Cooperative effect of electron correlation and spin-orbit coupling on the electronic and magnetic properties of Ba 2 Na Os O 6

The electronic and magnetic properties of the cubic double perovskite ${\mathrm{Ba}}_{2}\mathrm{Na}\mathrm{Os}{\mathrm{O}}_{6}$ were examined by performing first-principles density functional theory calculations and analyzing spin-orbit coupled states of an ${\mathrm{Os}}^{7+}$ $({d}^{1})$ ion at an octahedral crystal field. The insulating behavior of ${\mathrm{Ba}}_{2}\mathrm{Na}\mathrm{Os}{\mathrm{O}}_{6}$ was shown to originate from a cooperative effect of electron correlation and spin-orbit coupling. This cooperative effect is responsible not only for the absence of orbital ordering in ${\mathrm{Ba}}_{2}\mathrm{Na}\mathrm{Os}{\mathrm{O}}_{6}$ but also for a small magnetic moment and a weak magnetic anisotropy in ${\mathrm{Ba}}_{2}\mathrm{Na}\mathrm{Os}{\mathrm{O}}_{6}$.