  CoO has an odd number of electrons in its unit cell, and therefore is
expected to be metallic. Yet, CoO is strongly insulating owing to significant
electronic correlations, thus classifying it as a Mott insulator. We
investigate the magnetic fluctuations in CoO using neutron spectroscopy. The
strong and spatially far-reaching exchange constants reported in [Sarte et al.
Phys. Rev. B 98 024415 (2018)], combined with the single-ion spin-orbit
coupling of similar magnitude [Cowley et al. Phys. Rev. B 88, 205117 (2013)]
results in significant mixing between $j_{eff}$ spin-orbit levels in the low
temperature magnetically ordered phase. The high degree of entanglement,
combined with the structural domains originating from the Jahn-Teller
structural distortion at $\sim$ 300 K, make the magnetic excitation spectrum
highly structured in both energy and momentum. We extend previous theoretical
work on PrTl$_{3}$ [Buyers et al. Phys. Rev. B 11, 266 (1975)] to construct a
mean-field and multi-level spin exciton model employing the aforementioned spin
exchange and spin-orbit coupling parameters for coupled Co$^{2+}$ ions on a
rocksalt lattice. This parameterization, based on a tetragonally distorted
type-II antiferromagnetic unit cell, captures both the sharp low energy
excitations at the magnetic zone center, and the energy broadened peaks at the
zone boundary. However, the model fails to describe the momentum dependence of
the excitations at high energy transfers, where the neutron response decays
faster with momentum than the Co$^{2+}$ form factor. We discuss such a failure
in terms of a possible breakdown of localized spin-orbit excitons at high
energy transfers.
