Thickness-dependent evolutions of domain configuration and size in ferroelectric and ferroelectric-ferroelastic films

Non-monotonous thickness-dependent ferroelectric and ferroelectric-ferroelastic domain size scaling behaviors were revealed in ferroelectric films, including three distinct regions: (I) a classical ½ power law relationship for thick films, (II) a deviation from the ½ scaling relationship for an intermediate thickness range, and (III) an exponential increase in ultrathin films when decreasing the film thickness. The calculations indicate a much narrower region (II) in ferroelectric films with ferroelectric domains than that with ferroelectric-ferroelastic ones. As the film thickness decreases, the stable domain pattern also changes from a ferroelectric-ferroelastic domain to a ferroelectric one, which leads to the divergence of domain size scaling.