  We investigate the emergence of ferromagnetism in the two-dimensional
metal-halide CoBr$_2$, with a special focus on the role of electronic
correlations. The calculated phonon spectrum shows that the system is
thermodynamically stable unlike other Co halides. We apply two well-known
methods for the estimation of the Curie temperature. First, we do DFT+U
calculations to calculate exchange couplings, which are subsequently used in a
classical Monte Carlo simulation of the resulting Ising spin model. The
transition temperature calculated in this way is in the order of 100 K, but
shows a strong dependence on the choice of interaction parameters. Second, we
apply dynamical mean-field theory to calculate the correlated electronic
structure and estimate the transition temperature.This results in a similar
estimate for a noticeable transition temperature of approximately 100
K,however, without the strong dependence on the interaction parameters. The
effect of electron-electron interactions are strongly orbital selective, with
only moderate correlations in the three low-lying orbitals (one doublet plus
one singlet), and strong correlations in the doublet at higher energy. This can
be traced back to the electronic occupation in DMFT, with five electrons in the
three low-lying orbitals and two electrons in the high-energy doublet, making
the latter one half-filled. Nevertheless, the overall spectral gap is governed
by the small gap originating from the low-lying doublet+singlet orbitals, which
changes very weakly with interaction U. In that sense,the system is close to a
Mott metal-to-insulator transition, which has been shown previously to be a
hot-spot for strong magnetism.
