Multimodal Topological Textures Arising from Coupled Structural Orders in SrTiO$_3$

Abstract

Magnetic spin topological textures recently found their electrical counterparts in polar topologies emerging from the condensation of inhomogeneous polar atomic distortions. Here, we further extend the concept to other non-polar atomic degrees of freedom. Taking SrTiO$_3$ as a prototypical example, we investigate from second-principles atomistic simulations, the equilibrium domain structures and topological textures associated with the natural antiferrodistortive rotations of its oxygen octahedra. % Besides the common 90$^\circ$ antiferrodistortive domain walls (twin boundaries), we identify new metastable 180$^\circ$ domain walls oriented along the $\lbrace100\rbrace_\mathrm{pc}$ direction, when compressive epitaxial strain is applied. These domains exhibit complex antiferrodistortive Bloch- and Néel-like configurations with the later being the most favorable. We also stabilize antiferrodistortive vortex and antivortex structures which are accompanied by co-localized polarization vortices and a complex pattern of the local strain field, giving rise to a trimodal topological structures. Our results extends the concept of topological ordering to non-polar structural degrees of freedom and highlights the role of lattice-mediated couplings in stabilizing complex textures in perovskite oxides.

Figures (7)

• Figure 1: Oxygen octahedra rotations following an out-of-phase antiferrodistortive mode along an axis perpendicular to the plane of the paper. The pristine and staggered local rotations of the TiO$_6$ octahedra are shown.
• Figure 2: Relaxed 90$^\circ$ domain wall along the $\lbrace110\rbrace_{\rm pc}$ direction of the oxygen octahedral rotations in SrTiO$_3$. Arrows indicate the in-plane local rotations in degrees accounting with the phase shift explained on the main text where as colors indicate (a) the out of plane rotations (b) the local strains in % along $x$ and (c) the local strains in % along $y$.
• Figure 3: Relaxed (a) pure (b) Bloch and (c) Néel 180$^\circ$ domain wall along the $\lbrace100\rbrace_{\rm pc}$ direction of the oxygen octahedral rotations under -2.1% epitaxially strained SrTiO$_3$. Arrows indicate the in-plane components of the oxygen octahedral rotations in degrees accounting with the phase shift explained on the main text whereas colors indicate either their out-of-plane component or the local strain relaxations along $x$ in % as indicated on the labels.
• Figure 4: Fully relaxed vortex texture on a 40$\times$40$\times$2 supercell under no mechanical boundary conditions. (a) Oxygen octahedral rotation pattern, (b) polarization pattern and (c) local strain pattern. Arrows indicate the in-plane components of the corresponding vector field. The color wheel encodes their in-plane orientation, providing a complementary visualization to the arrows. The red and blue dots in (c) serve as visual guides to help identify the positions of some vortices and antivortices in the local strain field.
• Figure A1: Different initial geometries for the domain walls studied on the work. Arrows indicate in-plane components of the oxygen octahedra rotations with the corresponding phase shift as explained in the main text whereas color bars indicate their out of plane component.