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Physical Properties of Nano-crystalline Sm$_2$CoMnO$_6$: structure, magnetism, spin-phonon coupling and dielectric study

Structural, magnetic, and dielectric properties of Sm$_2$CoMnO$_6$ have been studied. X-ray diffraction and Rietveld analysis show that the sample crystallizes in the monoclinic structure with \textit{P2$_1$/n} space group. Magnetic study shows that the sample undergoes a paramagnetic to ferromagnetic phase transition around $T_c$ $\sim$148 K and a low-temperature ordering of Sm$^{3+}$ moments. Temperature-dependent Raman study shows spin-phonon coupling present in this material. Dielectric response of Sm$_2$CoMnO$_6$ shows strong frequency dependence with large dispersion and large dielectric constant. Deviated from ideal Debye's model is found in impedance spectroscopy. Further, the activation energy obtained from tangent loss and complex impedance suggests that the relaxation process is due to electron hopping. AC conductivity has been studied to understand the conduction mechanism. The detailed analysis of AC conductivity shows that quantum mechanical tunneling of charges is involved in the conduction mechanism. The exponent obtained from AC conductivity measurements confirms the non-Debye's nature of Sm$_2$CoMnO$_6$.