Spin and orbital transport in rare earth dichalcogenides: The case of EuS$_2$
We perform first-principles calculations to determine the electronic, magnetic and transport properties of rare-earth dichalcogenides taking a monolayer of the H-phase EuS$_2$ as a representative. We predict that the H-phase of the EuS$_2$ monolayer exhibits a half-metallic behavior upon doping with a very high magnetic moment. We find that the electronic structure of EuS$_2$ is very sensitive to the value of Coulomb repulsion $U$, which effectively controls the degree of hybridization between Eu-$f$ and S-$p$ states. We further predict that the non-trivial electronic structure of EuS$_2$ directly results in a pronounced anomalous Hall effect with non-trivial band topology. Moreover, while we find that the spin Hall effect closely follows the anomalous Hall effect in the system, the orbital complexity of the system results in a very large orbital Hall effect, whose properties depend very sensitively on the strength of correlations. Our findings thus promote rare-earth based dichalcogenides as a promising platform for topological spintronics and orbitronics.