Abstract
We study the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in a monolayer MoS${}_{2}$. We show that the rotation of the itinerant electron spin due to the spin-orbit coupling causes a twisted interaction between two magnetic adatoms, which consists of different RKKY coupling terms: the Heisenberg, Dzyaloshinsky-Moriya, and Ising interactions. We find that the interaction terms are very sensitive to the Fermi energy values and change dramatically from doped to undoped systems. A finite doping causes all parts of the interaction to oscillate with the distance of two magnetic impurities $R$, and the interaction behaves like ${R}^{\ensuremath{-}2}$ for a long distance between two localized spins. We explore a beating pattern of oscillations of the RKKY interaction that occurs for the doped system.
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