Relativistic Spin-Momentum Locking in Altermagnets

Spin–momentum locking in altermagnets has been deeply explored in the nonrelativistic limit. Including spin–orbit coupling, altermagnets exhibit antisymmetric exchange interactions, leading to spin cantings. Therefore, the spin-momentum locking differs among the three spin components, S x, S y, and S z, forming the relativistic spin-momentum locking. We considered orthorhombic YVO 3 and hexagonal MnTe. For YVO 3, the relativistic locking comprises s-, d xy -, and d xz -wave. In MnTe, the dominant component S y of MnTe inherits the polarized charge distribution and the nonrelativistic spin-momentum locking bulk g-wave, but the breaking of the C 6 z rotational symmetry by the Néel vector lowers the symmetry from g-wave to d-wave. The relativistic spin-momentum locking for MnTe is composed of d xz -, d yz - and s-wave. Despite small magnitudes in real space, the canted spin components contribute significant spectral weight in k-space, impacting k-space properties, such as the spin-Hall conductivity and spin photocurrents.