First-principles study of symmetry lowering and polarization in $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3∕\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ superlattices with in-plane expansion

The crystal structure and local spontaneous polarization of ${\left(\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\right)}_m∕{\left(\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3\right)}_n$ superlattices are calculated using first-principles density-functional theory. The in-plane lattice constant is constrained to be 1% larger than the $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ (ST) substrate to take into account the in-plane expansion observed in recent experiments. The symmetry is lowered to monoclinic space group $Cm$ allowing for polarization along the [110] and [001] directions. The polarization component in the [110] direction is found to develop only in the $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ layers and falls to zero in the $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ (BT) layers, whereas the polarization in the [001] direction is approximately uniform throughout the superlattice. These findings are consistent with recent experimental data and first-principles results for epitaxially strained BT and ST.

Figure 1

(Color online) Magnitude of $P_{\text{local}}$ in the [110] and [001] directions. $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$, $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$, and interface cells are labeled as S, B, and I, respectively.

Figure 2

(Color online) [001] and [110] components and magnitude of $P_{\text{local}}$.