Direct Observation of Strain-Induced Ferroaxial Transition in Quasi-1D BaTiS₃

The properties of ferroic materials are dictated by their symmetry, particularly, a broken symmetry results in a phase transition that can be represented using an order parameter. Ferroelectricity is characterized by an electric polarization vector that is invariant under time-reversal operation. Ferromagnetism is described by a magnetization vector that is invariant under spatial-inversion operation. In contrast to these two well-studied ferroic orders, the ferroaxial transition — that is characterized by a rotational structural distortion with an axial vector symmetry — is relatively unexplored.The symmetry requirement for a ferroaxial transition is broken mirror symmetry in a plane parallel to the rotation axis, and ferroaxial order is invariant under both spatial- and time-reversal operations. Ferroaxial order has shown an intimate ties with emergent properties, such as magnetoelectric couplings in multiferroicsand chiral materials.^1-2Here, we report direct, atomic-scale observation of a strain-induced ferroaxial transition in a single crystal of a quasi-1D chalcogenide, BaTiS₃. Using a combining aberration-corrected scanning transmission electron microscope imaging and density-functional-theory calculations, we show that a biaxial strain of 2% along a plane perpendicular to 1D chains of TiS₆ octahedra in BaTiS₃ transforms it from a higher symmetry <i>P</i>6₃<i>cm</i> phase to a ferroaxial <i>P</i>6₃ phase, which is characterized by a rotational distortion of the TiS₆ octahedra along the axis containing the chains.<br/>The global refinement of X-ray diffraction suggests an average structure with a space group of <i>P</i>6₃<i>cm</i>. To induce a biaxial strain, we welded a BaTiS₃ lamella to two lateral sides of a TEM half-grid. For another lamella, we attached it to a TEM half-grid with only one lateral side fixed such that strain relaxation was possible through the unconstrained side. We performed atomic resolution high-angle annular dark-field imaging of both samples and performed local crystallography by extracting and analyzing the atomic positions from the acquired images. In the biaxially strained sample, we observe a rotational distortion of TiS₆ octahedra accompanied with an outward displacement of the Ba sublattice, suggesting the presence of ferroaxial order. We also observe nanoscale (~10 nm) domains consisting of three ordered distorted Ba sublattice configurations separated by an undistorted Ba sublattice. By comparing the average Ba-Ba distance in the strained BaTiS₃ lamella to the unstrained one, we find the presence of ~3.45 % tensile strain in the former BaTiS₃ lamella.<br/>We used DFT calculations to gain further insights into the microscopic details of this ferroaxial transition in BaTiS₃ under biaxial strain. We find that the ferroaxial transition from <i>P</i>6₃<i>cm</i> to <i>P</i>6₃space group can be accomplished through the freezing of two distortion modes (<i>Γ</i>1 and <i>Γ</i>2) in the high-symmetry<i> P</i>6₃<i>cm </i>phase. These modes involve the rotational distortion of TiS₆ octahedra and outward displacements of Ba atoms in <i>ab</i>-plane, both of which are observed in the STEM images. Using DFT calculations, we show that ferroaxial order in <i>P</i>6₃ phase can be stabilized over the <i>P</i>6₃<i>cm</i> phase for biaxial strains &gt;2%, which further supports the STEM observations. We will also discuss the effect of the ferroaxial transition on the electronic and optical properties of BaTiS₃.<br/>Acknowledgements: This work was supported by ARO MURI grant # W911NF-21-1-0327 and NSF through DMR-2122070, DMR-2122071 and DMR-2145797. Electron microscopy performed at Oak Ridge National Laboratory’s (ORNL) Center for Nanophase Materials Sciences (CNMS), which is a DOE Office of Science User Facility.<br/>1. Jin W, Drueke E, Li S, et al. Observation of a ferro-rotational order coupled with second-order nonlinear optical fields. Nature Physics, 2020, 16(1): 42-46.<br/>2. ayashida T, Uemura Y, Kimura K, et al. Visualization of ferroaxial domains in an order-disorder type ferroaxial crystal. Nature communications, 2020, 11(1): 1-8.