Topological band degeneracies from spin-space symmetries*

Crystalline symmetries have always played a crucial role in the classification of solids, culminating in the 1651 magnetic space groups, which capture spatial symmetries as well as time reversal. Yet, once we need to describe an electron spin, the well-known extension to double groups introduces an easily overlooked assumption: Spin and spatial actions are tightly coupled and of the same order, e.g., a fourfold spatial rotation is only combined with a fourfold spin rotation. We find magnetic textures, for which such a description is generally insufficient, instead spin-space groups are needed [1,2].

To clarify the band topological implications of such spin-space symmetries in electronic systems, we discuss enforced nodal surfaces and how they evolve with spin-orbit coupling. Further, we identify emergent spin-symmetries of spin-orbit coupled nonmagnetic phases, which pin Weyl points even when time-reversal symmetry is broken.

[1] Brinkman, W. F., et al. (1966),

[2] Corticelli, A., et al. (2022)