  In the present work, we study the magnetic properties of the NbS2 monolayer
by first-principles calculations. The transition metal dichalcogenides (TMDC)
are a family of laminar materials presenting exciting properties such as charge
density waves (CDW), superconductivity and metal-insulating transitions among
others. 2H-NbS2 is a particular case within the family, because it is the only
one that is superconductor without exhibiting a CDW order. Although no long
range magnetic order was experimentally observed in the TMDC, we show here that
the single monolayer of NbS2 is on the verge of a spin density wave (SDW)
phase. Our calculations indicate that a wave-like magnetic order is stabilized
in the NbS2 monolayer in the presence of magnetic defects or within zig-zag
nanoribbons, due to the presence of unpaired electrons. We calculate the real
part of the bare electronic susceptibilty and the corresponding nesting
function of the clean NbS2 monolayer, showing that there are strong electronic
instabilities at the same wavevector asociated with the calculated SDWs, also
corresponding with one of the main nesting vectors of the Fermi surface. We
conclude that the physical mechanism behind the spin-wave instabilities are the
nesting properties, accentuated by the quasi 2D character of this system, and
the rather strong Coulomb interactions of the 4d band of the Nb atom. We also
estimate the amplitude of the spin-fluctuations and find that they are rather
large, as expected for a system on the verge of a quantum critical transition.
