Insights into crystal structure, temperature-dependent magnetization and dielectric relaxation mechanism in Bi substituted samarium iron garnet

The single phase $S{m}_{3-x}B{i}_{x}F{e}_5{O}_{12}$ with $x=0.0,0.2,0.4$ and $0.6$ samples are synthesized by solid-state reaction method. We have systematically studied the structural, morphological, temperature dependent magnetic and electric properties. All the samples crystallize in simple cubic crystal structure and belongs to $Ia\bar{3}d$ space group. The lattice constant and bond angle between $Fe\left(a\right)-O-Fe\left(d\right)$ network is enhanced with Bi substitution. As a result, the ferrimagnetic transition temperature is also enhanced from $565K$ to $569K$. We have examined the applicability of Bloch's and Cojocaru's laws to our temperature-dependent magnetization data and find that Bloch's $T^{3/2}$ law is not suitable due to geometrical asymmetry, long wavelength excitation, and local atomic disorders. However, Cojocaru's law which accounts for the geometrical aspects, provides a better fit to our magnetization data. Further, the impedance plots at room temperature exhibit no relaxation which is attributed to the limited mobility of charge carriers. On the other hand, the high temperature impedance data represents dielectric relaxation at a particular frequency. This frequency is used to determine the relaxation time which is fitted to Arrhenius law and activation energy is evaluated. The activation energy lies in between $0.24-0.32eV$ which corresponds to the singly ionized oxygen vacancies. The conduction mechanism is analyzed with Variable range hopping model and the average hopping length and hopping energies are also determined for these garnet samples.