Hidden Spin-Splitting and Multiferroicity at the Surfaces of Antiferromagnets

Achieving controllable spin and ferroic functionalities in materials with collinear-compensated magnetic order is of paramount importance for the advancement of spintronics. Here, we reveal that natural surface symmetry breaking in common antiferromagnets (AFMs) provides a pervasive platform to simultaneously unlock hidden spin-splitting and emergent multiferroicity. Through a rigorous symmetry analysis, we classify the two-dimensional surfaces of three-dimensional AFMs into three distinct types. We show that while type-I surfaces retain spin degeneracy, type-II and type-III surfaces manifest spin-splitting, realizing altermagnetic and ferrimagnetic surface states, respectively. Importantly, the breaking of inversion symmetry at AFM surfaces generically allows spontaneous surface electric polarization for all three surface types, providing an excellent platform for magnetoelectric response. Furthermore, utilizing magnetic space groups, we establish specific symmetry criteria for identifying these surface types and screen material databases to propose representative candidates. Crucially, we show that this surface spin-splitting gives rise to emergent anomalous transport phenomena, such as an anomalous Hall effect explicitly confined to the surface, despite its absence in the bulk. Our findings reveal the rich magnetic structures and hidden spin splitting, multiferroicity, and magnetoelectric coupling at AFM surfaces, providing new fundamental insights and a viable route toward antiferromagnetic spintronic devices.