Mechanism of carrier-induced ferromagnetism in magnetic semiconductors

Taking into account both random impurity distribution and thermal fluctuations of localized spins, we have performed a model calculation for the carrier (hole) state in Ga${}_{1-x}$Mn${}_x$As by using the coherent potential approximation (CPA). The result reveals that a {\it p}-hole in the band tail of Ga${}_{1-x}$Mn${}_x$As is not like a free carrier but is rather virtually bounded to impurity sites. The carrier spin strongly couples to the localized {\it d} spins on Mn ions. The hopping of the carrier among Mn sites causes the ferromagnetic ordering of the localized spins through the double-exchange mechanism. The Curie temperature obtained by using conventional parameters agrees well with the experimental result.