  The novel properties of a uniaxially-expanded TiN bulk arising from
increasing the layer spacing from equilibrium are explored using a
first-principles approach. We reveal a novel nonmagnetic-magnetic transition
from a TiN bulk to its monolayer. We also investigate the electronic and
magnetic structures of a few TiN atomic layers. We find that the bilayer and
trilayer, like the TiN bulk, are nonmagnetic poor metals. On the other hand,
the monolayer TiN is found to carry a magnetic moment on its Ti atoms, and
likely be a semiconductor. The unpaired electron giving rise to magnetism on Ti
is primarily in the orbital perpendicular to the layers, and we find it is
freed to give rise to magnetism when the layers are slightly separated. We find
two different antiferromagnetic states possible on the monolayer, as well as
one ferromagnetic, with one of the antiferromagnetic being the lowest energy.
The exchange couplings between Ti atoms in such a monolayer are calculated to
be antiferromagnetic for both the nearest-neighbor and next-nearest-neighbor
sites. We also analyze the binding nature of both the monolayer and bilayer TiN
by searching for the predominant binding orbitals.
