Structural, magnetic and transport properties of Heusler alloys Ti$_2$V$Z$ ($Z$ = P, Sb)

We presents a comprehensive study of the structural, magnetic, electronic, mechanical, and thermoelectric properties of Heusler alloys Ti$_2$V$Z$ ($Z$ = P, Sb) with different atomic ordering in the cubic structure using the density functional theory. It is demonstrated that the ground state of the considered compounds is the inverse Heusler structure of XA type, exhibiting a negligible magnetic moment. Besides, both compounds exhibit spin gapless semiconducting behavior, characterised by an energy gap at the Fermi level in the spin-down channel. The tetragonal distortion of the XA structure leads to a ferromagnetic state and metallic behavior. The optimal charge carrier doping concentrations, which enhance the figure of merit, are established. The thermoelectric figure of merit of Ti$_2$VP and Ti$_2$VSb alloys is determined to be 0.45 and 0.35 at 1000 K, respectively.