  Electronic structure calculations from first-principles are employed to
design some new half-metallic fully-compensated ferrimagnets (or as they are
widely known half-metallic antiferromagnets) susceptible of finding
applications in spintronics. Cr$_2$MnZ (Z= P, As, Sb, Bi) compounds have 24
valence electrons per unit cell and calculations show that their total spin
moment is approximately zero for a wide range of lattice constants in agreement
with the Slater-Pauling behavior for ideal half-metals. Simultaneously, the
spin magnetic moments of Cr and Mn atoms are antiparallel and the compounds are
ferrimagnets. Mean-field approximation is employed to estimate their Curie
temperature, which exceeds room temperature for the alloy with Sb. Our findings
suggest that Cr$_2$MnSb is the compound of choice for further experimental
investigations. Contrary to the alloys mentioned above half-metallic
antiferromagnetism is unstable in the case of the Cr$_2$FeZ (Z= Si, Ge, Sn)
alloys.
