Engineering spin-orbit effects and Berry curvature by deposition of Eu on WSe$_{2}$

Motivated by recent progress in 2D spintronics, we present Eu deposited on a 1H-WSe$_2$ as a promising platform for engineering spin-orbit effects and Berry curvature. By first-principles calculations based on density functional theory, we show that Eu/WSe$_2$ exhibits intriguing properties such as high magnetic anisotropy, valley-dependent polarization of spin and orbital angular momenta, and their Rashba textures. These originate from magnetic and spin-orbit proximity effects at the interface and the interplay between localized $4f$ magnetic moments of Eu and mobile charge carriers of WSe$_2$. We find a pronounced anomalous Hall effect in the proposed system. Thus, we promote $4f$ rare-earth metals deposited on top of a transition-metal dichalcogenides as a promising platform for 2D spintronics.