Doped transition-metal dichalcogenides monolayers exhibit exciting magnetic properties for the benefit of two-dimensional spintronic devices. Using density functional theory (DFT) incorporating Hubbard-type of correction (DFT$+U$) to account for the electronic correlation, we study the magnetocrystalline anisotropy energy (MAE) characterizing Mn-doped MS$_2$ (M=Mo, W) monolayers. A single isolated Mn dopant exhibits a large perpendicular magnetic anisotropy of 35 meV (8 meV) in the case of Mn-doped WS$_2$ (MoS$_2$) monolayer. This value originates from the Mn in-plane orbitals degeneracy lifting due to the spin-orbit coupling. In pairwise doping, the magnetization easy axis changes to the in-plane direction with a weak MAE compared to single Mn doping. Our results suggest that diluted Mn-doped MS$_2$ monolayers, where the Mn dopants are well separated, could potentially be a candidate for the realization of ultimate nanomagnet units.
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