In this study, we investigate the impact of \(Cr\) substitution on the structural, magnetic, impedance, and ac conductivity characteristics of polycrystalline single-phase \(D{y}_{3}F{e}_{5-x}C{r}_{x}{O}_{12}\) \(\left(x=0.0-0.5\right) (Cr-DyIG)\) samples. Our findings reveal a reduction in lattice constant values with the increase in \(Cr\) concentration and it is attributed to the smaller ionic radii of \(C{r}^{3+}\) in comparison to \(F{e}^{3+}\) ions. Consecutively, the ferrimagnetic transition temperature \(({T}_{c})\) decreases from \(549\) to \(509\text{ K}\) as \(x\) varies from \(0.0\) to \(0.5\) . The low-temperature magnetization passes through magnetic compensation \(({T}_{comp})\) and spin-reorientation transition \(({T}_{SR})\) that arises due to the exchange interactions between rare earth ions and \(F{e}^{3+}\) moments. Moreover, the substitution of \(Cr\) has enhanced the room temperature saturation magnetization of the base material from \(3.33\text{ emu}/\text{g}\) to \(8.92\text{ emu}/\text{g}\) . Further, Nyquist plots were analyzed to assess contributions from grains, grain boundaries, and electrodes, while Mott’s Variable Range Hopping model was applied to relaxation dynamics to determine hopping length and energies. Also, analysis of ac conductivity using Jonscher’s Power Law reveals that the parent sample primarily exhibits large polaron hopping, while \(Cr\) -doped samples show small polaron hopping as the main mode of electrical conduction.
