Emergent Three-Dimensional Electric Dipole Sinewave in Bulk Perovskite Oxides

The magnetic and electric dipoles of ferroics play a central role in their fascinating properties. In particular, topological configurations have shown promising potential for use in novel electromechanical and electronic devices. Magnetic configurations from simple collinear to complex topological are well-documented. In contrast, many complex topological features in the electric counterpart remain unexplored. Here, we report the first example of three-dimensional electric dipole sinewave topological structure in a PbZrO₃-based bulk perovskite, which presents an interesting triple-hysteresis loop macroscopically. This polar configuration consists of two orthogonal sinewave electric dipole modulations decoded from a polar incommensurate phase by advanced diffraction and atomic-resolution imaging techniques. The resulting topology is unraveled to be the competition between the antiferroelectric and ferroelectric states, stabilized by the modulation of the Pb 6s² lone pair and the antiferrodistortive effect. These findings further reinforce the similarity of the magnetic and electric topologies.