  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.
