  We investigated optical spin orientation and dynamic nuclear polarization
(DNP) in individual self-assembled InGaAs/GaAs quantum dots (QDs) doped by a
single Mn atom, a magnetic impurity providing a neutral acceptor A$^0$ with an
effective spin $J=1$. We find that the spin of an electron photo-created in
such a quantum dot can be efficiently oriented by a quasi-resonant
circularly-polarized excitation. For the electron spin levels which are made
quasi-degenerate by a magnetic field compensating the exchange interaction
$\Delta_e$ with A$^0$, there is however a full depolarization due the
anisotropic part of the exchange. Still, in most studied QDs, the spin
polarized photo-electrons give rise to a pronounced DNP which grows with a
longitudinal magnetic field until a critical field where it abruptly vanishes.
For some QDs, several replica of such DNP sequence are observed at different
magnetic fields. This striking behavior is qualitatively discussed as a
consequence of different exchange interactions experienced by the electron,
driving the DNP rate via the energy cost of electron-nucleus spin flip-flops.
