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.

表现出相竞争，阶数参数共存和紧急阶数参数拓扑的系统构成了现代凝聚态物理的主要部分。在这里，通过应用一系列表征技术和模拟，我们观察到在PbTiO ₃ / SrTiO ₃超晶格中可以发现所有这些作用。通过探索这些结构的超晶格周期，温度和场相关的演化，我们观察到了几个新特征。首先，可以工程化由共相的共存，该相共存是由带电环形序的低温涡旋相和高温铁电a ₁ / a ₂之间的一阶相变介导的阶段。在室温下，涡流和铁电相共存，形成中尺度，纤维化的分层上层建筑。涡旋相具有轴向极化，该极化由周围铁电畴的净极化确定，因此它具有多阶参数状态，属于一类回旋型电环化合物。最后，将电场施加到该混合相系统允许涡旋和铁电相之间相互转换，伴随着压电和非线性光学响应的​​量级变化。我们的发现提出了新的交叉耦合功能。