We investigated the polar behavior of the double perovskite (Bi,Sr)${}_2$MgNbO${}_6$ using first-principles density-functional theory calculations. We find that the magnitude (75 $\mu$C/cm${}^2$) and direction (along [111]) of the polarization are comparable to our previous results for the $A$-site size difference (Bi,Sr)${}_2$ZnNbO${}_6$ and (Bi,Pb)${}_2$ZnNbO${}_6$ systems. However, comparisons with the (Bi,Sr)${}_2$ZnNbO${}_6$ compound indicate that the presence of Zn modestly enhances the off-centering of the Sr and Nb cations as well as the Born effective charges of both Bi and Nb. Analogous to the corresponding Pb-based perovskites, Pb(Mg${}_{1/3}$Nb${}_{2/3}$)O${}_3$ and Pb(Zn${}_{1/3}$Nb${}_{2/3}$)O${}_3$, we demonstrate that the differences in the experimentally observed critical temperatures are related to the differences in polarization between the two materials. A local dipole analysis indicates that the most significant contribution arises from the enhanced cooperative couplings with the larger Zn displacements.

• Received 20 January 2011

DOI:https://doi.org/10.1103/PhysRevB.83.115130