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Structural, magnetization, phonon behavior, and dielectric response ofnano-crystalline Gd$_2$CoMnO$_6$ have been presented in this paper. The studyshows that the material crystallizes in $\textit{P2$_1$/n}$ phase group of themonoclinic crystal structure. XPS measurement shows Co$^{2+}$ and Mn$^{4+}$oxidation states are present in the sample. Magnetization study reveals thatthe sample undergoes a ferromagnetic ordering of Co$^{2+}$ and Mn$^{4+}$magnetic ions around $T_c$ $\sim$132 K. However we have seen that with theapplication of external magnetic field the phase transition is largelysuppressed. Raman study reveals the presence spin-phonon coupling inGd$_2$CoMnO$_6$. Dielectric study reveals that the sample shows largedielectric constant and strong dispersion in mid frequency range. Thedielectric loss shows there are two relaxation processes present in thematerial with different relaxation time and which are driven by thermallyactivated relaxation mechanics. Further, the Nyquist plot and AC conductivitystudy show that this sample is non-Debye's in nature.

Suppression of magnetic phase transition at high magnetic field and  non-Debye's nature of nano-crystalline Gd$_2$CoMnO$_6$: a detail study of  physical properties