Odd-parity-wave magnetism

The discovery of altermagnets was enabled by an unorthodox symmetry framework—crystallographic spin groups—allowing for the systematic classification of all collinear spontaneous exchange symmetry breakings [1,2]. This raises a question of whether more magnets with so far unknown symmetries and electronic structures can be realised.

In our talk, we first revisit the decades-long debate over whether odd-parity p-wave magnetic orders exist [3]. We resolve this debate using the spin group formalism [4,3]. We demonstrate that odd-parity-wave orders emerge in noncentrosymmetric, noncollinear magnets with a combined translation and time-reversal symmetry. Within these systems, we identify distinct subclasses, including: collinear (coplanar) order in the momentum-space electronic band structure in systems with coplanar (noncoplanar) real space order of the crystal, and p- and f-wave orders with one and three symmetry-enforced spin-unpolarized nodal surfaces [4,5]. We then show how p-wave magnets can host giant transport anisotropy [4] and Edelstein [6] effects of non-relativistic origin.

Contrary to common assumptions, we show that odd-parity-wave magnets can exhibit non-relativistic spin-split electronic band structures while preserving time-reversal symmetry—unlike ferromagnets and altermagnets, which break it. Our first-principles calculations and symmetry analysis predict large non-relativistic spin splittings of several hundred meV and over 70 realistic material candidates.

Our work opens a broad range of opportunities for exploring odd-parity-wave magnetism, with potential applications in spintronics and topological physics.

[1]: PRX 12, 031042 (2022); arXiv:2105.05820

[2]: PRX 12, 040501 (2022); arXiv:2204.10844

[3]: Newton 1, 6, 100162 (2025); arXiv:2411.00717. This review (perspective) contains a comprehensive list of original works.

[4]: arXiv:2309.01607

[5]: ABH, Priessnitz, Mitscherling, Sinova, Jungwirth & Šmejkal (in prep.)

[6]: Nat. Commun. 16, 7270 (2025); arXiv:2411.16378