Different shapes of spin textures as a journey through the Brillouin zone*

Crystallographic point group symmetry (CPGS) have long been known to classify compounds that have spin-orbit-induced spin splitting. While taking a journey through the Brillouin zone (BZ) from one k-point to another for a fixed CPGS, it is expected that the wave vector point group symmetry (WPGS) can change, and consequently, a qualitative change in the spin polarization pattern (SPP) can occur. However, the nature of the SPP change is generally unsuspected. We determine a full classification of the linear-in-k SP patterns based on the polarity and chirality reflected in the WPGS. Specifically, the SP is bound to be parallel to the rotation axis and perpendicular to the mirror planes, and hence, symmetry operation types in WPGSs impose symmetry restriction to the SPP. For instance, the SPP is always parallel to the wave vector k in nonpolar chiral WPGSs since they contain only rotational symmetries. Examples of actual compounds with such prototypical spin textures verified by first principles DFT are given (Physical Review B 104, 104408 (2021)) and await experimental spin-ARPRES testing. Additionally, we use the determined relation between WPGS and SPP as a design principle to select compounds with multiple SPPs at different k valleys. Based on high-throughput calculations for 1481 compounds, we find 37 previously fabricated materials with multiple SPPs.