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Ground-state structure, orbital ordering and metal-insulator transition in double-perovskite PrBaMn2O6

In recent years, A-site ordered half-doped double-perovskite manganites $\rm RBaMn_2O_6$ (R=rare earth) have attracted much attention due to their remarkable physical properties and a prospect of application as magnetoresistance, multiferroic, and oxygen storage materials. The nature of the ground state in ${\rm RBaMn_2O_6}$ as well as sequence of phase transitions taking place at cooling are not yet well understood due to complexity in both experimental and theoretical studies. Here we address the origin of the ground-state structure in PrBaMn$_2$O$_6$ as well as its electronic and magnetic properties. Utilizing GGA+U approach and specially designed strategy to perform structural optimization, we show that the system has two competing AFM-A and AFM-CE magnetic structures with very close energies. The AFM-A structure is a metal, while AFM-CE is an insulator and the transition to the insulating state is accompanied by the charge Mn$^{3+}$/Mn$^{4+}$, and orbital $3x^2-r^2$/$3y^2-r^2$ orderings. This orbital ordering results in strong cooperative Jahn-Teller (JT) distortions, which lower the crystal symmetry. Our findings give a key to understanding contradictions in available experimental data on ${\rm PrBaMn_2O_6}$ and opens up the prospects to theoretical refinements of ground-state structures in other ${\rm RBaMn_2O_6}$ compounds.