Spin-orbit coupling and Jahn-Teller effect in $T_d$ symmetry: an \textit{ab initio} study on the substitutional nickel defect in diamond

We analyze the spin-orbit and Jahn-Teller interactions in $T_d$ symmetry that are relevant for substitutional transition metal defects in semiconductors. We apply our theory to the substitutional nickel defect in diamond and compute the appropriate fine-leve structure and magneto-optical parameters by means of hybrid density functional theory. Our calculations confirm the intepretations of previous experimental findings that the 2.56-eV and 2.51-eV optical centres are associated with this defect. Our analysis of the electronic structure unravels possible mechanisms behind the observed optical transitions and the optically detected magnetic resonance signal, too.