Electric field control of chirality

Abstract

Polar textures have attracted substantial attention in recent years as a promising analog to spin-based textures in ferromagnets. Here, using optical second-harmonic generation–based circular dichroism, we demonstrate deterministic and reversible control of chirality over mesoscale regions in ferroelectric vortices using an applied electric field. The microscopic origins of the chirality, the pathway during the switching, and the mechanism for electric field control are described theoretically via phase-field modeling and second-principles simulations, and experimentally by examination of the microscopic response of the vortices under an applied field. The emergence of chirality from the combination of nonchiral materials and subsequent control of the handedness with an electric field has far-reaching implications for new electronics based on chirality as a field-controllable order parameter.

Fig. 1.. Different mechanisms for achieving chirality.

(A) HAADF-STEM displacement map of polar vortex array. Colors indicate the curl of the local polarization. Circles represent the core of the vortices, and crosses represent the center points of the PbTiO₃ layer. (B) Phase-field modeling of vortex array demonstrating pronounced buckling of vortices. (C) CW (blue curled arrow) and CCW (orange curled arrow) vortices coupled with antiparallel axial components of the polarization. Filled red and blue circles represent the direction of the axial polarization (along the ${[1\overline{1}0]}_o$ direction), and light colors represent lower values. Straight arrows represent the direction of the local polarization along the [001]_o (horizontal) or [110]_o (vertical) directions. Within the right-hand rule discussed in (20), both vortices in the sketch are right handed. (D) Asymmetry between up- and down-polarized domains (along [110]_o), superimposed on an offset that generates a mismatch between left and right polarization along the [001]_o direction. In the sketch, at the center of the ferroelectric layer, the two vortices point predominantly to the left. The handedness of the two vortices is opposite, but one of them is slightly larger than the other, giving the whole system a net chirality. (E) Schematic representation of the right-handed and left-handed domains experimentally observed, separated by a domain wall (dashed square at the center). The two sources of chirality (antiparallel axial components at the center of consecutive vortices plus an offset of its center) coexist within a domain. At the domain wall, the sense of rotation of a vortex is reversed, keeping constant the sense of the axial polarization. (F) Vortices of (E) after performing a mirror symmetry operation, represented by “R.” Schematics with the three orthogonal reflections of the polar texture supercell to determine their chiral nature are presented in fig. S1.

Fig. 2.. Vortex domain structure.

SHG images taken with (A) right circularly (RC) and (B) left circularly (LC) polarized excitation. (C) SHG-CD calculated from the images shown in (A) and (B) using Eq. 2. (D) Lateral PFM image, with red arrows indicating regions of opposite polarization along [001]_o. (E) Weak-beam dark-field TEM image (DF-TEM) image of vortex domains. The arrow shows the location of antiphase domain wall. (F) HAADF-STEM displacement map at a vortex domain wall. Colors indicate the direction of atomic displacement with respect to the color wheel. a.u., arbitrary units.

Fig. 3.. 4D STEM analysis of in-plane vortices.

(A) Large-area HAADF-STEM showing the in-plane vortices along the ${[1\overline{1}0]}_o$ direction with domain boundaries indicated by the gray dotted line. (B) A representative CBED pattern from the vortex structure is shown in (A), which identifies the reflections that were used to form the 4D STEM images in (C) and (D). (C) Lateral and (D) axial polarization components extracted from orange square region indicated in (A). (E and F) Line scans from different regions across the domains, which show lateral and axial polarization out of phase and in phase, respectively.

Fig. 4.. Electric field switching of chirality.

(A and B) SHG-CD for alternating applied electric fields of ±50 kV/cm as indicated by the white arrows. (B) SHG-CD for the same region shown in (A) but with inverted electric field polarities. (C and D) Data along dashed white lines in (A) and (B) with repeated reversal of the electric field polarity. Subsequent scans are shown going from red/blue to orange/green for (A)/(B). (E) Hysteresis of the chiral switching measured using SHG-CD (blue) and calculated helicity (green), both of which are normalized. Polarization was measured from an electric field applied along the [001]_o in-plane direction (red) and calculated polarization hysteresis curve from second principles (orange).

Fig. 5.. Reversal of vortex buckling.

(A to C) DF-TEM showing atomic-scale restructuring during chiral phase switch. Yellow arrows indicate the direction of polarization, and red circles indicate the vortex core location. (D to F) Phase-field modeling demonstrating the reversal of buckling pattern with applied field.