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Using a combination of experimental and computational techniques, changes in the domain structures seen in freestanding single-crystal platelets of BaTiO${}_{3}$ have been described in terms of a second-order phase transition. The transition is driven by the change in the length-to-width ratio of the platelet sidewalls and results in a symmetry breaking of a complex, quadrant domain pattern. The phenomenon can be described by a Landau formalism in which (1) the order parameter is not the polarization but rather is the degree to which the domain pattern becomes off-centered, and (2) the shape anisotropy of the platelet substitutes for temperature in the conventional Landau expansion as the controlling thermodynamic variable. Bistability, in terms of the direction in which the domain pattern moves off center, coupled with the spontaneous macroscopic polarization and toroidal moment that result from this off-centering, prompt the possibility of a new form of memory storage.

Shape-induced phase transition of domain patterns in ferroelectric platelets