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

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