Abstract

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 a 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 noncollinear 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.