  Motivated by a recent experiment[Nature {\bf 442}, 176 (2006)], we present a
quantitative microscopic theory to investigate the inverse spin-Hall effect
with spin injection into aluminum considering both intrinsic and extrinsic
spin-orbit couplings using the orthogonalized-plane-wave method. Our
theoretical results are in good agreement with the experimental data. It is
also clear that the magnitude of the anomalous Hall resistivity is mainly due
to contributions from extrinsic skew scattering, while its spatial variation is
determined by the intrinsic spin-orbit coupling.
