First-Principles Study of the Geometric and Electronic Structures and Optical Properties of Vacancy Magnesium Ferrite

This study aims to determine the effect of Mg-vacancy (Mg7Fe16O32), Fe-vacancy (Mg8Fe15O32), and O-vacancy (Mg8Fe16O31) on the geometric and electronic structure and physical properties of the normal spinel MgFe2O4 (Mg8Fe16O32) via density functional theory (DFT). The bandgap of the Mg8Fe16O32 was computed using the generalized gradient approximation (GGA) + Hubbard (U) approach with (RPBE, PBE, PW91, PBESOL, WC) and (LDA/CA-PZ) and compared with the experimental values. The GGA/RPBE + U method was determined to yield the best results; therefore, it was selected for the structural and optical property analysis of the normal spinel MgFe2O4 with vacancy defects. In addition, the bandgaps, magnetic moments, and formation energy were examined. Spontaneous formation of the structures with vacancy defects is impossible; however, formation of the O-vacancy was determined to be the most probable, followed by that of the Fe-vacancy and Mg-vacancy under specific conditions. The Fe-vacancy and Mg-vacancy changed the semiconducting character of MgFe2O4 to half-metallic behavior. The optical properties (refractive index, reflectivity, dielectric function, optical conductivity, and loss function) for the studied structure were calculated and discussed.