Effect of $A$-site size difference on polar behavior in $M$BiScNbO$_6$ ($M$=Na, K, and Rb) perovskite: Density functional calculations

We investigated the effect of $A$-site size difference in the double perovskites BiScO$_3$-$M$NbO$_3$ ($M$=Na, K, and Rb) using first-principles calculations. The materials studied have increasing ionic radii at the $A$-site ($r_{\rm{Na}^+}<$ $r_{\rm{K}^+}<$ $r_{\rm{Rb}^+}$) but are otherwise chemically similar. We find that the polarization of these materials is 70-90 $\mu$C/cm$^2$ along the rhombohedral direction, which increases as the $A$-site size difference becomes larger. The main contribution to the high polarization comes from large off-centerings of Bi ions, which are strongly enhanced by the suppression of octahedral tilts as the $M$-ion size increases. A high Born effective charge of Nb also contributes to the polarization and this contribution is also enhanced by increasing the $M$-ion size. This work was supported by ONR and DOE, BES, Materials Sciences and Engineering.