Chromium analogues of Iron-based superconductors

We theoretically investigate the $d^4$ (Cr$^{2+}$) compound BaCr$_2$As$_2$ and show that, despite non-negligible differences in the electronic structure, its many-body physics mirrors that of BaFe$_2$As$_2$, which has instead a $d^6$ (Fe$^{2+}$) configuration. This reflects a symmetry of the electron correlation effects around the half-filled $d^5$ Mott insulating state. The experimentally known metallic antiferromagnetic phase is correctly modeled by dynamical mean-field theory, and for realistic values of the interaction it shows a moderate mass enhancement of order $\sim$2. This value decreases if the ordered moment grows as a result of a stronger interaction. The antiferromagnetic phase diagram for this $d^4$ shows similarities with that calculated for the $d^6$ systems. Correspondingly, in the paramagnetic phase the influence of the half-filled Mott insulator shows up as a crossover from a weakly correlated to an orbitally differentiated "Hund's metal" phase which reflects an analogous phenomenon in $d^6$ iron compounds including a strong enhancement of the compressibility in a zone just inside the frontier between the normal and the Hund's metal. The experimental evidence and our theoretical description place BaCr$_2$As$_2$ at interaction strength slightly below the crossover which implies that negative pressures and/or electron doping (e.g. Cr $\rightarrow$ Mn,Fe or Ba $\rightarrow$ Sc,Y,La) might strongly enhance the compressibility, thereby possibly inducing a pairing instability in this non-superconducting compound.