Phase coexistence and electric-field control of toroidal order in oxide superlattices

Systems that exhibit phase competition, order parameter coexistence, and emergent order parameter topologies constitute a major part of modern condensed-matter physics. Here, by applying a range of characterization techniques, and simulations, we observe that in PbTiO₃/SrTiO₃ superlattices all of these effects can be found. By exploring superlattice period-, temperature- and field-dependent evolution of these structures, we observe several new features. First, it is possible to engineer phase coexistence mediated by a first-order phase transition between an emergent, low-temperature vortex phase with electric toroidal order and a high-temperature ferroelectric a₁/a₂ phase. At room temperature, the coexisting vortex and ferroelectric phases form a mesoscale, fibre-textured hierarchical superstructure. The vortex phase possesses an axial polarization, set by the net polarization of the surrounding ferroelectric domains, such that it possesses a multi-order-parameter state and belongs to a class of gyrotropic electrotoroidal compounds. Finally, application of electric fields to this mixed-phase system permits interconversion between the vortex and the ferroelectric phases concomitant with order-of-magnitude changes in piezoelectric and nonlinear optical responses. Our findings suggest new cross-coupled functionalities.