First-principles calculations to investigate optoelectronic of transition-metal half-Heusler alloys MTiSn (M = Pd and Pt) for optoelectronics applications

The structural, mechanical, optical, and electronic properties of half-Heuslers MTiSn (M = Pd and Pt) are investigated using FP-LAPW incorporating the GGA-PBE. MTiSn crystallize in ferromagnetic (FM) and cubic structure (F-43m; C1_b) with lattice constants of 6.216 Å and 6.241 Å, respectively, in good agreement with the available data. Elastic constants $C_{\mathrm{ij}}$ reveal that MTiSn meet the mechanical stability criteria with notable thermodynamic properties. Also, we have conducted a detailed analysis of optical properties, encompassing the dielectric function, absorption coefficient, optical conductivity, optical refractivity, and extinction coefficient. It is found that PtTiSn shows higher optical responses than PdTiSn at low and high energy ranges. In terms of electronic properties, MTiSn demonstrate narrow bandgap semiconductor characteristics with an indirect bandgap of $E_g$ = 0.507 eV (M = Pd) and $E_g$ = 0.782 eV (M = Pt). The notable optoelectronic responses have also been examined, indicating the high potential of MTiSn materials for optoelectronic applications.