  3$d$ based double perovskite materials have received much attention in recent
years due to their exotic magnetic structure and magneto-electric coupling. In
this work we have prepared and studied the nano-crystalline sample of
Ho$_2$CoMnO$_6$. Structural, magnetic, Raman and dielectric properties have
been studied in detail. The structural analysis shows that the sample
crystallize in monoclanic crystal structure with $\textit{P2$_1$/n}$ phase
group. The X-ray photoelectron spectroscopy have been employed to confirms the
charge state of cations presents in the material. Magnetic study shows that the
sample undergoes a paramagnetic to ferromagnetic phase transition around $T_c$
$\sim$85 K. The isothermal magnetization measurements shows hysteresis curve
hence confirm ferromagnetic behavior at low temperature. Temperature dependent
Raman study reveals that there is spin phonon coupling in the sample marked by
deviation in phonon mode from anharmonic behavior. Dielectric response of
Ho$_2$CoMnO$_6$ shows the large dispersion and large dielectric constant.
Impedance spectroscopy and electrical modulus study reveal that system shows
deviation from ideal Debye model. AC conductivity have been studied as a
function of both temperature and frequency. We found that the conduction
mechanism is obeyed by Jonscher's model. The exponent factor $n$ is suggest
that the material deviates from ideal Debye model.
