Abstract:

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 (SOC) 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 results directly give rise to our further discovery of SOC-free topological phases, including Z2 topological classification and topological semimetals, protected by new symmetries.
References
[1] Liu et al. arXiv:2103.15723 (PRX 2022).
[2] Liu et al. arXiv:2107.09984