Charge conduction and relaxation in Ca$_{1−x}$Dy$_x$BaFe$_4$O$_7$

The paper presents in-depth studies of the dielectric properties and conduction dynamics of Dy-doped CaBaFe$_4$⁢O$_7$ which is a recently characterized magnetoelectric material with strong potentials for technological applications as it shows a near-room-temperature ferrimagnetic transition along with strong ferrimagnetic moment, and gigantic electric polarization change. This work demonstrates the direct correlation of the dielectric and electrical transport properties of Ca$_{1−𝑥}$⁢Dy$_𝑥$⁢BaFe$_4$⁢O$_7$ (𝑥=0, 0.01, 0.03, and 0.05) with structural distortion through various dc, ac conduction, high-energy x-ray diffraction studies, and modeling of the data. CaBaFe$_4$⁢O$_7$ has a unique structure characterized by alternate stacking of FeO4 tetrahedra in triangular and kagomé layers. Large structural distortion, competing magnetic interactions, exchange striction effects, and possible charge ordering are expected to play a major role in the dielectric and electrical properties of the material. We report observation of short-range polaron hopping conduction mechanism in the low-temperature regime and signature of large polaronic nature of charge carriers. Modeling of the electric modulus using Havriliak-Negami equation points out both distribution and cooperativeness in the polaron dynamics which can be correlated to the interplay of structural distortion, and the background electric field due to the polar nature of the materials. The Havriliak-Negami parameters closely follow orthorhombic distortion of the structures.