Unconventional SOC-activated Altermagnetic Spin Splitting and Half-Angle Locking of Spin Transport

Conventional altermagnetic spin splitting arises from staggered exchange and sublattice-dependent anisotropic hopping without requiring spin-orbit coupling (SOC). Here we derive a low-energy effective model showing that SOC and staggered exchange can jointly activate additional spin splitting on momentum planes where the nonrelativistic contribution vanishes. In hexagonal $α$-MnTe, this SOC-activated contribution produces d-wave spin splitting near $Γ$ with out-of-plane spin polarization. Its leading angular pattern counter-rotates by half the in-plane Néel-vector rotation angle. First-principles spin-transport calculations reveal a corresponding approximate half-angle locking between the Néel-vector orientation and the electric-field directions maximizing the signed longitudinal and transverse spin conductivities. Analytical transport calculations based on the effective model trace this locking to the same angular coupling between momentum and the Néel vector that governs the spin-splitting pattern. Our findings connect the microscopic mechanism of SOC-activated altermagnetic spin splitting to directional spin transport, providing a theoretical basis for probing Néel-vector orientation and controlling spin-current generation.