We calculate the electronic states of the Mn-doped semiconductors and show
that resonant states are formed at the top of the down spin valence band du
e to magnetic impurities and that they give rise to a strong and long-range
d ferromagnetic coupling between Mn moments. We propose that the coupling o
f the resonant states, in addition to the intra-atomic exchange interaction
between the resonant and nonbonding states, is the origin of the ferromagn
etism of (Ga-Mn)As. The mechanism is thus called "double resonance." The re
sonant states bring about the spin-dependent resistivity to produce magneto
resistive properties in (Ga-Mn)As and their junctions.