Mechanical coupling of polar topologies and oxygen octahedra rotations in PbTiO$_3$/SrTiO$_3$ superlattices

TL;DR

The study shows that in PbTiO$_3$/SrTiO$_3$ superlattices, a strain-mediated mechanical coupling links PbTiO$_3$ polarization textures (including $a_1/a_2$ domains, polar vortices, and polar bubbles) with specific SrTiO$_3$ oxygen octahedra rotation patterns. Using second-principles atomistic simulations fitted to DFT data, the authors demonstrate a biunivocal relationship where each PbTiO$_3$ texture imposes a corresponding SrTiO$_3$ rotation pattern, and conversely, freezing SrTiO$_3$ rotations drives the PbTiO$_3$ topology. The coupling is reciprocal and primarily strain-driven, with SrTiO$_3$ rotations not penetrating PbTiO$_3$ and a constrained-relaxation protocol recovering the PbTiO$_3$ textures when rotations are fixed. These findings suggest that SrTiO$_3$ actively shapes polarization landscapes and offer a pathway to stabilizing complex topological states in oxide superlattices and potentially enabling cross-coupled control in multiferroics.

Abstract

PbTiO$_3$/SrTiO$_3$ artificial superlattices recently emerged as a prototypical platform for the emergence and study of polar topologies. While previous studies mainly focused on the polar textures inherent to the ferroelectric PbTiO$_3$ layers, the oxygen octahedra rotations inherent to the paraelectric SrTiO$_3$ layers have attracted much little attention. Here, we highlight a biunivocal relationship between distinct polar topologies -- including $a_1/a_2$ domains, polar vortices, and skyrmions -- within the PbTiO$_3$ layers and specific patterns of oxygen octahedra rotations in the SrTiO$_3$ layers. This relationship arises from a strain-mediated coupling between the two materials and is shown to be reciprocal. Through second-principles atomistic simulations, we demonstrate that each polar texture imposes a corresponding rotation pattern, while conversely, a frozen oxygen octahedra rotation dictates the emergence of the associated polar state. This confirms the strong coupling between oxygen octahedra rotations in SrTiO$_3$ and polarization in PbTiO$_3$, highlighting their cooperative role in stabilizing complex polar textures in related superlattices.

Figures (6)

• Figure 1: Schematic illustration of oxygen octahedra rotations following an out-of-phase antiferrodistortive mode along an axis perpendicular to the plane of the paper in a perovskite structure. The pristine and the staggered local rotations of the TiO$_6$ octahedra are shown.
• Figure 2: (a) Schematic representation of the (PbTiO$_3$)$_{6}$/(SrTiO$_3$)$_{6}$ used for the relaxation of the $a_1$/$a_2$ phase. (b) Planar $xy$-view of the polarization profile on a central PbTiO$_3$ layer as depicted by the dashed line and scissors. (c) Planar $xy$-view of the antiferrodistortive profile on a central SrTiO$_3$ layer as depicted by the dashed line and scissors. In both panels, arrows represent the in-plane components of the corresponding vector fields. The scale for arrow length is indicated on each panel in units of C/m$^2$. The color map denotes the local in-plane strain components along the $x$ or $y$ directions as indicated by the labels on the colorbar computed in % taking $3.917$Å as a reference.
• Figure 3: (a) Schematic representation of the (PbTiO$_3$)$_{10}$/(SrTiO$_3$)$_{10}$ used for the relaxation of the polar vortex phase. (b) Front $xz$-view of the polarization profile on the supperlattice as schematized by the dashed line and scissors. (c) Planar $xy$-view of the antiferrodistortive profile on a central SrTiO$_3$ layer as schematized by the dashed line and scissors. In both panels, arrows represent the in-plane components of the corresponding vector fields in C/m$^2$ and degrees respectively. The scale for arrow length is indicated on each panel. The color map denotes the local in-plane strain components along the $x$ or $z$ directions as indicated by the labels on the colorbar computed in % taking $3.917$Å as a reference. For visualization purposes, local strain values in the PbTiO$_3$ layers are divided by a factor of 2 to allow both PbTiO$_3$ and SrTiO$_3$ to be shown on a common color scale without oversaturating the plot and to preserve visibility in the SrTiO$_3$ region.
• Figure 4: Polar bubble phase on the (PbTiO$_3$)$_{6}$/(SrTiO$_3$)$_{6}$ superlattice. (a) Planar $xy$-view with the polarization map on a PbTiO$_3$ layer near the interfase and antiferrodistortive map on the SrTiO$_3$ on a central layer. Color maps indicate the poalrization and antiferrodistortive rotations along the $z$-direction. (b) Planar $xy$-view of the in-plane polarization profile on the supperlattice. (c) Planar $xy$-view of the in-plane antiferrodistortive profile on a central SrTiO$_3$ layer. In both panels, arrows represent the in-plane components of the corresponding vector fields. The scale for arrow length is indicated on each panel. The color map denotes the local in-plane strain components along the $x$, $y$ and $z$ directions as indicated by the labels on the colorbar computed in % taking $3.885$Å as a reference.
• Figure 5: Polar vortex phase obtained after the constrained relaxation fixing the TiO$_6$ octahedral rotations on the SrTiO$_3$ to the values encountered on the first part of the manuscript. Clockwise counter-clockwise vortices are displaced towards the top/bottom interfaces and a net in-plane polarization along the $x$-direction is developped on the PbTiO$_3$