Computational Discovery of a Novel Semiconductor: A Vacancy-Ordered Fe$_{\mathbf{1.5}}$TiSb Heusler Phase

Many full- and half-Heusler phase compounds are half-metallic ferromagnets, and are attractive for spintronic applications due to their relatively high Curie temperatures. However, while it is known that defects such as vacancies (on the X site of an X$_2$YZ Heusler phase) can lead to a loss of half-metallic character, their effect on the stability and order of these compounds has not been adequately explored. To address this shortcoming, we perform a binary cluster expansion (CE) of Fe and vacancies on the Fe sublattice of the Fe$_x$Vac$_{2-x}$TiSb Heusler compound. From our CE, we computationally predict the stability of a novel semiconductor phase with an interesting new structure type: $R3m$ spacegroup with composition Fe$_{1.5}$TiSb, i.e., between the full- and half-Heusler compositions. By comparing the electronic structure of all the competing structures at $x=1.5$, we find that the gap opened in the minority-spin channel due to vacancies strongly correlates with the stability of the structure. We study the effect of vacancies on the structural order in Fe$_{1.5}$TiSb by generating special quasi-random structures (SQSs) as approximations to the true disordered state, and find that the material undergoes an order-disorder transition at elevated temperatures of $\sim$1450~K.