Fig. 3: Electric-field-driven topological phase transition between polar Solomon rings and vertex structures in BiFeO3 nanocrystals.

a, b OOP (a) and IP (b) PFM phase images for the domain pattern in BiFeO3 nanocrystal when the electric fields of 0 V, −4 V, 2 V, 3 V, and −2 V are applied to the scanning probe, respectively. c Phase-field simulations for the domain evolution in BiFeO3 nanocrystal when exposed to different poling voltages. d The corresponding line profile for the OOP polarization projection along the dashed circular loop in c.