Concentration-Driven Tuning of Structural, Electronic, Magnetic, and Optical Properties in Fe-Doped Anatase TiO2: A Hybrid FP-LAPW GGA/GGA+U and PINN Investigation

A concentration-dependent investigation of Fe-doped anatase TiO2 was performed using the full-potential linearized augmented plane wave method implemented in WIEN2k, combined with GGA, GGA+U, and physics-informed neural network (PINN) modeling. Fe concentrations of 3.125%, 6.25%, 12.5%, and 25% were examined using 2 × 2 × 2 anatase TiO2 supercells. Fe incorporation systematically expands the anatase lattice, with the equilibrium volume increasing from 17.14 Å3/f.u. for pristine TiO2 to 18.49 Å3/f.u. within GGA and up to 18.91 Å3/f.u. using Hubbard-corrected treatments at 25% Fe. The bulk modulus decreases from 179.2 GPa to 160.5 GPa in GGA, indicating concentration-driven lattice softening, while the formation energy becomes more negative, reaching −10.91 eV/f.u. for GGA+UTi+UFe at 25% Fe. Electronically, Fe doping introduces localized Fe-3d impurity states within the forbidden gap, narrowing the band gap from 2.18 eV for pristine TiO2 to 1.23 eV in GGA and to 1.59 eV in GGA+UTi+UFe at 25% Fe. The ferromagnetic magnetic moment increases with Fe concentration, reaching 4.41 μB/f.u. for the combined Hubbard correction. Optical calculations reveal enhanced dielectric, conductivity, absorption, reflectivity, and loss responses in the visible-to-near-UV range due to Fe-3d/O-2p/Ti-3d hybridization. The PINN model closely reproduces the FP-LAPW/GGA+U trends, including band gaps from 2.25 eV at 3.125% Fe to 1.48 eV at 25% Fe, demonstrating its usefulness as an efficient surrogate for correlated-property prediction. These results establish Fe doping as an effective route for multifunctional tuning of anatase TiO2 for photocatalytic, photovoltaic, optoelectronic, and spintronic applications.