Spontaneous Vortex Nanodomain Arrays at Ferroelectric Heterointerfaces

The polarization of BiFeO$_{3}$ subjected to different electrical boundary conditions by hetero-interfaces is imaged with atomic resolution using a Cs-corrected transmission electron microscope. Unusual nanodomains are seen and their role in providing polarization closure is understood through phase-field simulations. Hetero-interfaces are key to the performance of ferroelectric devices and this first observation of vortex arrays at ferroelectric hetero-interfaces reveals properties unlike the surrounding film including mixed Ising-N\'{e}el domain walls, which will affect switching behavior, and a drastic increase of in-plane polarization. Imaging this magnetic analogous effect at ferroelectric hetero-interfaces provides the ability to see device-relevant interface issues.