Size effects of topological vortex domain in BiFeO₃ nanoisland by phase-field simulations

Bismuth ferrite nanoislands offer unique advantages in ferroelectric applications due to their ability to form stable topological vortex domains, which are crucial for advanced device designs. These vortex domains, driven by topological properties, hold significant potential for enhancing non-volatile memory and energy storage applications. In this study, we systematically investigate the effects of three key geometric factors—height, length-to-height ratio, and slope—on the stability of vortex domains using phase-field simulations. Our results demonstrate that larger length-to-height ratios, higher slopes, and smaller heights promote the formation and stability of vortex domains. Conversely, negative slopes hinder vortex formation, but increasing the length-to-height ratio compensates for this effect, stabilizing switchable vortex domains. A phase diagram is constructed to illustrate the combined influence of these three parameters, identifying conditions that favor vortex stability. These findings provide valuable insights into the geometric design of ferroelectric nanoislands with tailored topological domain structures, which could significantly impact the development of next-generation ferroelectric devices and logic units based on topological vortex configurations.