  Contrary to prior calculations, the Ni-rich ordered structures of the Cr-Ni
alloy system are found to be antiferromagnetic under semi-local
density-functional theory. The optimization of local magnetic moments
significantly increases the driving force for the formation of CrNi$_2$, the
only experimentally observed intermetallic phase. This structure's ab initio
magnetism appears well described by a Heisenberg Hamiltonian with longitudinal
spin fluctuations; itinerant Cr moments are induced only by the strength of
exchange interactions. The role of magnetism at temperature is less clear and
several scenarios are considered based on a review of experimental literature,
specifically a failure of the theory, the existence of an overlooked magnetic
phase transition, and the coupling of antiferromagnetism to chemical ordering.
Implications for related commercial and high-entropy alloys are discussed for
each case.
