Emergent Atomic Scale Polarisation Vortices in BaTiS3

Abstract

Topological defects, such as vortices and skyrmions in magnetic and dipolar systems, can give rise to properties that are not observed in typical magnets and dielectrics. Here, we report the discovery of long-range ordered periodic dipole arrays of atomic-scale vortices and antivortices in the unconventional charge-density-wave (CDW) phase of BaTiS3, a quasi-1D chalcogenide. Synchrotron X-ray diffraction (XRD) reveals the presence of a multi-q ordering in BaTiS3 that confines vortex-vortex-antivortex polarisation triplets to the a-b plane with alternating handedness along the c-axis. The multi-q displacive distortions are characterised by three distinctive off-centre TiS6 configurations, whose ratios are independently confirmed by 47/49Ti solid-state nuclear magnetic resonance (SSNMR). Using first-principles calculations and phenomenological modelling, we show that the dipolar vortex unit cell in BaTiS3 arises from the coupling between multiple lattice instabilities arising from flat, soft phonon bands. This mechanism contrasts with classical dipolar textures in ferroelectric heterostructures that emerge from the competition between electrostatic and strain energies. The observation of dipolar vortices in BaTiS3 brings the ultimate scaling limit for real-space dipolar topological structures down to about a nanometre and unveils the intimate connection between crystal symmetry and real-space topology. Our work sets up zero-filling semiconducting materials with competing structural instabilities as a playground for realising and understanding quantum polarisation topologies.