Coupling of the triplet states of a negatively charged exciton in a quantum dot with the spin of a magnetic atom

Two electrons in a quantum dot (QD) can form triplet states. We analyze the exchange coupling of the triplet states of the negatively charged exciton in a QD (${\mathrm{X}}^{\ensuremath{-}}$, two electrons and one hole) with the spin of a magnetic atom (Mn). Two techniques are used to access the spin structure of this magnetic complex: the resonant excitation of the excited states of ${\mathrm{X}}^{\ensuremath{-}}$-Mn and the analysis of the emission of a negatively charged biexciton in a magnetic dot (${\mathrm{XX}}^{\ensuremath{-}}$-Mn). The photoluminescence (PL) excitation of ${\mathrm{X}}^{\ensuremath{-}}$-Mn reveals excited states with a circularly polarized fine structure which strongly depends on the Mn spin state ${S}_{z}$ and gives rise to negative circular polarization emission. This fine structure arises from the coupling of the triplet states of an excited charged exciton with the Mn atom (${\mathrm{X}}^{\ensuremath{-}*}$-Mn), and its ${S}_{z}$ dependence can be described by a spin effective model. The recombination of ${\mathrm{XX}}^{\ensuremath{-}}$-Mn leaves in the dot a charged exciton in its excited state, and the PL structure is controlled by the coupling of triplet states of ${\mathrm{X}}^{\ensuremath{-}*}$ with the Mn spin. An analysis of the polarization and magneto-optic properties of this emission gives access to the electron-hole exchange interaction within the triplet states. Comparing the fine structures of the singlet ${\mathrm{X}}^{\ensuremath{-}}$-Mn and of the triplets of ${\mathrm{X}}^{\ensuremath{-}*}$-Mn, we can independently study the different sources of anisotropy in the QD: the valence band mixing and the exchange interaction in an anisotropic potential.