  Antiferromagnetic spintronics is an on-going growing field of research.
Employing both standard density functional theory and the $GW$ approximation
within the framework of the FLAPW method, we study the electronic and magnetic
properties of seven potential antiferromagnetic semiconducting Heusler
compounds with 18 (or 28 when Zn is present) valence electrons per unit cell.
We show that in these compounds G-type antiferromagnetism is the ground state
and that they are all either emiconductors (Cr$_2$ScP, Cr$_2$TiZn, V$_2$ScP,
V$_2$TiSi, and V$_3$Al) or semimetals (Mn$_2$MgZn and Mn$_2$NaAl). The
many-body corrections have a minimal effect on the electronic band structure
with respect to the standard electronic structure calculations.
