First-principles study of symmetry lowering in relaxed BaTiO$_3$/SrTiO$_3$ superlattices

The crystal structure and local spontaneous polarization of (BaTiO$_3$)$_m$/(SrTiO$_3$)$_n$ superlattices is calculated using a first-principles density functional theory method. The in-plane lattice constant is 1\% larger than the SrTiO$_3$ substrate to imitate the relaxed superlattice structure and the symmetry is lowered to monoclinic space group $Cm$ which allows polarization to develop along the [110] and [001] directions. The polarization component in the [110] direction is found to develop only in the SrTiO$_3$ layers and falls to zero in the BaTiO$_3$ 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.