Symmetries govern macroscopic physical quantities, and the electronic and spin properties of crystals. Here, we demonstrate that the spin-orbit-induced spin polarization at the Brillouin zone border for noncentrosymmetric and nonsymmorphic space groups is dictated by the wave function symmetries instead of, as commonly held, the point group symmetry of a wave vector. This is confirmed and exemplified by a group-theoretical analysis and density-functional theory calculations on several space groups and realistic materials. Our results are expected to enrich the fundamental understanding of symmetry-dictated spin-orbit physics and broaden the range of spintronic materials.

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• Spin polarization
• Spin-orbit coupling
• Spintronics
• Density functional theory
• Group theory
• k dot p method