Emergent chirality in the electric polarization texture of titanate superlattices

Abstract

Chirality is a geometrical property by which an object is not superimposable onto its mirror image, thereby imparting a handedness. Chirality determines many important properties in nature-from the strength of the weak interactions according to the electroweak theory in particle physics to the binding of enzymes with naturally occurring amino acids or sugars, reactions that are fundamental for life. In condensed matter physics, the prediction of topologically protected magnetic skyrmions and related spin textures in chiral magnets has stimulated significant research. If the magnetic dipoles were replaced by their electrical counterparts, then electrically controllable chiral devices could be designed. Complex oxide BaTiO₃/SrTiO₃ nanocomposites and PbTiO₃/SrTiO₃ superlattices are perfect candidates, since "polar vortices," in which a continuous rotation of ferroelectric polarization spontaneously forms, have been recently discovered. Using resonant soft X-ray diffraction, we report the observation of a strong circular dichroism from the interaction between circularly polarized light and the chiral electric polarization texture that emerges in PbTiO₃/SrTiO₃ superlattices. This hallmark of chirality is explained by a helical rotation of electric polarization that second-principles simulations predict to reside within complex 3D polarization textures comprising ordered topological line defects. The handedness of the texture can be topologically characterized by the sign of the helicity number of the chiral line defects. This coupling between the optical and novel polar properties could be exploited to encode chiral signatures into photon or electron beams for information processing.

Keywords: chirality; electric polarization; resonant soft X-ray diffraction; second-principles calculations; topological textures.

Fig. 1.

Self-organized arrays of electric polarization textures in (PbTiO₃)_n/(SrTiO₃)_n superlattices exhibit a chiral RSXD pattern. (A) These polar arrays produce diffraction satellites that decorate the specular reflection along the lateral direction, [100]_χ, for X-rays tuned near the titanium L₃ edge. Specular scattering plane is shown in blue. Red and blue helices illustrate opposing circular polarizations of incident X-rays. Sample azimuth is indicated by Φ. (B) (Upper) Line cut of scattered intensity versus lateral momentum transfer (q_lateral) using right- (red) and left-circularly (blue) polarized X-rays for n = 16. (Lower) XCD is the difference in intensity for the two helicities. (C) (Upper) Resonance profiles through the titanium L_3,2 edges at q_lateral = +q_{χ_pair} for both X-ray helicities (red and blue) and (Lower) their XCD (green) for n = 14. Fluorescence absorption spectrum (black curve in Upper) shows electronic states similar to that of Pb(Zr_0.2Ti_0.8)O₃ (14). (D) Map of XCD intensity at q_lateral = +q_{χ_pair} across an n = 14 sample. Regions of positive (negative) XCD indicate where chiral polar arrays have positive (negative) helicity.

Fig. 2.

Mirrored diffraction vectors detect opposite rotational patterns in chiral textures. RSXD is sensitive to anisotropic TiO₆ distortions, so that a helical rotation of the electric polarization can produce RSXD peaks with antisymmetric XCD. (A) Conical blue arrows indicate the direction of polarization, which rotates helically along the lateral direction, [100]_χ. The distorted perovskite cell is depicted for several orientations, as is the distorted TiO₆ octahedron for an up-polarized unit cell. (B) The cyclic modulation of polarization for this same helix is highlighted by folding the lateral dimension into a circle. The diffraction vector with q_lateral > 0 (red arrow) senses a clockwise helical rotation of polarization, whereas the diffraction vector with q_lateral < 0 (blue arrow) detects a counterclockwise rotation.

Fig. 3.

Rotational symmetry of chiral polar arrays observed in azimuthal pattern of XCD. (A) XCD intensity plotted versus azimuth, ϕ_spot, for each diffraction spot from the polar arrays. Red circles indicate XCD > 0; blue squares indicate XCD < 0. Filled markers were measured at n_SL = 4; hollow markers were measured at n_SL = 3. Gray regions show experimentally inaccessible sample geometries. (B) Diffraction patterns for two sample orientations (separated by 180° azimuthally) exhibit similar XCD (red and blue circles) relative to the scattering geometry: Φ = 0° (Left) and 180° (Right). Curved arrows indicate ϕ_spot, measured from the in-plane projection (dashed green arrow) of the incoming X-rays. Sample is depicted with counterrotated polarization cores (small black arrows) and alternating axial polarization (green and magenta) domains. (C) Polarization structure is averaged over both orientations in the (010)_χ cross-section. These polar cores possess a chiral texture that is robust versus a twofold rotation. Error bars in A represent uncertainty in fitting the XCD spectra at each azimuth (Azimuthal XCD Measurements).

Fig. 4.

Resonance profiles for (PbTiO₃)_n/(SrTiO₃)_n superlattices through the titanium L₃ edge at (A) q_lateral = +q_{χ_pair} for n = 14 and (B) q_lateral = +q_a-domain = +2π/d_a-domain for n = 4, where d_a-domain ∼ 70 nm. (Upper) The polarization-averaged diffraction intensity (red) for both X-ray helicities, and (Lower) XCD (green). Insets show planar view HR-STEM images of (A) an array of polar cores ordered along [100]_χ (horizontal scale bar: 50 nm) and (B) an array of ferroelectric a domains ordered along [110]_χ (horizontal scale bar: 200 nm). Superlattices with chiral polar arrays exhibit strong XCD in A that is characteristic of the chiral arrangement of electric polarization in the texture. In superlattices with smaller layer thickness, the polarization arranges into periodic a domains only, with no chiral structure and correspondingly negligible XCD.

Fig. 5.

Second-principles calculations of electric polarization textures and their topological properties for n = 10. (A–C) Three different local minima, degenerate in energy. Each texture contains a pair of counterrotated cores yet has different chiral properties. Black arrows indicate the local dipoles, projected onto the (010)_χ plane. A large axial component of the polarization along ±[010]_χ, represented by the green and magenta domains, is observed. (D–F) Simplified cartoon with cylinders representing the cores and arrows that show their rotational and axial polarization components. A right-hand rule reveals the chirality of each cylinder. By curling one’s fingers in the direction of polar rotation around the core, the thumb points (anti-)parallel to the axial polarization for a (left-) right-handed core. (G–I) Maps of helicity. When the handedness of the two cores is the same, the system as a whole is chiral and the enantiomers can be distinguished by the sign of the integrated helicity (ℋ). Results obtained at temperature of 10 K.