Introduction to Spin Groups and Altermagnetism

Altermagnets exhibit d-, g-, or i-wave spin order that is collinear, compensated, and breaks time-reversal symmetry in electronic structure [1–3]. In the first part of this overview talk, we will discuss how the prediction of an unusual anomalous Hall effect and an unusual electronic structure [2] motivated the spin-symmetry delimitation of altermagnets [1].

We will then introduce spin-group theory [1,2,4–7], which describes nonrelativistic exchange fields in magnetic solids (i.e., magnetic systems without spin–orbit coupling). Beyond identifying the altermagnetic class, spin-group theory also predicts a distinct family of compensated spin-polarized magnets—the antialtermagnets—characterized by odd-parity (p-, f-, or h-wave) spin order [4]. Antialtermagnets display an alternating spin polarization similar to that of altermagnets, yet preserve time-reversal symmetry in a manner analogous to antiferromagnets [4]. We will conclude this first part with a summary of photoemission detection of both nonrelativistic and relativistic altermagnetic spin splitting and spin polarization in MnTe [3].

In the second part of the talk, we will explore emerging research directions inspired by insights from spin-group theory, including topological and two-dimensional altermagnets [2,6], altermagnetic multiferroics and altermagnetoelectric effect [7], and altermagnetic spin currents and current- induced spin-polarisation phenomena [8].

[1] PRX 12, 031042 (2022),

[2] Science Adv. 6, 23 (2020), PNAS 118 42 (2021)

[3] Nature 626, 517 (2024), arXiv:2511.01690 (2025)

[4] arXiv:2309.01607v3 (2024), Nature Commun. 16 (1), 7270 (2025)

[5] arXiv:2506.22860, Nature in press, Newton 1, 6, 100162 (2025)

[6] arXiv:2309.02355 (2023), Phys. Rev. B 111, 085147 (2025).

[7] arXiv:2411.19928 (2024).

[8] PRX 12, 011028 (2022), arXiv:2503.12203 (2025), arXiv:2508.09748, under review in Nature Phys. (2025)