Spin polarized edge states in proximitized ferromagnetic transition metal dichalcogenides

Transition metal dichalcogenide (TMD) monolayers deposited on a ferromagnetic substrate such as europium oxide (EuO) experience proximity-induced ferromagnetism. We explore the nature of states appearing at the edge of proximitized TMD ribbons and nanoflakes by means of a real-space three-orbital tight-binding model that incorporates the magnetic interaction effects induced by the substrate. For commensurate structures, such as MoTe₂ on EuO, we study spin and orbital composition of states for zigzag and armchair edges. We find that states at zigzag borders are extended and strongly spin-polarized, exhibiting the competition of exchange and spin-orbit coupling. The real-space approach also allows the description of incommensurate systems, such as MoS₂ on EuO. The competition of magnetic and lattice periodicities has strong effects on the states, especially on their dispersion and spin texture.