We study the effect of the non-magnetic 3\textit{d} atoms on the magnetic
properties of the half-metallic (HM) semi-Heusler alloys Co1−xCuxMnSb
and Ni1−xCuxMnSb (0≤x≤1) using first-principles
calculations. We determine the magnetic phase diagram of both systems at zero
temperature and obtain a phase transition from a ferromagnetic to an
antiferromagnetic state. For low Cu concentrations the ferromagnetic RKKY-like
exchange mechanism is dominating, while the antiferromagnetic superexchange
coupling becomes important for larger Cu content leading to the observed
magnetic phase transition. A strong dependence of the magnetism in both systems
on the position of the Fermi level within the HM gap is obtained. Obtained
results are in good agreement with the available experimental data