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 N\'eel-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.