DFT+U investigation of magnetocrystalline anisotropy of Mn-doped transition-metal dichalcogenide monolayers

Doped transition-metal dichalcogenide monolayers exhibit exciting magnetic properties for the benefit of two-dimensional spintronic devices. Using density functional theory (DFT) incorporating Hubbard-type correction ($\mathrm{DFT}+U$) to account for the electronic correlation, we study the magnetocrystalline anisotropy energy (MAE) characterizing Mn-doped $M{\mathrm{S}}_{2}$ ($M$ = 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 ${\mathrm{WS}}_{2}$ (${\mathrm{MoS}}_{2}$) 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 $M{\mathrm{S}}_{2}$ monolayers, where the Mn dopants are well separated, could potentially be a candidate for the realization of ultimate nanomagnet units for future magnetic storage applications.