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Abstract Solomon rings, upholding the symbol of wisdom with profound historical roots, were widely used as decorations in ancient architecture and clothing. However, it was only recently discovered that such topological structures can be formed by self-organization in biological/chemical molecules, liquid crystals, etc. Here, we report the observation of polar Solomon rings in a ferroelectric nanocrystal, which consist of two intertwined vortices and are mathematically equivalent to a$${4}_{1}^{2}$$ $4_1^2$link in topology. By combining piezoresponse force microscopy observations and phase-field simulations, we demonstrate the reversible switching between polar Solomon rings and vertex textures by an electric field. The two types of topological polar textures exhibit distinct absorption of terahertz infrared waves, which can be exploited in infrared displays with a nanoscale resolution. Our study establishes, both experimentally and computationally, the existence and electrical manipulation of polar Solomon rings, a new form of topological polar structures that may provide a simple way for fast, robust, and high-resolution optoelectronic devices. 

Polar metals have recently garnered increasing interest because of their promising functionalities. Here we report the experimental realization of an intrinsic coexisting ferromagnetism, polar distortion and metallicity in quasi-two-dimensional Ca3Co3O8. This material crystallizes with alternating stacking of oxygen tetrahedral CoO4 monolayers and octahedral CoO6 bilayers. The ferromagnetic metallic state is confined within the quasi-two-dimensional CoO6 layers, and the broken inversion symmetry arises simultaneously from the Co displacements. The breaking of both spatial-inversion and time-reversal symmetries, along with their strong coupling, gives rise to an intrinsic magnetochiral anisotropy with exotic magnetic field-free non-reciprocal electrical resistivity. An extraordinarily robust topological Hall effect persists over a broad temperature–magnetic field phase space, arising from dipole-induced Rashba spin–orbit coupling. Our work not only provides a rich platform to explore the coupling between polarity and magnetism in a metallic system, with extensive potential applications, but also defines a novel design strategy to access exotic correlated electronic states. 

Dielectric capacitors with ultrahigh power densities are fundamental energy storage components in electrical and electronic systems. However, a long-standing challenge is improving their energy densities. We report dielectrics with ultrahigh energy densities designed with polymorphic nanodomains. Guided by phase-field simulations, we conceived and synthesized lead-free BiFeO 3 -BaTiO 3 -SrTiO 3 solid-solution films to realize the coexistence of rhombohedral and tetragonal nanodomains embedded in a cubic matrix. We obtained minimized hysteresis while maintaining high polarization and achieved a high energy density of 112 joules per cubic centimeter with a high energy efficiency of ~80%. This approach should be generalizable for designing high-performance dielectrics and other functional materials that benefit from nanoscale domain structure manipulation.