garnet via experimental and ab-initio methods*

Rare earth iron garnets (R₃Fe₅O₁₂) are fascinating materials with various exciting properties, almost as diverse as their compositions. They are remarkably stable ferrimagnetic insulators with the highest Faraday rotation known to date. Furthermore, the presence of the rare earth ion induces spin-orbit effects. These properties have made them relevant for the spintronics community. However, computational studies for these compositions are scarce. This talk presents a computational and experimental study of Sm₃Fe₅O₁₂, analyzing its crystal and electronic structures. Density functional theory (DFT) under the generalized gradient approximation (GGA) agrees with the Rietveld refined lattice parameter of 12.5231(3) Å from X-ray diffraction. Meanwhile, introducing the Hubbard-U correction (DFT+U) results in a band gap of 2.27 eV, which matches the 2.26-2.27 eV from UV-Vis spectra, and is identified as a direct transition between minority spin states. Effective Hubbard-U values were calculated analytically at 4.3092 eV for tetrahedral iron and 6.0926 eV for octahedral iron. We thus propose a model to identify the band-gap in Sm₃Fe₅O₁₂, taking into account the structure's ferrimagnetism and energy level distribution, enabling a better understanding of its electronic structure.