Noncollinear exchange interaction in transition metal dichalcogenide edges

We study the Ruderman-Kittel-Kasuya-Yosida effective exchange interaction between magnetic impurities embedded on the edges of transition-metal dichalcogenide flakes, using a three-orbital tight-binding model. Electronic states lying midgap of the bulk structure have strong one-dimensional (1D) character, localized on the edges of the crystallite. This results in exchange interactions with $1/r$ (or slower) decay with distance $r$, similar to other 1D systems. Most interestingly, however, the strong spin-orbit interaction in these materials results in sizable non-collinear Dzyaloshinskii-Moriya interactions between impurities, comparable in size to the usual Ising and in-plane components. Varying the relevant Fermi energy by doping or gating may allow one to modulate the effective interactions, controlling the possible helical ground state configurations of multiple impurities.