  In this work, we report on an $ab-initio$ computational study of the
electronic and magnetic properties of transition metal adatoms on a monolayer
of NbSe$_2$. We demonstrate that Cr, Mn, Fe and Co prefer all to sit above the
Nb atom, where the $d$ states experience a substantial hybridization. The
inter-atomic exchange coupling is shown to have an oscillatory nature
accompanied by an exponential decay, in accordance with what theory predicts
for a damped Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. Our results
indicate that the qualitative features of the magnetic coupling for the four
investigated adatoms can be connected to the fine details of their Fermi
surface. In particular, the oscillations of the exchange in Fe and Co are found
to be related to a single nesting vector, connecting large electrons and hole
pockets. Most interestingly, this behavior is found to be unaffected by changes
induced on the height of the impurity, which makes the magnetism robust to
external perturbations. Considering that NbSe$_2$ is a superconductor down to a
single layer, our research might open the path for further research into the
interplay between magnetic and superconducting characteristics, which could
lead to novel superconductivity engineering.
