Toroid, altermagnetic, and noncentrosymmetric ordering in metals

V.P. Mineev^†
Landau Institute for Theoretical Physics, Russian Academy of Sciences, prosp. Akademika Semenova 1A, Chernogolovka, Moscow Region, 142432, Russian Federation

This article is dedicated to the 60th anniversary of the Landau Institute for Theoretical Physics and presents a review of normal and superconducting properties of toroidal, altermagnetic, and noncentrosymmetric metals. Metals with toroidal order are compounds not possessing symmetry in respect of space and time inversion but are symmetric in respect of the product of these operations. An electric current propagating through samples of such a material causes its magnetization. Superconducting states in toroidal metals are a mixture of singlet and triplet states. Superconductivity is gapless even in ideal crystals without impurities. Altermagnets are antiferro- magnetic metals that have a specific spin splitting of electron bands determined by time inversion in combinations with rotations and reflections of a crystal lattice. Similar splitting takes place in metals whose symmetry does not have a spatial inversion operation. Both of these types of materials have an anomalous Hall effect. A current propagating through a noncentrosymmetric metal causes magnetiza- tion, but this is not the case in altermagnets. On the other hand, in altermagnets, there is a specific piezomagnetic Hall effect. Superconducting pairing in noncentrosymmetric metals occurs between electrons occupying states in one zone, whereas, in alter- magnets, we are dealing with interband pairing, which is unfavorable for the formation of a superconducting state.

Typically, an English full text is available in about 1 month from the date of publication of the original article.

Keywords: magnetism, superconductivity, strongly correlated electronic systems
PACS: 71.27.+a, 74.20.−z, 75.85.+t (all)
DOI: 10.3367/UFNe.2025.06.039944
URL: https://ufn.ru/en/articles/2025/11/f/
Citation: Mineev V P "Toroid, altermagnetic, and noncentrosymmetric ordering in metals" Phys. Usp. 68 (11) (2025)

Received: 27th, March 2025, accepted: 8th, June 2025

Оригинал: Минеев В П «Тороидальный, альтермагнитный и нецентросимметричный порядок в металлах» УФН 195 1221–1231 (2025); DOI: 10.3367/UFNr.2025.06.039944

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