  We show here the existence of the indirect coupling of electron and magnetic
or nuclear ion spins in self-assembled quantum dots mediated by
electron-electron interactions. With a single localized spin placed in the
center of the dot, only the spins of electrons occupying the zero angular
momentum states couple directly to the localized spin. We show that when the
electron-electron interactions are included, the electrons occupying finite
angular momentum orbitals interact with the localized spin. This effective
interaction is obtained using exact diagonalization of the microscopic
Hamiltonian as a function of the number of electronic shells, shell spacing,
and anisotropy of the electron-Mn exchange interaction. The effective
interaction can be engineered to be either ferromagnetic or antiferromagnetic
by tuning the parameters of the quantum dot.
