  Applying the dynamical coherent potential approximation to a simple model, we
have systematically studied the carrier states in $A_{1-x}$Mn$_xB$-type diluted
magnetic semiconductors (DMS's). The model calculation was performed for three
typical cases of DMS's: The cases with strong and moderate exchange
interactions in the absence of nonmagnetic potentials, and the case with strong
attractive nonmagnetic potentials in addition to moderate exchange interaction.
When the exchange interaction is sufficiently strong, magnetic impurity bands
split from the host band. Carriers in the magnetic impurity band mainly stay at
magnetic sites, and coupling between the carrier spin and the localized spin is
very strong. The hopping of the carriers among the magnetic sites causes
ferromagnetism through a {\it double-exchange (DE)-like} mechanism. We have
investigated the condition for the DE-like mechanism to operate in DMS's. The
result reveals that the nonmagnetic attractive potential at the magnetic site
assists the formation of the magnetic impurity band and makes the DE-like
mechanism operative by substantially enhancing the effect of the exchange
interaction. Using conventional parameters we have studied the carrier states
in Ga$_{1-x}$Mn$_x$As. The result shows that the ferromagnetism is caused
through the DE-like mechanism by the carriers in the bandtail originating from
the impurity states.
