Emergent Surface Altermagnetism.

Research on altermagnetism has thus far primarily focused on spin-polarized bulk electronic states in magnetic materials. In this work, we advance the field by introducing the concept of surface altermagnetism (SAM), wherein altermagnetic spin polarization emerges at the surfaces of collinear antiferromagnets (AFMs) or altermagnets (AMs). To lay the theoretical groundwork for this phenomenon, we construct a thorough symmetry-based framework that systematically connects bulk spin groups to surface spin groups for both types of systems. Through symmetry analysis, we identify all symmetry-breaking surfaces capable of supporting SAM, identifying 35 for PT-symmetric AFMs and 61 distinct cases for bulk AMs. Moreover, we show that 203 collinear spin space groups-including 100 without and 103 with the [C_{2}∥P] operation-permit the appearance of SAM on the surface of tT-symmetric AFMs via the breaking of fractional translational symmetries. The proposed framework is verified using tight-binding models and first-principles calculations, with practical material implementations shown in representative compounds like NaMnP, LiMnAs, and CrSb. Our results establish SAM as a robust, symmetry-protected magnetic state, extending altermagnetic phenomena to material surfaces and paving the way for advanced, field-free spin manipulation in next-generation spintronic technologies.