Symmetry Classification of Non-Relativistic Hidden Spin Polarization in Noncollinear Magnets

Hidden spin polarization (HSP), in which spin-polarized states exist locally while the total spin polarization are hidden in momentum space, has been extensively studied in nonmagnetic and collinear magnetic systems, but remains largely unexplored in noncollinear magnets. Here we establish a unified symmetry framework for HSP in noncollinear magnetic materials based on spin-group theory. We show that spin symmetries systematically constrain nonrelativistic spin polarization, giving rise to four distinct split spin-texture (SST) types for each local sector, denoted as SST-1, SST-2, SST-3, and SST-4. Based on these splitting forms, together with the dimensionality of the associated local spin textures and the symmetry relations between different local sectors, we further classify HSP into three categories: HSP-1, HSP-2, and HSP-3. We illustrate these categories using tight-binding models and representative material examples, including SrFe$_2$Se$_2$O, USb, Sr$_2$Mn$_3$Sb$_2$O$_2$, PrFeAsO, and GdMn$_2$Si$_2$. A survey of the MAGNDATA database further identifies 133, 7, and 139 candidate noncollinear magnetic materials hosting HSP-1, HSP-2, and HSP-3, respectively. In addition, our symmetry analysis and first-principles calculation show that many of these materials can exhibit nonzero spin-related response tensors. These results establish a general framework for understanding HSP in noncollinear magnets and highlight their potential for spin-dependent functionalities.