Band-Geometry-Driven Spin Photocurrent in Centrosymmetric Altermagnets

Geometric responses give rise to novel phenomena in charge and spin transport, which have been extensively studied in the context of the quantum geometry of Bloch states in periodic solids. In contrast, the geometry of Hamiltonian eigenvalues is often considered trivial. Here, we demonstrate that this seemingly trivial contribution can in fact generate a transverse spin current-reminiscent of the spin Hall effect-in the recently discovered class of centrosymmetric altermagnets. Using quantum perturbation theory, we identify two leading mechanisms under optical excitation combined with a static electric field: an effective-mass term and a group-velocity term, both rooted in the underlying band geometry and thus tied to spin splitting and band anisotropy that do not require inversion-symmetry breaking. Through a symmetry-based analysis of all centrosymmetric spin point groups, we establish how these mechanisms give rise to highly selective and switchable spin transport without accompanying charge flow. First-principles calculations on prototypical altermagnets α-MnTe and MnF_{2} confirm our predictions, revealing experimentally accessible spin conductivities under moderate external fields.