  The results of first-principles electronic structure calculations for the
nitrogen-rich nickel nitrides $ {\rm NiN} $ and $ {\rm Ni_2N} $ are presented.
The calculations are based on density functional theory and used the
generalized gradient approximation (GGA) as well as the GGA$ +U $ approach. The
latter turned out to be crucial for a correct description of the crystal phase
stability and magnetic instabilities of both compounds. While for $ {\rm NiN} $
GGA calculations predict a non-magnetic ground state with the zincblende
structure, GGA$ +U $ calculations result in a half-metallic ferromagnet with
the rocksalt structure in line with indications from the neighboring
transition-metal nitrides making $ {\rm NiN} $ a possible candidate for
spin-filter devices. For $ {\rm Ni_2N} $ GGA calculations likewise lead to a
non-magnetic behavior, which is contrasted with a ferrimagnetic ordering
obtained from the GGA$ +U $ approach. This ground state results from complex
three-dimensional exchange interaction via $ \sigma $-type and $ \pi $-type
overlap of the Ni $ 3d $ orbitals with the N $ 2p $ orbitals and may explain
the reported sensitivity of the magnetic ordering to details of the crystal
structure. For both nitrides, experimental data are called for to confirm our
predictions.
