Cooperative effect of electron correlation and spin-orbit coupling on the electronic and magnetic properties of ${\mathrm{Ba}}_2\mathrm{Na}\mathrm{Os}{\mathrm{O}}_6$

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 ${\mathrm{Os}}^{7+}$ $\left(d^1\right)$ 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 ${\mathrm{Ba}}_2\mathrm{Na}\mathrm{Os}{\mathrm{O}}_6$.

Figure 1

(Color online) Structure of cubic double perovskite ${\mathrm{Ba}}_2\mathrm{Na}\mathrm{Os}{\mathrm{O}}_6$.

Figure 2

(Color online) Band structures calculated for ${\mathrm{Ba}}_2\mathrm{Na}\mathrm{Os}{\mathrm{O}}_6$ using different methods. (a) GGA, (b) $\mathrm{GGA}+\mathrm{U}$ with $U_{\mathit{eff}}=0.2\mathrm{Ryd}$, (c) $\mathrm{GGA}+\mathrm{SOC}$, and (d) $\mathrm{GGA}+\mathrm{SOC}+\mathrm{U}$ with $U_{\mathit{eff}}=0.2\mathrm{Ryd}$. In (a) and (b) the solid and dashed lines refer to the up- and down spin bands, respectively. In (d) the valence band top is taken as the zero-energy point.

Figure 3

(Color online) DOS of ${\mathrm{Ba}}_2\mathrm{Na}\mathrm{Os}{\mathrm{O}}_6$ obtained from the $\mathrm{GGA}+\mathrm{SOC}+\mathrm{U}$ calculation. The inset shows the PDOS plots calculated for the Os and O atom contributions to the $t_{2g}$ bands.