Multifunctional properties of quaternary Heusler alloys RuGdMnAl and CoHfVGa: structural stability, half-metallicity, and thermoelectric performance investigated using first principles.

The structural, electronic, magnetic, elastic, phonon, and thermoelectric properties of the quaternary Heusler alloys RuGdMnAl and CoHfVGa were investigated using spin-polarized density functional theory within the FP-LAPW method implemented in the WIEN2k package. The dynamical stability of both compounds was confirmed by phonon dispersion calculations, which show the absence of imaginary phonon modes throughout the Brillouin zone. Thermodynamic stability was confirmed through negative formation energies, while the calculated elastic parameters satisfy the Born-Huang criteria, indicating mechanically stable and ductile behavior. Electronic structure calculations reveal that RuGdMnAl exhibits half-metallic ferromagnetism with an indirect minority-spin band gap of 0.220 eV, whereas CoHfVGa has a ferromagnetic semiconducting electronic structure with pronounced exchange-induced spin splitting and indirect band gaps of 0.349 eV and 1.026 eV for the majority- and minority-spin channels, respectively. The calculated magnetic moments obey the Slater-Pauling rule, confirming robust ferromagnetic ordering and high spin polarization. Additional GGA+U and spin-orbit coupling calculations performed for RuGdMnAl confirm the robustness of its ferromagnetic ground state and reveal a small magnetocrystalline anisotropy with the [100] direction as the easy magnetization axis. Thermoelectric transport properties, evaluated using the semi-classical Boltzmann transport formalism, show enhanced Seebeck coefficients and electrical conductivity for both compounds. The maximum electronic contribution to the thermoelectric figure of merit ZT e reaches 0.55 for RuGdMnAl and 1.0 for CoHfVGa at elevated temperatures, highlighting their strong potential for spintronic and high-temperature thermoelectric applications.