Ferroelectric Topological Defects in Hexagonal Manganites

Hexagonal rare-earth manganites, as prototypical improper ferroelectrics in which structural distortions give rise to ferroelectricity, exhibit unique physical phenomena that are absent in conventional proper ferroelectrics. Owing to their Z₂ × Z₃ topologically protected ferroelectric domain structure, characterized by the convergence of six domains at vortex core, hexagonal manganites can host charged domain walls exhibiting multiple distinct conductive states and unconventional physical effects such as the half-wave rectification effect within a single bulk single crystal, opening up promising avenues for the practical applications. Moreover, as an excellent experimental platform for verifying the Kibble-Zurek mechanism, hexagonal manganites not only possess a broad application potential but also embody rich and fundamental physical insights. Given a series of recent advances in this field, it is essential to systematically summarize and discuss the key findings, current progress, and future research perspectives concerning the hexagonal manganite system. In this review, the origin of ferroelectricity in hexagonal manganites are first clarified, followed by a discussion of the formation and transformation mechanisms of unique ferroelectric domain structures, as well as the intrinsic mechanical properties. Subsequently, the manipulation of topological defects are compared, including electric fields, thermal treatment, oxygen vacancies, and stress-strain fields. Building upon these discussions, the distinct physical effects observed in hexagonal manganites are comprehensively summarized, such as domain wall conductance, dielectric and ferroelectric properties, and thermal conductivity. Finally, based on a detailed summary of the major achievements, the unresolved issues that warrant further investigation are highlighted, thereby offering guidance for future research directions and providing valuable insights for the broader study of ferroelectric materials.