Spin-Group Symmetry in Magnetic Materials with Negligible Spin-Orbit Coupling

Symmetry formulated by group theory plays an essential role with respect to the laws of nature, from fundamental particles condensed-matter systems. Here, combining symmetry analysis and model calculations, we elucidate that crystallographic groups a vast number magnetic materials light elements, in which neglect relativistic spin-orbit coupling (SOC) is appropriate approximation, are considerably larger than conventional groups. Thus, description involves partially decoupled spin spatial rotations, dubbed group, required. We derive classifications point describing coplanar collinear structures, irreducible corepresentations space illustrating more energy degeneracies disallowed One consequence new antiunitary symmetries protect SOC-free Z2 topological phases unprecedented surface-node structures. Our work not only manifests physical reality weak SOC, but also sheds on understanding all solids without SOC unified theory.Received 21 May 2021Revised 11 January 2022Accepted 18 February 2022DOI:https://doi.org/10.1103/PhysRevX.12.021016Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution this must maintain attribution author(s) published article’s title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasTopological matterPhysical SystemsTopological materialsTechniquesDensity functional calculationsGroup theoryCondensed Matter, Materials & Applied Physics