Symmetry formulated by group theory plays an essential role with respect to the laws of nature, from fundamental particles to condensed matter systems. In this talk, we elucidate that the crystallographic symmetries of a vast number of magnetic materials with light elements, in which the neglect of relativistic spin-orbit coupling is an appropriate approximation, are considerably larger than the conventional magnetic groups . Thus, a symmetry description that involves partially-decoupled spin and spatial rotations, dubbed as spin group, is required. We then derive the classifications of spin “point groups” describing coplanar and collinear magnetic structures, and the irreducible co-representations of spin “space groups” illustrating more energy degeneracies that are disallowed by magnetic groups. These new symmetries directly give rise to further discoveries without any relativistic origins, including spin splitting, Z2 topological classification and new quasiparticles [1,2]. Using angle-resolved photoemission spectroscopy measurements and density functional theory calculations, we demonstrate the existence of such spin splitting effect in a noncoplanar antiferromagnet MnTe2 , and the spectral evidence of chiral Dirac fermions in a collinear antiferromagnet CoNb3S6 .
 Liu et al. Phys. Rev. X 12, 021016 (2022)
 Liu et al. The Innovation 3, 100343 (2022)
 Zhu et al. arXiv:2303.04549
 Zhang et al. arXiv:2301.12201