  We present an Anderson-type model Hamiltonian with exchange coupling between
the localized spins and the confined holes in the quantum dots to study the
ferromagnetism in diluted magnetic semiconductor (DMS) quantum dot arrays
embedded in semiconductors. The hybridization between the quantum-confined
holes in the DMS quantum dots and the itinerant holes in the semiconductor
valence band makes hole transfer between quantum dots, which can induce the
long range ferromagnetic order of the localized spins. In addition, it makes
the carrier spins both in the DMS quantum dots and in the semiconductors
polarized. The spontaneous magnetization of the localized spins and the spin
polarization of the holes are calculated using both the Weiss mean field
approximation and the self-consistent spin wave approximation, which are
developed for the present model.
