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Antiferromagnetic spintronics is an on-going growing field of research.Employing both standard density functional theory and the $GW$ approximationwithin the framework of the FLAPW method, we study the electronic and magneticproperties of seven potential antiferromagnetic semiconducting Heuslercompounds 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 stateand 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). Themany-body corrections have a minimal effect on the electronic band structurewith respect to the standard electronic structure calculations.

Design of L2_1-type antiferromagnetic semiconducting full-Heusler compounds: A first principles DFT+GW study