  Electronic states and magnetic properties of single $Mn$ impurity and dimer
doped in narrow-gap and wide-gap $III$-$V$ semiconductors have been studied
systematically. It has been found that in the ground state for single $Mn$
impurity, $Mn$-$As(N)$ complex is antiferromagnetic (AFM) coupling when $p$-$d$
hybridization $V_{pd}$ is large and both the hole level $E_{v}$ and the
impurity level $E_{d}$ are close to the midgap; or very weak ferromagnetic (FM)
when $V_{pd}$ is small and both $E_{v}$ and $E_d$ are deep in the valence band.
In $Mn$ dimer situation, the $Mn$ spins are AFM coupling for half-filled or
full-filled $p$ orbits; on the contrast, the Mn spins are double-exchange-like
FM coupling for any $p$-orbits away from half-filling. We propose the strong
{\it p-d} hybridized double exchange mechanism is responsible for the FM order
in diluted $III$-$V$ semiconductors.
