Domain evolution in bended freestanding BaTiO3 ultrathin films: a phase-field simulation

Perovskite ferroelectric oxides are usually considered to be brittle materials, however, recent work [Dong et al., Science 366, 475 (2019)] demonstrated the super-elasticity in the freestanding BaTiO3 thin films. This property may originate from the ferroelectric domain evolution during the bending, which is difficult to observe in experiments. Therefore, understanding the relation among the bending deformation, thickness of the films, and the domain dynamics is critical for their potential applications in flexible ferroelectric devices. Here, we reported the dynamics of ferroelectric polarization in the freestanding BaTiO3 ultrathin films in the presence of large bending deformation up to 40{\deg} using phase-field simulation. The ferroelectric domain evolution reveals the transition from the flux-closure to a/c domains with "vortex-like" structures, which caused by the increase of out-of-plane ferroelectric polarization. Additionally, by varying the film thickness in the identical bending situation, we found the a/c phase with "vortex-like" structure emerges only as the film thickness reached 12 nm or higher. Results from our investigations provide instructive information for the microstructure evolution of bending ferroelectric perovskite oxide films, which could serve as guide for the future application of ferroelectric films on flexible electronic devices.