Stability of spin-gapless semiconducting behavior in Ti 2 Co Si , Ti 2 Mn Al , and Ti 2 V As Heusler compounds

${\mathrm{Ti}}_{2}\mathrm{Co}\mathrm{Si}$, ${\mathrm{Ti}}_{2}\mathrm{Mn}\mathrm{Al},$ and ${\mathrm{Ti}}_{2}\mathrm{V}\mathrm{As}$ Heusler compounds have been identified as spin-gapless semiconductors when grown in the inverse XA lattice structure of the full-Heusler compounds. Especially ${\mathrm{Ti}}_{2}\mathrm{Mn}\mathrm{Al}$ and ${\mathrm{Ti}}_{2}\mathrm{V}\mathrm{As}$ combine this unique property with a zero magnetization being also fully compensated ferrimagnets. All three compounds are usual metals in the ground-state cubic $\mathrm{L}{2}_{1}$ lattice structure of the Heusler compounds. We present extensive first-principles electronic band structure calculations keeping the unit cell volume constant and varying the $c/a$ ratio and thus both the in-plane and out-of-plane lattice parameters. Our results suggest that while ${\mathrm{Ti}}_{2}\mathrm{Mn}\mathrm{Al}$ keeps its cubic character, this is not the case for ${\mathrm{Ti}}_{2}\mathrm{Co}\mathrm{Si}$ and ${\mathrm{Ti}}_{2}\mathrm{V}\mathrm{As}$ which prefer to crystallize in tetragonal $\mathrm{L}{2}_{1}$-like lattice structures with sizable $c/a$ ratios. In this tetragonal structure both compounds are usual nonmagnetic metals loosing their unique properties. Our results suggest that the stability of the cubic structure should be confirmed for all novel Heusler compounds under study and should not be considered as given. The exact behavior of each compound is materials specific and cannot be easily predicted.