  The fine structure of excited excitonic states in a quantum dot with an
embedded magnetic ion is studied theoretically and experimentally. The
developed theory takes into account the Coulomb interaction between charged
carriers, the anisotropic long-range electron-hole exchange interaction in the
zero-dimensional exciton, and the exchange interaction of the electron and the
hole with the $d$-electrons of a Mn ion inserted inside the dot. Depending on
the relation between the quantum dot anisotropy and the exciton-Mn coupling the
photoluminescence excitation spectrum has a qualitatively different behavior.
It provides a deep insight into the spin structure of the excited excitonic
states.
