  Room-temperature superparamagnetism due to a large magnetic anisotropy energy
(MAE) of a single atom magnet has always been a prerequisite for nanoscale
magnetic devices. Realization of two dimensional (2D) materials such as
single-layer (SL) MoS$_{2}$, has provided new platforms for exploring magnetic
effects, which is important for both fundamental research and for industrial
applications. Here, we use density functional theory (DFT) to show that the
antisite defect (Mo$_{S}$) in SL MoS$_{2}$ is magnetic in nature with a
magnetic moment of $\mu$ of $\sim$ 2$\mu_{B}$ and, remarkably, exhibits an
exceptionally large atomic scale
MAE$=\varepsilon_{\parallel}-\varepsilon_{\perp}$ of $\sim$500 meV. Our
calculations reveal that this giant anisotropy is the joint effect of strong
crystal field and significant spin-orbit coupling (SOC). In addition, the
magnetic moment $\mu$ can be tuned between 1$\mu_{B}$ and 3$\mu_{B}$ by varying
the Fermi energy $\varepsilon_{F}$, which can be achieved either by changing
the gate voltage or by chemical doping. We also show that MAE can be raised to
$\sim$1 eV with n-type doping of the MoS$_{2}$:Mo$_{S}$ sample. Our systematic
investigations deepen our understanding of spin-related phenomena in SL
MoS$_{2}$ and could provide a route to nanoscale spintronic devices.
