  To understand the magnetic property of layered van der Waals materials CrOX
(X = Cl, Br), we performed the detailed first-principles calculations for both
bulk and monolayer. We found that the charge-only density functional theory
combined with the explicit on-site interaction terms (so-called cDFT$+U$) well
reproduces the experimental magnetic ground state of bulk CrOX, which is not
the case for the use of spin-dependent density functional (so-called sDFT$+U$).
Unlike some of the previous studies, our results show that CrOX monolayers are
antiferromagnetic as in the bulk. It is also consistent with our magnetic force
linear response calculation of exchange couplings $J_{\rm ex}$. The result of
orbital-decomposed $J_{\rm ex}$ calculations shows that the Cr
$t_\textrm{2g}$-$t_\textrm{2g}$ component mainly contributes to the
antiferromagnetic order in both bulk and monolayer. Our result and analysis
show that taking the correct Hund's physics into account is of key importance
to construct the magnetic phase diagram and to describe the electronic
structure.
