  We present an extensive density functional theory study of the electronic,
magnetic and transport properties of GaAs and AlAs digital ferromagnetic
heterostructures. These can be obtained by $\delta$-doping with Mn the GaAs
layers of a GaAs/AlAs superlattice. Our analysis spans a range of Mn
concentrations and considers the presence of compensating defects such as As
antisites.
  In the defect-free case all the heterostructures studied present an
half-metallic electronic structure. In contrast when As antisites are present
the half-metallic state is destroyed and the heterostructures behave as dirty
planar metals. In this case they show a large $p$-type metallic conductance in
the Mn plane mainly due to majority spin electrons, and an $n$-type
hopping-like conductance in the GaAs planes mainly due to minority spin
electrons. This suggests that if the As antisites can be kept far from the Mn
planes, spatial separation of the different spin currents can be achieved.
Finally we show that in the case of AlAs/(Ga,Mn)As digital ferromagnetic
heterostructures the AlAs/GaAs valence band offset produces an additional
confining potential for the holes responsible for the ferromagnetism. Therefore
the ferromagnetic coupling between the Mn ions becomes larger and more robust
to the presence of As antisites.
