Orbital relaxation length from first-principles scattering calculations

The orbital Hall effect generates a current of orbital angular momentum perpendicular to a charge current. Experiments suggest that this orbital current decays on a long length scale that is of the order of the spin-flip diffusion length or longer. We examine this suggestion using first-principles quantum mechanical scattering calculations to study the decay of orbital currents injected from an orbitally polarized lead into thermally disordered bulk systems of selected transition metals. We find that the decay occurs over only a few atomic layers. On this length scale the orbital current may be converted into a spin current if the spin Hall angle is sufficiently large, as for Pt. In Cu, Cr, and V with small spin Hall angles, the conversion into a spin current is negligible in the bulk and significant conversion only occurs at interfaces.