  A number of L2$_1$ phase alloys (composition X$_2$YZ) are half-metallic.
Although this structure is typically described in terms of an fcc Bravais
lattice with a 4 atom basis, it can be viewed more simply as a variant of bcc
or B2 in which planes of X$_2$ alternate with planes of YZ along the 001
direction. Using ab-initio electronic structure calculations, we have
investigated planar insertions along 001 into the L2$_1$ structure. For most
scenarios, insertion of single or double atomic layers of Cr into Co$_2$MnGe or
Co$_2$MnSi did not destroy the half-metallic property. One insertion of a Cr
layer into Co$_2$MnGe was observed to increase the gap. In fact, we observed
that for a large number of insertions using various transition metals or
combinations of transition metals and non-transition metals, the band gap in
the minority channel at the Fermi energy remains. An ad hoc rule that seems to
partially capture the tendency to form half-metals can be formulated as: "001
planar insertions that can plausibly yield 8 down spin electrons on the X$_2$
layer and 4 down spin electrons on the YZ layer yield half-metals".
