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

Abstract

Half-Heusler compounds extit{XYZ}, also called semi-Heusler compounds, crystallize in the MgAgAs structure, in the space group $Far43m$. 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 the most appropriate description of these compounds from the viewpoint of electronic structures is one of a extit{YZ} zinc blende lattice stuffed by the extit{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 Ti$^{4+}$ + (CoSb)$^{4-}$; the latter unit is isoelectronic and isostructural with zinc-blende GaSb. For both the 8- and 18-electron compounds, when extit{X} is fixed as some electropositive cation, the computed band gap varies approximately as the difference in Pauling electronegativities of extit{Y} and extit{Z}. What is particularly exciting is that this simple idea of a covalently bonded extit{YZ} lattice can also be extended to the very important extit{magnetic} half-Heusler phases; we describe these as valence compounds extit{ie.} possessing a band gap at the Fermi energy albeit only in one spin direction. The extit{local} moment in these magnetic compounds resides on the extit{X} site.