Anomalous Hall effect induced by a pure longitudinal spin injection

Recently, a nonvanishing anomalous Hall resistivity was observed accompanying a pure spin injection into aluminum through a ferromagnetic contact [Nature 442, (2006) 176]. In this paper, we present a quantitative explanation of this experimental observation considering intrinsic spin–orbit coupling, as well as an extrinsic spin–orbit interaction induced by electron-impurity scattering. In connection with this, we evaluate the band structure and wave function of aluminum by the orthogonalized-plane-wave method and determine the contributions to anomalous Hall resistivity from side-jump and skew scatterings after numerically solving a spatially dependent Boltzmann equation. The obtained Hall resistivity is in good agreement with the experimental data.