Cooperative effects of Jahn-Teller distortion, magnetism and Hunds coupling in the insulating phase of BaCrO$_3$

We employ a combination of density functional theory and dynamical mean-field theory to investigate the electronic structure of the recently synthesized insulator BaCrO$_3$. Our calculations show that Hunds coupling is responsible for strong correlation effects, which are however not sufficient to turn the system insulating. A finite Jahn-Teller distortion lifting the orbital degeneracy is necessary to stabilize an insulating state with orbital ordering and consequent magnetic ordering.