Chiral soft mode transition driven by strain in ferroelectric bubble domains

Abstract

Chirality in solids is attracting growing attention as a potential ferroic order, yet virtually no paradigmatic example of a soft-mode achiral-to-chiral phase transition has been firmly established to date. Here we identify ferroelectric bubble domains as a model system that undergoes a strain-driven achiral-to-chiral transition exhibiting the hallmarks of spontaneous symmetry breaking. Using second-principles atomistic simulations, we uncover chiral phonon modes in ferroelectric/dielectric superlattices that soften under epitaxial strain following textbook soft-mode behaviour. The transition is accompanied by a change in topological character, highlighting an interplay between chirality and topology in these systems. This work provides a concrete step towards establishing chirality as a genuine ferroic order in solids.

Figures (18)

• Figure 1: (a) 3D view of the electric bubble lattice in a ${\rm{(PTO)}}_9$/$\rm{{(STO)}}_3$ superlattice under in-plane compressive strain $\eta$. Each arrow indicates the electric dipole associated with a single 5-atom perovskite unit cell. (b) Dipole field in the middle PTO layer. (c) Low-frequency phonon spectrum computed for the bubble lattice shown in (a). The chiral phonon branch is highlighted in dark blue. (d) The eigenmode of the lowest frequency optical phonon displays a Bloch component all along the bubble's domain wall.
• Figure 2: (a) Energy landscape of the ferroelectric bubble lattice as a function of the chiral mode amplitude $Q$ under different epitaxial strains, showing the transition from a single-well (achiral) to a double-well (chiral) potential in the tensile regime. The chiral mode amplitude is scaled to its relaxed magnitude $Q_0$ at 0% strain. (b) Squared frequency of the chiral phonon at the $\Gamma$ point as a function of epitaxial strain, illustrating the linear softening towards the critical strain ($\eta_c$) characteristic of a soft-mode-driven phase transition.
• Figure 3: Bubble lattice structures obtained by condensing the chiral soft mode at different points of the Brillouin zone: (a) $\Gamma$-point (uniform chirality, ferrochiral order), (b) $Y$-point, and (c) $M$-point modulations. The $Y$ and $M$ modes yield arrays of bubbles with alternating handedness (antiferrochiral order).
• Figure 4: Vertically modulated chiral bubble structures. (a) Chiral bubble with uniform handedness. (b–c) Vertically modulated chirality with one and two Ising rings across the PTO layers, respectively, obtained from higher-frequency eigenmodes. Dipole field only at the domain walls is shown for clarity. (d) Layer-resolved in-plane polarization magnitude, showing nodal patterns analogous to harmonic modes.
• Figure S1: Evolution of the dipole field in the bulk-like PbTiO$_3$ (PTO) layer for bubble domains with a $3 \times 3$ perovskite u.c. square section, as a function of epitaxial strain $\eta$ in the 9PTO/3STO superlattice without an external electric field. The colourbar representing the magnitude of out-of-plane polarization follows the same scale as in Fig. 1(a) of the main text.