  Based on first-principles electronic structure calculations, we analyze the
chemical and magnetic mechanisms stabilizing the cubic phase in Fe$_2$-based
Heusler materials, which were previously predicted to be tetragonal when being
chemically ordered. In agreement with recent experimental data, we found that
these compounds crystallize within the so-called "inverted" cubic Heusler
structure perturbed by a certain portion of the intrinsic chemical disorder.
Understanding these mechanisms is a necessary step to guide towards the
successful future synthesis of the stable Fe$_2$-based tetragonal phases, which
are very promising candidates for the fabrication of rare-earth-free permanent
magnets.

Materials Science