Spin-phonon coupling and dielectric spectroscopy in nano-crystalline Pr<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e978" altimg="si109.svg"><mml:msub><mml:mrow /><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>CoMnO<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e986" altimg="si110.svg"><mml:msub><mml:mrow /><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msub></mml:math> double perovskite manganite

In this paper, we present the spin-phonon coupling and dielectric response of nano-crystalline Pr$_2$CoMnO$_6$ employing Raman spectroscopic study. is a manganite compound , it undergoes paramagnetic to ferromagnetic (PM-FM) phase transition around $T_c$ $\sim$172 K. Temperature-dependent scattering experiment carried out across study behavior in material. The results from reveal an obvious softening phonon mode involving stretching vibrations (Co/Mn)O$_6$ octahedra temperature regions, indicating close correlation between magnetism lattice conform spin coupling. Further, have detailed on response, impedance spectroscopy, electric modulus AC conductivity ceramics range 20 K - 300 frequency 1kHz 5.5MHz. We found shows strong dependence with large dispersion constant. It that thermally activated relaxation mechanism involve material deviated Debye's model which confirmed by Nyquist plot complex modules behavior.