Quantized even number of vortices in a confined PTO/STO ferroelectric heterostructure with edge pinning effect

Polar vortices in ferroelectric heterostructures exhibit rich physical phenomena, but controlling their number and stability remains challenging. We investigate polar vortices in laterally confined lead titanate slabs embedded in a strontium titanate matrix on a dysprosium scandate substrate. Phase-field simulations and transmission electron microscopy show that lateral confinement favors discrete, even numbers of vortices. Energy analysis attributes this preference to competition among Landau, elastic, electrostatic and gradient contributions. Simulations and in situ electrical biasing observations further reveal that polar vortices near slab edges remain stable while interior regions switch under applied field, and vortex configurations recover after the applied voltage is removed. Here, we show that lateral confinement and edge pinning provide a route to controlling the number and switching behavior of polar vortices in ferroelectric heterostructures. The authors show that lateral confinement favors even numbers of polar vortices in ferroelectric heterostructures and that edge pinning stabilizes vortices during electrical switching.