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After briefly reviewing phenomenological theories, which have led to the prediction of anomalous Hall effect (AHE) in unconventional antiferromagnets, I will turn to the microscopic origin of these phenomena. Тhe key factor is the form of relativistic spin-orbit (SO) interaction in centrosymmetric lattices. The SO interaction in the bonds surrounding each magnetic site has components with the same sign as well as sign-alternating components. While the former are responsible for the weak spin ferromagnetism, the latter give rise to AHE. The SO interaction in the centrosymmetric lattice behaves as an antiferromagnetic object and changes its sign when moving from one magnetic sublattice to another. Thus, the SO interaction collaborates with the Nеel field: both obey the {S|t} symmetry, which combines the 180-degrees rotation of spins with the lattice shift t connecting antiferromagnetic sublattices. This {S|t} symmetry has dramatic consequences: (i) It preserves the spin degeneracy of the bands; (ii) Nevertheless, the time-reversal symmetry is broken, resulting in finite AHE; and (iii) The {S|t} symmetry allows us to use the generalized Bloch theorem and describe the unconventional antiferromagnet as a ferromagnet with one magnetic site per cell. This naturally explains the emergence of AHE in centrosymmetric antiferromagnets.

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Keyword: antiferromagnetism, time-reversal symmetry, anomalous Hall effect, orbital magnetization, weak ferromagnetism, altermagnetism

Conference: The 17th TOYOTA RIKEN International Workshop Ruthenates and Emerging Quantum Materials (REQM2025) (2025-12-02 - 2025-12-06)

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Manuscript type: Not a journal article

MDR DOI: https://doi.org/10.48505/nims.6046

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Updated at: 2025-12-22 11:37:04 +0900

Published on MDR: 2025-12-22 16:22:07 +0900