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The Pauli exclusion principle combined with interactions between fermions is a unifying basic mechanism that can give rise to quantum phases with spin order in diverse physical systems. Transition-metal ferromagnets, with isotropic ordering respecting crystallographic rotation symmetries and with a net magnetization, are a relatively common manifestation of this mechanism, leading to numerous practical applications, e.g., in spintronic information technologies. In contrast, superfluid 3He has been a unique and fragile manifestation, in which the spin-ordered phase is anisotropic, breaking the real-space rotation symmetries, and has zero net magnetization. The recently discovered altermagnets share the spin-ordered anisotropic zero-magnetization nature of superfluid $^3$He. Yet, altermagnets appear to be even more abundant than ferromagnets, can be robust, and are projected to offer superior scalability for spintronics compared to ferromagnets. Our Perspective revisits the decades of research of the spin-ordered anisotropic zero-magnetization phases including, besides superfluid $^3$He, also theoretically conceived counterparts in nematic electronic liquid-crystal phases. While all sharing the same extraordinary character of symmetry breaking, we highlight the distinctions in microscopic physics which set altermagnets apart and enable their robust and abundant material realizations.
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Altermagnetism: An unconventional spin-ordered phase of matter
The Pauli exclusion principle combined with interactions between fermions is a basic mechanism across condensed-matter systems giving rise to a spontaneous breaking of the spin-space rotation symmetry of spin-ordered phases. Ferromagnetism is a conventional manifestation of spin ordering that leads to numerous applications (e.g., in spintronic information technologies). Altermagnetism, whose recent discovery was largely motivated by spintronics, stands apart from conventional magnetism in the sense that it spontaneously breaks not only spin-space but also real-space rotation symmetries, while it preserves a symmetry combining spin-space and real-space rotations. This is realized on crystals by a collinear compensated ordering of spins with a characteristic d-, g-, or i-wave symmetry. This perspective goes beyond the theory of spin arrangements on crystals by connecting altermagnetism to basic notions in condensed matter physics. Specifically, we reflect on the analogies and distinctions of altermagnetism as compared to superfluid 3He and theories of spin ordering in the momentum space generated by other higher-partial-wave instabilities of a Fermi liquid. On one hand, all these physical systems have in common the extraordinary combination of spontaneous breaking of spin-space and real-space rotation symmetries. On the other hand, we point out that there are key differences, both at the symmetry level and, particularly, at the level of microscopic mechanisms of ordering. These explain the comparatively large abundance, robustness, and utility of altermagnetism, as predicted by the symmetry classification of spin arrangements on crystals and ab initio calculations, and supported by initial experiments.
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- Award ID(s):
- 2225920
- PAR ID:
- 10674106
- Publisher / Repository:
- Newton
- Date Published:
- Journal Name:
- Newton
- Volume:
- 1
- Issue:
- 6
- ISSN:
- 2950-6360
- Page Range / eLocation ID:
- 100162
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1016/j.newton.2025.100162
