A variety of topological polar configurations have been created in complex oxides by precisely mediating the electrical and mechanical boundary conditions1, 2, 3. For example, vertices (meeting points of two or more domain walls)4, 5, 6, vortices (require a non-zero polarization curl)7, polar skyrmions8 and polar merons9 have been synthesized in (PbTiO3)n/(SrTiO3)n superlattices or directly written in ferroelectrics by scanning probe techniques. These topological structures host unique properties which allow the development of novel electronics including negative capacitance field-effect transistors10, 11 and high-density non-volatile memories12.

Practical applications of topological structures require the ability to manipulate them by using external stimuli and comprehensive understanding of their dynamic properties13, 14, 15. To date, extensive theoretical and experimental studies have been carried out to explore the evolution of topological structures under electric and mechanical fields16, 17, 18, 19. For example, in PbTiO3/SrTiO3 superlattices, reversible phase transition between flux-closure arrays and trivial ferroelectric phase driven by either electrical or mechanical fields have been observed20. In such a similar system, vortex arrays switch to out-of-plane and in-plane polarization by electric fields and mechanical loading, respectively21, 22. However, in these studies, these topological structures in the oxide superlattice always appear as arrays and thus the switching of them exhibits a collective behavior, usually involving multiple topological structures. For instance, one clockwise vortex is always sandwiched between two anticlockwised ones in a PbTiO3 layer7, and similar for flux-closure domains6. Under external fields, they usually emerge and disappear simultaneously20, 21, 22. Therefore, the dynamic property of isolated topological polar structures under external stimuli is little known and the ability to control individual topological polar structures which is critical for practical applications, e.g., data storage, for which one-by-one writing and erasing is required, is still challenging.

In this work, we choose the three-fold vertex as a model system to study dynamic properties of isolated topological polar structures. Three-fold vertices are intersections of a 180° domain wall and two 90° domain walls in ferroelectrics5, 23 (Supplementary Fig. 1). They consist of smoothly rotated dipoles at the meeting point of domain walls, thus are considered as a type of topological polar structures2, 23. The winding number which is employed to characterize topological structures24, 25, is calculated to be \(+\frac{1}{2}\) for three-fold vertices (Supplementary Fig. 1). Although three-fold vertices have been observed before4, 5, 6, the dynamic behavior of isolated ones under electric fields has never been reported. The observation of isolated three-fold vertices at ferroelectric films4 suggests the possibility to explore dynamic properties of isolated ones while the other topological polar structures such as vortices and polar skyrmions usually appear as arrays in (PbTiO3)n/(SrTiO3)n superlattices7, 8. However, the main challenge is that three-fold vertices are usually generated on insulating substrates, for which the polarization charge at the interface is not completely screened26. Therefore, it is difficult to apply an electric field to study the dynamic behavior of three-fold vertices due to the lack of the bottom electrode.

Here, we demonstrate the controlled formation and motion of isolated three-fold vertices in a PbTiO3 thin film on DyScO3 with a SrRuO3 buffer layer by an applied electric field. We elaborately use the atomic-thin diffusion layer SrTiO3 to induce incomplete screening while remain the SrRuO3 as the bottom electrode to achieve the application of external electric field. Under electric fields, 180° domain walls expanding to the interface, leading to the formation of isolated three-fold vertices. We directly observe a long-range motion of isolated three-fold vertices along the interface in a controllable and reversible manner. Phase-field simulations verify the role of SrTiO3 layer and reveal microstructural evolution details of the nucleation and propagation of isolated three-fold vertices. These results elucidate the high mobility of isolated three-fold vertices and suggest extraordinary dynamic properties of isolated topological polar structures which may enable new applications.