  NiS, exhibiting a text-book example of a first-order transition with many
unusual properties at low temperatures, has been variously described in terms
of conflicting descriptions of its ground state during the past several
decades. We calculate these physical properties within first-principle
approaches based on the density functional theory and conclusively establish
that all experimental data can be understood in terms of a rather unusual
ground state of NiS that is best described as a self-doped, nearly compensated,
antiferromagnetic metal, resolving the age-old controversy. We trace the origin
of this novel ground state to the specific details of the crystal structure,
band dispersions and a sizable Coulomb interaction strength that is still
sub-critical to drive the system in to an insulating state. We also show how
the specific antiferromagnetic structure is a consequence of the less-discussed
90 degree and less than 90 degree superexchange interactions built in to such
crystal structures.
