  First-principles simulations have been performed for [001]-ordered Mn/Ge and
Mn/GaAs "digital alloys", focusing on the effects of i) a larger band-gap and
ii) a different semiconducting host on the electronic structure of the magnetic
semiconductors of interest. Our results for the exchange constants in Mn/Ge,
evaluated using a frozen-magnon scheme, show that a larger band-gap tends to
give a stronger nearest-neighbor ferromagnetic coupling and an overall enhanced
in-plane ferromagnetic coupling even for longer-ranged coupling constants. As
for the chemical effects on the exchange constants, we show that Mn/GaAs shows
a smaller nearest-neighbor ferromagnetic coupling than Mn/Ge, but exchange
constants for higher Mn-Mn distance show an overall increased ferromagnetic
behavior in Mn/GaAs. As a result, from the magnetic-coupling point of view, the
two systems behave on average rather similarly.
