Magnetic anisotropy of 4f atoms on a WSe2 monolayer: a DFT + U study

Inspired by recent advancements in the field of single-atom magnets, particularly those involving rare-earth (RE) elements, we present a theoretical exploration employing DFT+U calculations to investigate the magnetic properties of selected 4f atoms, specifically Eu, Gd, and Ho, on a monolayer of the transition-metal dichalcogenide WSe₂ in the 1H-phase. This study comparatively examines RE with diverse 4f orbital fillings and valence chemistry, aiming to understand how different coverage densities atop WSe₂ affect magnetocrystalline anisotropy. We observe that RE lacking 5d occupation exhibit larger magnetic anisotropy energies at high densities, while those with outer 5d electrons show larger anisotropies in dilute configurations. Additionally, even half-filled 4f shell atoms with small orbital magnetic moments can generate substantial energy barriers for magnetization rotation due to prominent orbital hybridizations with WSe₂. Open 4f shell atoms further enhance anisotropy barriers through spin-orbit coupling effects. These aspects are crucial for realizing stable magnetic information units experimentally.