concentration of free charge carriers. The enhancement of induced strain, mixed valence ratio of Fe²⁺/Fe³⁺and Mn⁴⁺/Mn²⁺, localized states, and free charge carrier concentration are confirmed from the XRD, XPS, and optical studies, respectively. The dielectric relaxation mechanism of MnFe_2-xDy_xO₄follows a modified Havriliak-Negami relaxation model with conductivity contribution. Complex impedance analyses further validate the contribution of grain-grain boundary mechanisms to the dielectric properties confirmed through Nyquist plots. A comprehensive analysis of conductivity reveals the significant impact of Dy substitution on the electrical conductivity of MnFe₂O₄. This influence is strongly related to the variations in the concentration of free charge carriers within the MnFe_2-<i>x</i>Dy<i>_x</i>O₄system. The understanding of the underlying physics governing the dielectric properties of Dy-substituted MnFe₂O₄not only enhances the fundamental knowledge of material behavior but also opens new avenues for the design and optimization of advanced electronic and communication devices.