Advances in Research

The paper presents a first-principles analysis of the structural relaxation, spin-resolved electronic structure, and frequency-dependent optical response of a tetragonal Co₂MnSi model. Geometry optimisation and spin-polarised electronic calculations were carried out within density functional theory using the PBE generalised-gradient approximation, a plane-wave scheme employing ultrasoft pseudopotentials, a 60 Ry kinetic-energy cutoff, and an 8 × 8 × 8 k-point mesh. Optical functions were subsequently evaluated with a 500 eV cutoff and a 9 × 9 × 9 mesh for light polarised along [100]. The optimised P4/mmm cell has a = b = 2.85 Å, c = 5.58 Å, and a volume of 45.27 ų. The total energy stabilises near −365.90944 Ry, and the self-consistent-field cycle becomes essentially stationary after the first few iterations. The supplied spin-resolved density of states and band dispersion are consistent with a candidate half-metallic solution: one spin channel retains finite states at the Fermi level, whereas the other displays an apparent gap of roughly 0.5–1.0 eV. Within this idealised calculation, that electronic topology corresponds to complete spin polarisation at the Fermi level. The optical response is strongest outside the visible range. The static real dielectric component is approximately 59.24, the absorption coefficient reaches about 2.93 × 10⁵ cm⁻¹ at 8.55 eV, the reflectivity maximum occurs near 21.86 eV, the main optical-conductivity feature appears near 7.5 eV, and the dominant loss-function peak lies near 22.6 eV. These results point to a strong far-ultraviolet and extreme-ultraviolet response. Because the modelled P4/mmm phase is not the conventional cubic L2₁ structure of Co₂MnSi, and because phase-stability, magnetic-order, magnetic-moment, phonon, spin-orbit, and convergence-comparison data were not available, the findings should be interpreted as predictions for the supplied tetragonal model rather than as proof of the equilibrium bulk phase.