Promoting p -based Hall effects by p−d−f hybridization in Gd-based dichalcogenides

We conduct a first-principles study of Hall effects in rare-earth dichalcogenides, focusing on monolayers of the H-phase $\mathrm{Eu}{X}_{2}$ and $\mathrm{Gd}{X}_{2}$, where $X=\mathrm{S}$, Se, and Te. Our predictions reveal that all $\mathrm{Eu}{X}_{2}$ and $\mathrm{Gd}{X}_{2}$ systems exhibit high magnetic moments and wide band gaps. We observe that while in the case of $\mathrm{Eu}{X}_{2}$ the $p$ and $f$ states hybridize directly below the Fermi energy, the absence of $f$ and $d$ states of Gd at the Fermi energy results in the $p$-like spin-polarized electronic structure of $\mathrm{Gd}{X}_{2}$, which mediates $p$-based magnetotransport. Notably, these systems display significant anomalous, spin, and orbital Hall conductivities. We find that in $\mathrm{Gd}{X}_{2}$, the strength of correlations controls the relative position of the $p, d$, and $f$ states and their hybridization, which has a crucial impact on $p$-state polarization and the anomalous Hall effect, but not the spin and orbital Hall effects. Moreover, we find that the application of strain can significantly modify the electronic structure of the monolayers, resulting in quantized charge, spin, and orbital transport in ${\mathrm{GdTe}}_{2}$ via a strain-mediated orbital inversion mechanism taking place at the Fermi energy. Our findings suggest that rare-earth dichalcogenides hold promise as a platform for topological spintronics and orbitronics.