Spin transport of compensated metals in combination with Baber-type momentum relaxation

We present a theoretical framework elucidating the spin transport characteristics in combination with Baber-type momentum relaxation induced by electron-hole collisions. Our framework incorporates momentum relaxation caused by lattice imperfections and spin relaxation mediated by nonmagnetic disorder coupled to the spin-orbit interaction (SOI). The relaxation time approximation is used for solving the coupled Boltzmann equation (BE). Starting with the semiclassical BE, we systematically derive a system of coupled drift-diffusion equations for electrons and holes. Analytical solutions to these coupled drift-diffusion equations reveal the existence of two types of electron-hole coupled spin modes, which exhibit distinct spin relaxation mechanisms, each driven by either Baber scattering or the SOI. Under specific conditions, these spin modes acquire a spatially oscillatory nature, with a damping length similar to the diffusion lengths of typical metals. In particular, when Baber scattering occurs without accompanying spin relaxation in the presence of other momentum and spin relaxation processes, a spatial oscillatory characteristic without damping is predicted for the anti-total spin current mode composed of electron and hole (electron in the hole band) spin currents arranged in an antisymmetric configuration.