  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.
