Anomalous Polar Textures and Exotic Phases in Quasi-1D Chalcogenide

Topological structures in ferroic materials have been studied extensively and garnered much attention due to their multiple prospective applications ranging from low-power electronics to high-performance optoelectronic devices. Specifically, topological patterns of electric dipoles such as polar vortices and polar skyrmions have been recently demonstrated in oxide superlattices and thin films. These patterns form a few to tens of nanometer-scale polar textures due to their long-range dipole interactions and geometrically confined boundary conditions. In this work, we explore the anomalous polar textures in quasi-1D BaTiS₃, where several competing structural distortions lead to different exotic phases such as charge-ordered phase consisting of atomic-scale polar vortices, a high-mobility ground-state phase, and a strain-induced chiral phase. Starting from high-symmetry room-temperature phase (<i>P</i>6₃<i>cm</i>), the quasi-1D BaTiS₃ undergoes two phase transitions, (i) second-order transition (240-250 K) to a charge-ordered phase (<i>P</i>3<i>c</i>1) and (ii) a first-order transition (150-190 K) to a high-mobility ground-state phase (<i>P</i>2₁).¹ Combining the single-crystal XRD and first-principles calculations, we identified the underlying structures of each three phases. Room temperature <i>P</i>6₃<i>cm</i> phase consists of the anti-polar displacements along the <i>c</i>-axis with ferrielectric polarization along the out-of-plane direction. In the charge-ordered <i>P</i>3<i>c</i>1 phase, the atomic-scale polar vortices emerge with different chiralities on a larger size unit cell. In the ground state high-mobility phase (<i>P</i>2₁), striped pattern of antipolar displacements are observed both along in-plane and out-of-plane directions, making the net dipole moment as zero. This high-mobility phase exhibits chiral optical Raman response, implying an anomalous polar textures with optical activity. Notably, using a scanning transmission electron microscope (STEM) imaging, we directly observed a strain-induced ferroaxial transition, which is characterized by rotational distortion of the TiS₆ octahedra and Ba outward movements in the <i>a</i>-<i>b</i> plane.<br/>Next, we will focus on the evolution of atomically thin clockwise counter-clockwise (CW-CCW) vortex pairs in the second-order transition. These polar vortices lie on a triangular-lattice network of Ti atoms along in-plane direction, which intrinsically hosts the frustration of electric dipoles in neighboring atoms. This resembles small skyrmions in magnetic materials, which often arises by resolving the exchange frustrations.^2,3 Using the first-principles electronic structure calculations and Monte Carlo simulations, we will discuss the possible mechanism to form the polar vortices on a 2D triangular lattice. We find that the coupling between several collinear antiferroelectric modes is the key to realize the non-collinear dipole textures such as vortices. Using group theoretical methods, we extracted three primary order parameters (K₃, Λ₃, M₂^-), which are all located at zone-boundaries, and developed a Landau model to microscopically understand the couplings between these modes. Based on the results, we find the CW-CCW vortex pairs can be further stabilized with more complex orders, involving non-coplanar orders along the in-plane direction with a finite scale macroscopic polarization along the out-of-plane direction. We expect that these results could pave the way to control the polar textures with multiple functionalities in ferroelectrics.