Effect of spin polarization on multifunctional physical properties of the quaternary Heusler alloys CrZCoSn (Z = Zr, Hf) for energy technologies: A comprehensive DFT study

In this study, we have performed first-principles calculations based on density functional theory (DFT), semi-classical Boltzmann theory, and full-potential linearized augmented plane wave (FP-LAPW) method with generalized gradient approximation (GGA) and Modified Becke-Johnson approach to investigate the structural, electrical, magnetic, optical, and thermoelectric properties of quaternary Heusler alloys CrZCoSn (Z=Zr, Hf). Our study reveals that both alloys are stable in the Type-1 (LiMgPdSn-type, space group F-43 m) structure, which is ferromagnetic in nature. The thermodynamic stability and ferromagnetic (FM) ground state of these HAs are confirmed by relative total energies and by calculated cohesive and formation energies, respectively. The existence of a band gap between the energy bands is elaborated with the hybridization of d-d orbitals among the constituent transition metals of HAs. The calculated magnetic moments of CrZrCoSn and CrHfCoSn alloys are 4.97 and 4.84 µ_B, respectively, while the specific heat (C_v) of these alloys is 92.1 and 93.36 J/mol^{- 1}K, respectively. These alloys exhibit bulk modules of 117.43 and 118.73 GPa, respectively. Optical characteristics reveal that absorption of electromagnetic radiation takes place across the near UV and visible ranges of the spectrum. The static values of refractive index n(ω) for CrZrCoSn and CrHfCoSn HAs are 5.5 and 5.7, respectively. Results suggest that narrow bandgap (E_g), high ZT, and spin polarization make our HAs promising candidates for various spintronic, optoelectronic, and thermoelectric applications.