We consider the effective coupling between impurity spins on surfaces of a thin-film Weyl semimetal within Ruderman-Kittel-Kasuya-Yoshida (RKKY) theory. If the spins are on the same surface, their coupling reflects the anisotropy and the spin-momentum locking of the Fermi arcs. By contrast when the spins are on opposite surfaces, their coupling is mediated by the Fermi arcs as well as by bulk states. In this case the coupling is both surprisingly strong and strongly thickness dependent, with a maximum at an optimum thickness. We demonstrate our results using analytical solutions of states in the thin-film geometry, as well using a two-surface recursive Greens function analysis of the tight-binding model.
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