  Using the emission of the positively charged exciton as a probe, we analyze
the dynamics of the optical pumping and the dynamics of the relaxation of a Mn
spin exchange-coupled with a confined hole spin in a II-VI semiconductor
quantum dot. The hole-Mn spin can be efficiently initialized in a few tens of
$ns$ under optical injection of spin polarized carriers. We show that this
optical pumping process and its dynamics are controlled by electron-Mn
flip-flops within the positively charged exciton-Mn complex. The pumping
mechanism and its magnetic field dependence are theoretically described by a
model including the dynamics of the electron-Mn complex in the excited state
and the dynamics of the hole-Mn complex in the ground state of the positively
charged quantum dot. We measure at zero magnetic field a spin relaxation time
of the hole-Mn spin in the $\mu s$ range or shorter. This hole-Mn spin
relaxation is induced by the presence of valence band mixing in self-assembled
quantum dots.
