  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.
