Band splitting in the altermagnet CrSb
Phys. Rev. B 114, 065130 – Published 23 July, 2026
DOI: https://doi.org/10.1103/mytl-kml2
Abstract
Altermagnets are a class of metallic magnets characterized by spin-split electron bands. As antiferromagnets they lack spontaneous bulk magnetization. The initial description of the momentum-dependent spin splitting of electron bands in altermagnets was based on the spin-group approach, which is valid when relativistic interactions are neglected. Then, spin-orbit coupling has been taken into account in accordance with time-reversal-odd, even-parity irreducible representations of centrosymmetric point groups considered by Fernandes et al. [Phys. Rev. B 109, 024404 (2024)]. Here, we show the inadequacy of this formal approach. The problem of electron band splitting should be discussed based on the crystal symmetry of a concrete altermagnet material. The band spin splitting in the hexagonal altermagnet CrSb is established using the magnetic group formalism that allows the discovery of the additional spin splitting missed in the frame of the exchange approximation. Another type of spin splitting takes place in so-called hidden altermagnets. These types of materials do not possess symmetry with respect to space and time inversion but are symmetric with respect to the product of these operations known as toroidal symmetry. Real-space spin splitting in materials with toroidal symmetry is demonstrated.
