Coupling of Electron and Magnetic Ion Spin in Quantum Dots by Electron-Electron Interaction

We have presented a microscopic model of interacting electrons with a magnetic ion spin localized in the centre of a self assembled quantum dot. We have found that the electrons occupying finite angular momentum orbitals interact with the localized spin through an effective exchange interaction mediated by electron-electron interactions. With a localized spin placed in the centre of the dot, only the spins of electrons occupying the zero angular momentum states of the s, d, shells couple directly to the localized spin via a contact exchange interaction. The effective interaction for p-shell electrons is obtained using exact diagonalization of the microscopic Hamiltonian as a function of the number of electronic shells, shell spacing and anisotropy of the exchange interaction. The anisotropy of exchange interpolates between the interaction types characteristics for conduction band electrons and valence band holes. The obtained results were found in good agreement with previously obtained results.