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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. 

Thin-film ferroelectrics have been pursued for capacitive and nonvolatile memory devices. They rely on polarizations that are oriented in an out-of-plane direction to facilitate integration and addressability with complementary metal-oxide semiconductor architectures. The internal depolarization field, however, formed by surface charges can suppress the out-of-plane polarization in ultrathin ferroelectric films that could otherwise exhibit lower coercive fields and operate with lower power. Here, we unveil stabilization of a polar longitudinal optical (LO) mode in the n=2 Ruddlesden–Popper family that produces out-of-plane ferroelectricity, persists under open-circuit boundary conditions, and is distinct from hyperferroelectricity. Our first-principles calculations show the stabilization of the LO mode is ubiquitous in chalcogenides and halides and relies on anharmonic trilinear mode coupling. We further show that the out-of-plane ferroelectricity can be predicted with a crystallographic tolerance factor, and we use these insights to design a room-temperature multiferroic with strong magnetoelectric coupling suitable for magneto-electric spin-orbit transistors.