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_<i>x</i>, S_<i>y</i>, and S_<i>z</i>, forming the relativistic spin-momentum locking. We considered orthorhombic YVO₃ and hexagonal MnTe. For YVO₃, the relativistic locking comprises s-, d_<i>xy</i>-, and d_<i>xz</i>-wave. In MnTe, the dominant component S_<i>y</i> of MnTe inherits the polarized charge distribution and the nonrelativistic spin-momentum locking bulk g-wave, but the breaking of the <i>C</i>_6<i>z</i> 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_<i>xz</i>-, d_<i>yz</i>- 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.