Supplementary Dataset and Computational Results Supporting “Crystal Field Induced Defect Compensation in Gd-Doped PbTiO₃ Preserving Ferroelectricity and f–Electron Magnetism Together with Finite-Temperature Multifunctionality”

This dataset provides numerical results supporting the manuscript “Crystal Field Induced Defect Compensation in Gd-Doped PbTiO₃ Preserving Ferroelectricity and f–Electron Magnetism Together with Finite-Temperature Multifunctionality.”The data include the computed electronic density of states (DOS), optical band gaps, magnetization and magnetic susceptibility curves, and spontaneous polarization values derived from first-principles DFT+U and crystal-field (CF/SPM) models.All calculations were performed using the all-electron WIEN2k code within PBE-GGA, GGA+U, and TB-mBJ frameworks. The CF parameters and spin–lattice effects were analyzed through combined DFT–SPM–CFT methodologies.Each Excel (.xlsx) file corresponds to a figure in the main article:DOS files represent total and site-projected densities of states for pristine and Gd-doped configurations.Optical gap files contain Tauc plots (direct and indirect transitions) obtained from the extinction coefficient k⊥(ω).Magnetization and Susceptibility (χ) files present temperature-dependent magnetic responses of Gd³⁺ in Pb₁₋ₓ₋δGdₓTiO₃ and PbTi₁₋ₓGdₓO₃₋δ systems under B = 0.1 T.Polarization data list Berry-phase spontaneous polarization P(λ) as a function of structural distortion for pristine and defect-compensated structures.These datasets enable reproducibility of all results, facilitate comparison with future DFT-based studies of f-electron doped ferroelectrics, and provide benchmarks for defect–magnetism–polarization coupling mechanisms in perovskite oxides.