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

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