Phases manifesting topological patterns in functional systems, like ferroelectric and ferromagnetic vortex superlattices, can manifest intricate and apparently ungovernable behavior, typical of frustrated nonergodic states with high-dimensional energy landscapes. This is also the case for potassium-tantalate-niobate (KTN) crystals. These transparent ferroelectrics manifest remarkable but little understood metastable domain patterns at optical (micrometer and above) scales near the cubic-to-tetragonal structural phase transition. Here, we formulate the topological breakdown model based on the competition between intrinsic scales of domain-domain collinear and noncollinear interactions associated with polarization-charge screening. The model is able to explain observed KTN mesoscopic domain patterns and phase diagram as a function of temperature and external electric field. Findings include a precise set of sharp and broad percolative transitions that are experimentally verified, validating our model. Our study identifies the central role played by competing topologically protected states, identifying a fundamental link between topological protection and frustration that supports a hitherto unexplored functional nonergodic arena.
Falsi et al. (2025) studied this question.