Strain manipulation of ferroelectric skyrmion bubbles in a freestanding PbTiO3 film: A phase field simulation

So far nanoscale topological polar structures have been mainly observed in ferroelectric superlattices, nanodots, and complex heterostructures, originating from the intricate interplay of built-in electric field, polarization, strain, and their gradient-related energies. However, solid substrates hinder the continuous strain manipulation of the ferroelectric topological textures. Recently, a breakthrough in fabricating freestanding films has demonstrated the possibility of continuous strain manipulation, but there has been little experimental or theoretical investigation of whether polar topological structures exist in freestanding films. Herein, by performing phase field simulation on ${(\mathrm{PbTi}{\mathrm{O}}_{3})}_{20}/{(\mathrm{SrTi}{\mathrm{O}}_{3})}_{10}$ freestanding bilayers, we observed the stabilized ferroelectric skyrmion bubbles in a ferroelectric layer. A thickness-dependent phase diagram indicates that the skyrmion bubbles exist when the ferroelectric layer is between eight and 30 unit cells. Meanwhile, we demonstrated that the uniaxial strain is an effective way to manipulate the skyrmion bubble in freestanding films, which not only induces consolidation and rearrangement of skyrmion bubbles, but also induces a phase transition from the topological skyrmion bubble state to a standard ${a}_{1}/{a}_{2}$ domain state. These results provide us guidance with a mechanical approach to control topological polar structures in freestanding films.