Altermagnetism: An unconventional spin-ordered phase of matter
T. Jungwirth, Rafael M. Fernandes, Eduardo Fradkin, A. H. MacDonald, Jairo Sinova, Libor Šmejkal
Abstract
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. Altermagnetism stands apart from conventional magnetism because it 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. In this perspective, we connect altermagnetism to basic notions in condensed matter physics. Specifically, we reflect on the analogies and distinctions of altermagnetism as compared to superfluid 3 He and theories of spin ordering in the momentum space generated by other higher-partial-wave instabilities of a Fermi liquid. While these physical systems have in common the combination of spontaneous breaking of spin-space and real-space rotation symmetries, there are key differences both at the symmetry level and 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.