Intrinsic defects and 4d/5d transition metal defects in Cr$_2$O$_3$: pathways for enhancing the Néel temperature

First-principles calculations are employed to explore avenues to increase the Néel temperature ($T_{\mathrm{N}}$) of the magnetoelectric antiferromagnet Cr$_2$O$_3$ through doping. Employing the hybrid functional method, we calculate the formation energy of intrinsic defects and transition metal dop