PT - JOURNAL ARTICLE
AU - Watanabe, Haruki
AU - Po, Hoi Chun
AU - Vishwanath, Ashvin
TI - Structure and topology of band structures in the 1651 magnetic space groups
AID - 10.1126/sciadv.aat8685
DP - 2018 Aug 01
TA - Science Advances
PG - eaat8685
VI - 4
IP - 8
4099 - http://advances.sciencemag.org/content/4/8/eaat8685.short
4100 - http://advances.sciencemag.org/content/4/8/eaat8685.full
SO - Sci Adv2018 Aug 01; 4
AB - The properties of electrons in magnetically ordered crystals are of interest both from the viewpoint of realizing novel topological phases, such as magnetic Weyl semimetals, and from the application perspective of creating energy-efficient memories. A systematic study of symmetry and topology in magnetic materials has been challenging given that there are 1651 magnetic space groups (MSGs). By using an efficient representation of allowed band structures, we obtain a systematic description of several basic properties of free electrons in all MSGs in three dimensions, as well as in the 528 magnetic layer groups relevant to two-dimensional magnetic materials. We compute constraints on electron fillings and band connectivity compatible with insulating behavior. In addition, by contrasting with atomic insulators, we identify band topology entailed by the symmetry transformation of bands, as determined by the MSG alone. We provide an application of our results to identifying topological semimetals arising in periodic arrangements of hedgehog-like magnetic textures.