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.
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