Hund's physics and the magnetic ground state of CrO X ( X = Cl , Br )

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