Magnetic exchange bias effect with magnetization reversal in double perovskite Er$_{\mathrm{2}}$CoMnO$_{\mathrm{6}}$ single crystal

We have successfully synthesized the high-quality single crystals of double perovskite Er$_{\mathrm{2}}$CoMnO$_{\mathrm{6}}$ by the conventional flux method with Bi$_{\mathrm{2}}$O$_{\mathrm{3}}$ flux, and have investigated their magnetic properties and magnetic exchange bias effects. The ferromagnetic order arises at $T_{\mathrm{C}} \quad =$63.5 K from the dominant Co$^{\mathrm{2+}}$ and Mn$^{\mathrm{4+}}$ superexchange interactions, mainly along the $c$ axis. A huge increase in the temperature dependence of specific heat divided by temperature occurs due to the Er$^{\mathrm{3+}}$ spin ordering at $T_{\mathrm{Er}}=$12 K. Magnetization reversal in temperature dependence of magnetic susceptibility and inverted hysteresis loop along the$ c$ axis in magnetic field dependence of magnetization are observed below $T_{\mathrm{Comp}}=$3.15 K, resulted from the interaction between Er$^{\mathrm{3+}}$ and Co$^{\mathrm{2+}}$/Mn$^{\mathrm{4+}}$ sublattices. The exchange bias effects are exhibited in the inverted hysteresis loops, and the maximum exchange bias field of 0.3 kOe is obtained after field cooling in $H_{\mathrm{FC}}=$0.190 kOe.