Switching the curl of polarization vectors by an irrotational electric field

Ferroelectric vortex domains are of significant interest due to their rich physics and potential applications. Here, we propose the crystallographic, strain, and electric conditions for spontaneous vortex domains and study the influence of oxygen octahedral tilt on vortex wall orientations. Using 109\ifmmode^\circ\else\textdegree\fi{} domain walls in $\mathrm{BiFe}{\mathrm{O}}_{3}$ films as an example, it is demonstrated that vortex domains result from bound charge-density waves, i.e., from alternating positive and negative bound charges. The vortex domains lead to a net curl of the polarization vectors that can be switched by an irrotational electric field.