4f Band Modulation by Spin-Orbit Coupling in Low-Dimensional Rare Earth Catalysts

Abstract

We report a first-principles study of Eu nano-sheets of varying thickness supported on a rutile TiO₂ surface, focusing on the influence of spin-orbit coupling (SOC) and sheet thickness on the Eu 4f electronic structure and its catalytic implications. Using both collinear and non-collinear density functional theory with on-site Coulomb corrections (DFT+U) and van der Waals dispersion, we construct and relax interface models comprising single atoms, monolayers, bilayers, and quadruple layers of Eu. Layer-resolved density of states (DOS) analysis reveal that SOC lifts the degeneracy of the Eu 4f states, broadening their spectrum and shifting their principal peaks (C) toward the Fermi-level. A clear correlation emerges between the distance of Eu atoms from the interfacial oxygen and the localisation as well as position of the 4f states: atoms farther from the interface exhibit sharper, more deeply bound 4f peaks, an effect that intensifies with increasing sheet thickness. Charge density and electronic localisation profiles confirm an ionic Eu-O interaction, while crystal orbital Hamilton population (COHP) analysis indicates that inter-facial anti-bonding Eu-O interactions weaken slightly with sheet growth but remain dominant in thinner configurations. These findings underscore the critical role of SOC and nano-sheet morphology in tuning the electronic states relevant to catalytic redox processes.