Effective interaction Hamiltonian of polaron pairs in diluted magnetic semiconductors

The magnetic interaction of a pair of bound magnetic polarons in diluted magnetic semiconductors is analyzed via a generalized Hubbard-type Hamiltonian for two carriers in the presence of effective magnetic fields arising from the magnetic polarization of their respective polarons. For the case where the magnetic fields at the two sites have equal magnitude but are allowed to have arbitrary directions, it is shown that the energy of the two polarons is minimized for a ferromagnetic configuration of the carrier spins (in contrast to the case of hydrogenic centers in nonmagnetic semiconductors) if polaron fields are strong enough. A modified Heisenberg-type Hamiltonian is constructed to describe the low energy states of the resulting system.