Understanding the trend in the Curie temperatures ofCo2-based Heusler compounds:Ab initiocalculations

The Curie temperatures for the Heusler compounds ${\mathrm{Co}}_2\mathrm{Ti}\mathrm{Al}$, ${\mathrm{Co}}_2\mathrm{V}\mathrm{Ga}$, ${\mathrm{Co}}_2\mathrm{V}\mathrm{Sn}$, ${\mathrm{Co}}_2\mathrm{Cr}\mathrm{Ga}$, ${\mathrm{Co}}_2\mathrm{Cr}\mathrm{Al}$, ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Al}$, ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Sn}$, ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Si}$, and ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}$ are determined ab initio from the electronic structure obtained with the local-density functional approximation and/or the generalized gradient approximation. Frozen spin spirals are used to model the excited states needed to evaluate the spherical approximation for the Curie temperature. The spherical approximation is found to describe the experimental Curie temperatures very well which, for the compounds selected, extend over the range from $95\text{to}1100\mathrm{K}$; as a function of the valence electron count, they show an approximately linear trend which finds an explanation by our calculations.