Exchange spin-orbit coupling and unconventional p-wave magnetism

• DOI: 10.48550/arxiv.2309.01607
• Publication Date: 2023-01-01
• Authors: Anna Birk Hellenes; T. Jungwirth; Jairo Sinova; Libor Šmejkal
• Keywords: Magnetism; Spin wave; Parity (physics); T-symmetry

The electronic structure of atoms is organized into even and odd-parity-wave s, p, d, ... orbitals. An analogous classification condensed matter phases emerged with the discovery conventional s-wave superconductivity in mercury, followed by discoveries unconventional p-wave superfluidity $^{3}$He d-wave cuprates. To date, known counterparts magnetism have been ferromagnets spin polarization structure, recently discovered altermagnets[1-3] higher even-parity wave polarization[1,2,4-7]. Here we identify long-sought magnetic counterpart superfluidity[8,9] -- magnet polarization[10,11]. We show that collinear spin-polarization arises a coplanar spin-symmetry subset class noncentrosymmetric noncolinear crystals combined time-reversal lattice translation symmetry. Contrary to common assumptions[12-15], noncollinear magnets from this universally exhibit nonrelativistic splittings these odd-parity preserve symmetry band structure. predict large splitings reaching 500 meV first-principles calculations 60 realistic material candidates. Inspired rich anisotropic properties superfluid $^{3}$He[8,9] our result opens up wide range possibilities investigate order parameters their exploitation spintronics topological physics[16-21].