Utilizing mechanical loads and flexoelectricity to induce and control complicated evolution of domain patterns in ferroelectric nanofilms

We have conducted a systematical investigation to reveal the stability and evolution path of various ferroelectric domain patterns in nanofilms subjected to mechanical loads and related flexoelectric field. Within a rigorous framework of flexoelectricity, a phase-field approach has been established for simulating the domain structure of ferroelectric nanofilms. The electromechanical fields of the nanofilms are numerically solved by a fast Fourier transform technique (FFT) based on the combination of Khachaturyan's microscopic elastic theory and Stroh's formalism of anisotropic elasticity. Using this approach, we simulate eight types of domain patterns that can be stabilized in the nanofilms. It is further demonstrated that these domain patterns can be significantly affected by the mechanical loads and related flexoelectric field and exhibit fruitful evolution paths. To adapt the applied mechanical strain and strain gradient, the domain pattern may remain stable, evolve into another polydomain pattern, or become a monodomain state (an effect of domain erasing). The domain fraction, detailed domain morphology, average stresses in the nanofilms, average polarization and temporal evolution characteristics of the domain patterns under various mechanical loads and sources of flexoelectric field have been analyzed. This investigation should provide instructive information for the practical application of ferroelectric nanofilms under complex and changeable mechanical conditions.