Engineered periodic quadrupole superstructure in ferroelectric thin films via flexoelectricity

Domain engineering of nanoferroelectrics becomes crucial due to the miniaturization of devices. Understanding the geometric ordering of nanodomains that self-organize into superstructures helps to develop modern domain engineering techniques. Here, using the phase field simulation, we find that large flexoelectricity in thin films can contribute to exotic in-plane needle-like and quadrupole superdomains. Our results indicate that by pressing a mesh of atomic force microscope tips on the film surface, the tip-induced flexoelectric field can tune the polarization nucleation during cooling and lead the nanodomains to evolve into periodic quadrupole patterns. Our work suggests a new approach to create and manipulate desired superstructures and offers a framework of developing engineering techniques in conjunction with phase-field modeling.