Interplay of Valley, Orbital, Spin, and Layer Degrees of Freedom in Ta$_2$CS$_2$ MXene

Abstract

We show that the MXene Ta$_2$CS$_2$ provides an excellent platform for hosting multiple coupled degrees of freedom, viz., valley, spin, orbital, and layer. The interplay among these degrees of freedom gives rise to a range of intriguing properties in reciprocal space, including valley-orbital and orbital-layer coupling. In the presence of spin-orbit interaction, these couplings lead to valley-dependent and layer-dependent spin splitting of the electronic bands. We further show that the intrinsic electric polarization in Ta$_2$CS$_2$ introduces an additional tuning parameter, enabling control over these coupled degrees of freedom and resulting in switchable valley-dependent orbital moments and Zeeman-like spin splitting. We demonstrate that these nontrivial orbital and spin textures manifest in the orbital and spin Hall effects, respectively. Our results establish noncentrosymmetric MXenes as a promising platform for exploring the interplay among multiple degrees of freedom, their tunability, and the resulting orbital and spin transport phenomena in these two-dimensional materials, thereby paving the way for next-generation spin-orbitronic devices.