Theoretical investigation of structural, elastic, mechanical, thermodynamic, electronic, and half-metallic ferromagnetic behavior of quaternary Ti₂Fe-based full-Heusler alloys Ti₂FeGe_1-xSn_x (x = 0, 0.25, 0.5, 0.75, and 1) for spintronic applications: DFT computation

The full-potential linearized augmented plane wave (FP-LAPW) method, as implemented in the WIEN2k program, was used to conduct first-principles calculations within the density functional theory framework to ascertain the electronic structure, mechanical stability, thermodynamic, magnetism, and half-metallic properties of the quaternary full-Heusler alloys Ti₂FeGe_1-xSn_x (x = 0, 0.25, 0.50, 0.75, 1). The generalized gradient approximation, in the Perdew-Burke-Ernzerhof parameterization, is employed for evaluating the exchange–correlation potential. Our results offer a theoretical analysis for the new mixed Ti₂FeGe_1-xSn_x (x = 0.25, 0.5, 0.75) alloys, for which no experimental or theoretical data are available yet. For the ternary parent alloys Ti₂FeGe and Ti₂FeSn, the computed lattice constants in their equilibrium inverse cubic CuHg₂Ti-type structure are 6.0871 Å and 6.3411 Å, respectively. Their optimized structural parameters, including lattice constant, bulk modulus, and the first derivative of the bulk modulus, correspond well with results derived from other published theoretical approaches. In addition, they exhibit a half-metallic nature in their electronic band structures and density of states, with total magnetic moments of 2.00 μ_B per formula unit, which is in good accordance with the Slater-Pauling rule, M_total = Z_total − 18, and an indirect band gap of 0.772 eV and 0.685 eV for Ti₂FeGe and Ti₂FeSn, respectively. Regarding the quaternary alloys, they are predicted to be half-metal ferromagnets. Furthermore, according to their mechanical properties, these ferromagnetic alloys are found to be elastically stable, ductile, and have an anisotropic behavior for all the concentrations considered. Finally, these results suggest that the studied alloys would make excellent candidates for upcoming spintronic applications.