Abstract: Altermagnets, a third class of collinear magnets, have zero net magnetization but spin-split bands, even without spin–orbit coupling. Their standard classification into six wave types (d-, g-, and i-wave in 2D and 3D) relies on magnetic point groups of mostly centrosymmetric crystals. In this talk, I will show that spinless time reversal replaces inversion, so altermagnetism extends to non-centrosymmetric crystals. We catalog the Brillouin-zone spin splitting of all 17 altermagnetic wallpaper groups and 422 altermagnetic space groups, 262 of which lack inversion, consistent with the literature. Furthermore, nonsymmorphic symmetries, such as glide mirrors and screw axes, enforce same-spin degeneracies on the zone boundary. Together with the opposite-spin degeneracies, they force hourglass band crossings, creating spin textures beyond the six wave types, such as an i-wave-like spin winding on a square lattice. Our catalog serves as a guide for finding new altermagnets.

Reference: C. Le, F. Cui, I.-F. Io, M. M. Hirschmann, X. Wu, and C.-K. Chiu, arXiv:2607.10857 (2026).