Covalent bonding and the nature of band gaps in some half-Heusler compounds

Half-Heusler compounds XYZ, also called semi-Heusler compounds, crystallize in the C1b MgAgAs structure, in the space group . We report a systematic examination of band gaps and the nature (covalent or ionic) of bonding in semiconducting 8- and 18-electron half-Heusler compounds through first-principles density functional calculations. We find that the most appropriate description of these compounds from the viewpoint of electronic structures is one of a YZ zinc blende lattice stuffed by the X ion. Simple valence rules are obeyed for bonding in the 8-electron compound. For example, LiMgN can be written Li+ + (MgN)− and (MgN)−, which is isoelectronic with (SiSi), forms a zinc blende lattice. The 18-electron compounds can similarly be considered as obeying valence rules. A semiconductor such as TiCoSb can be written Ti4+ + (CoSb)4−; the latter unit is isoelectronic and isostructural with zinc-blende GaSb. For both the 8- and the 18-electron compounds, when X is fixed as some electropositive cation, the computed band gap varies approximately as the difference in Pauling electronegativities of Y and Z. What is particularly exciting is that this simple idea of a covalently bonded YZ lattice can also be extended to the very important magnetic half-Heusler phases; we describe these as valence compounds, i.e. possessing a band gap at the Fermi energy albeit only in one spin direction. The local moment in these magnetic compounds resides on the X site.