Equiatomic quaternary Heusler alloys have recently emerged as promising multifunctional materials due to their tunable structural order, robust magnetism, and versatile transport properties. In this work, we present a comprehensive first-principles investigation of equiatomic XMnCrZ ( \(X = \textrm{Ti}, \textrm{Ni};\ Z = \textrm{Sb}, \textrm{Sn}\) ) alloys using density functional theory (DFT) and density functional perturbation theory (DFPT). Electronic structure analysis shows that \(\textrm{TiMnCrSb}\) and \(\textrm{TiMnCrSn}\) exhibit half-metallicity with nearly 100% spin polarization, in excellent agreement with the Slater–Pauling rule, while Ni-based alloys retain metallic behavior. The magnetic moments are primarily carried by Mn and Cr atoms, with Ti- and Ni-based alloys displaying distinct magnetic exchange interactions. The thermoelectric properties evaluated at the Fermi level reveal positive Seebeck coefficients for the Ni-based alloys and negative values for the Ti-based compounds. However, upon tuning the Fermi level to an optimal energy, \(\textrm{TiMnCrSb}\) exhibits a remarkable enhancement in its Seebeck coefficient, reaching a maximum of \(450.7~\mu \mathrm {V/K}\) at room temperature. While the other materials also display noticeable increases, \(\textrm{TiMnCrSb}\) stands out as the most promising candidate for efficient thermoelectric and multifunctional applications among the investigated EQHAs.
