  Half-metallic ferromagnetic full-Heusler alloys containing Co and Mn, having
the formula Co$_2$MnZ where Z a sp element, are among the most studied Heusler
alloys due to their stable ferromagnetism and the high Curie temperatures which
they present. Using state-of-the-art electronic structure calculations we show
that when Mn atoms migrate to sites occupied in the perfect alloys by Co, these
Mn atoms have spin moments antiparallel to the other transition metal atoms.
The ferrimagnetic compounds, which result from this procedure, keep the
half-metallic character of the parent compounds and the large
exchange-splitting of the Mn impurities atoms only marginally affects the width
of the gap in the minority-spin band. The case of [Co$_{1-x}$Mn$_x$]$_2$MnSi is
of particular interest since Mn$_3$Si is known to crystallize in the Heusler
$L2_1$ lattice structure of Co$_2$MnZ compounds. Robust half-metallic
ferrimagnets are highly desirable for realistic applications since they lead to
smaller energy losses due to the lower external magnetic fields created with
respect to their ferromagnetic counterparts.
