  We report on the micro-photoluminescence spectroscopy of InAs/GaAs quantum
dots (QD) doped by a single Mn atom in a magnetic field either longitudinal or
perpendicular to the optical axis. In both cases the spectral features of
positive trion (X+) are found to split into strongly circularly polarized
components, an effect very surprising in a perpendicular magnetic field. The
field-induced splitting is ascribed to the transverse Zeeman splitting of the
neutral acceptor complex A0 issued by the Mn impurity, whereas the circular
optical selection rules result from the p-d exchange which acts as a very
strong longitudinal magnetic field inhibiting the spin mixing by the transverse
field of the QD heavy-hole ground state. A theoretical model of the spin
interactions which includes (i) the local strain anisotropy experienced by the
acceptor level and (ii) the anisotropic exchange due to the out-of-center Mn
position provides a very good agreement with our observations.
