Resonant photoluminescence and dynamics of a hybrid Mn-hole spin in a positively charged magnetic quantum dot

We analyze, through resonant photoluminescence, the spin dynamics of an individual magnetic atom (Mn) coupled to a hole in a semiconductor quantum dot. The hybrid Mn-hole spin and the positively charged exciton in a CdTe/ZnTe quantum dot forms an ensemble of $\Lambda$ systems which can be addressed optically. Auto-correlation of the resonant photoluminescence and resonant optical pumping experiments are used to study the spin relaxation channels in this multilevel spin system. We identified for the hybrid Mn-hole spin an efficient relaxation channel driven by the interplay of the Mn-hole exchange interaction and the coupling to acoustic phonons. We also show that the optical $\Lambda$ systems are connected through inefficient spin-flips than can be enhanced under weak transverse magnetic field. The dynamics of the resonant photoluminescence in a p-doped magnetic quantum dot is well described by a complete rate equation model. Our results suggest that long lived hybrid Mn-hole spin could be obtained in quantum dot systems with large heavy-hole/light-hole splitting.