Emergent responses of spin-nodal planes
ORAL · Invited
Abstract
When electrons couple to a magnetic order, the electronic spin splitting can be expanded for small momenta. Assuming a well-defined spin axis, the spin splitting can be categorized into even-parity (s-, d-, g-, i-wave) and odd-parity (p-, f-, h-wave) components. Depending on the symmetries of the magnetic texture, regions in momentum space with opposite spin splitting are often separated by protected spin nodal lines (in 2D) and planes (in 3D). The odd-parity case allows for a p-wave spin splitting of electronic bands without the need for a correlation-driven Pomeranchuk instability [1].
I will discuss how the recent experimental realization of a short-period spin spiral satisfies the symmetry requirements for a p-wave magnet [2]. The perturbation of the idealized p-wave order with spin-orbit coupling and non-zero magnetization leads to an enhanced anomalous Hall effect due to gapped spin nodal planes.
Although Hall effects due to spin-orbit coupling have been observed in collinear altermagnets [3] and in coplanar 120° magnetic structures [4], they are not generally expected in magnetic spirals. By general arguments, p-wave magnets are found to produce an anomalous Hall effect when the momentum dependence of spin-orbit coupling complements the magnetic splitting.
Compared to p-wave magnets, f-wave magnets have a higher symmetry, and thus linear responses are more constrained. Notably, for f-wave magnets, the anisotropic Edelstein effect known for p-wave magnets [5] is absent. Nevertheless, at certain surfaces of f-wave magnets the symmetry is sufficiently reduced and an inhomogeneous, anisotropic Edelstein effect occurs.
[1] A. Hellenes et al., arXiv:2309.01607 (2023).
[2] R. Yamada, M.M.H., et al., Nature 646, 837–842 (2025).
[3] L. Šmejkal et al., Sci. Adv. 6, eaaz8809 (2020).
[4] S. Nakatsuji et al., Nature 527, 212-215 (2015).
[5] A. Chakraborty, et al. Nat Commun 16, 7270 (2025).
I will discuss how the recent experimental realization of a short-period spin spiral satisfies the symmetry requirements for a p-wave magnet [2]. The perturbation of the idealized p-wave order with spin-orbit coupling and non-zero magnetization leads to an enhanced anomalous Hall effect due to gapped spin nodal planes.
Although Hall effects due to spin-orbit coupling have been observed in collinear altermagnets [3] and in coplanar 120° magnetic structures [4], they are not generally expected in magnetic spirals. By general arguments, p-wave magnets are found to produce an anomalous Hall effect when the momentum dependence of spin-orbit coupling complements the magnetic splitting.
Compared to p-wave magnets, f-wave magnets have a higher symmetry, and thus linear responses are more constrained. Notably, for f-wave magnets, the anisotropic Edelstein effect known for p-wave magnets [5] is absent. Nevertheless, at certain surfaces of f-wave magnets the symmetry is sufficiently reduced and an inhomogeneous, anisotropic Edelstein effect occurs.
[1] A. Hellenes et al., arXiv:2309.01607 (2023).
[2] R. Yamada, M.M.H., et al., Nature 646, 837–842 (2025).
[3] L. Šmejkal et al., Sci. Adv. 6, eaaz8809 (2020).
[4] S. Nakatsuji et al., Nature 527, 212-215 (2015).
[5] A. Chakraborty, et al. Nat Commun 16, 7270 (2025).
*M.M.H. was supported by RIKEN Special Postdoctoral Researcher Program.
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Presenters
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Moritz M Hirschmann
- RIKEN