This study investigates the Half-Heusler (HH) ferromagnetic compound, GeKX (X = Ca and Sr) half-metallic (HM) characteristics through first-principle calculations within the density functional theory (DFT) framework. Utilizing spin-polarized calculations and employing the full-potential linearized augmented plane-wave (FP-LAPW) method and confirm the stability of both compounds in the ferromagnetic MgAgAs-type crystal structure with spacegroup 216 \(F\overline{4 }3m\) . The structural characteristics are explored by employing the generalized gradient approximation, PBE-GGA, and local spin density approximation LSDA, to treat the exchange and correlation energies. In this work computed lattice constants align well with reported results. Analysis of the electronic structure within the MgAgAs-type structure reveals the HM nature of these compounds, each possessing an integer magnetic moment of 1 μB. Various electronic properties such as electronic band structures, densities of states, Fermi surfaces, and the origin of ferromagnetism are discussed using TB-mBJ approach. The evaluation of elastic constants has verified the mechanical stability of these compounds. By computing elastic constants, the obtained values for the bulk modulus, Young’s modulus, shear modulus, and Poisson’s ratio. Employing ELATE software, for visually depicted the anisotropic elastic properties in three dimensions, including values of linear compressibility, shear modulus, Young’s modulus, and Poisson’s ratio, along with an analysis of anisotropic factors. Furthermore, we investigated the thermoelectric properties of GeKX (X = Ca and Sr) alloys using the BoltzTraP2 code and found that the value of the figure of merit ZT is almost unity for both compounds. The robust HM characteristics of these compounds make them interesting candidates for spintronic devices.
