Using the augmented plane wave method based on density functional theory and implemented in the WIEN2k code, we study the structural, elastic, electronic, and magnetic properties of FeCoGe, FeMnGe, and the parent half-Heusler (HH) alloys, as well as their derivative Fe2CoMnGe2 double half-Heusler (DHH) compounds. By analysing the stability of the HH structure in both the ferromagnetic and non-magnetic phases of FeCoGe and FeMnGe alloys, we determine that the latter phase of type II and type III FeCoGe and FeMnGe arrangements is the most stable. The Fe2CoMnGe2 DHH alloy, which is derived from the magnetic and structural ground states of FeCoGe and FeMnGe HH alloys, is found to be most stable in the type II arrangement. Among these materials, the FeMnGe HH alloy demonstrates greater resistance to reversible deformation by shear strain, indicated by its higher Young's modulus, while FeCoGe shows the best overall resistance to deformation. The electronic structures of FeCoGe, FeMnGe, and Fe2CoMnGe2 compounds reveal metallic behavior in the spin-up channel and semiconducting behavior in the spin-down channel. Their half-metallic gaps are 0.437 (0.181) eV, 0.543 (0.224) eV, and 0.353 (0.035) eV, respectively, with Fe2CoMnGe2 DHH retaining half-metallicity despite a lower band gap. The total magnetic moments for FeCoGe, FeMnGe, and Fe2CoMnGe2 are found to be 3, 1, and 4 μB, respectively. Given their half-metallic properties, these alloys show potential as candidates for spintronic applications.
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