On the magnetic structure and band gap of the double perovskite Ba2CuOsO6: Density functional analysis*

The ordered double-perovskite Ba$_{2}$CuOsO$_{6}$, consisting of 3d and 5d transition-metal magnetic ions (Cu$^{2+}$ and Os$^{6+}$, respectively), is a magnetic insulator. It obeys the Curie-Weiss law with $\theta \quad =$ -13.3 K. We evaluated the spin exchange interactions of Ba$_{2}$CuOsO$_{6}$ by performing energy-mapping analysis based on DFT$+$U calculations and determined the band gap of Ba$_{2}$CuOsO$_{6}$ by DFT$+$U and DFT$+$U$+$SOC calculations. The antiferromagnetic ordering of Ba$_{2}$CuOsO$_{6}$ is due largely to the spin exchange interactions between Cu2$+$ ions, which are enhanced by the empty eg orbitals of the intervening Os$^{6+}$ ions. Both electron correlation and spin-orbit coupling are necessary to open a band gap for Ba$_{2}$CuOsO$_{6}$.