Magnetoresistance generated from charge-spin conversion by anomalous Hall effect in metallic ferromagnetic/nonmagnetic bilayers

摘要

A theoretical formulation of magnetoresistance effect in a metallicferromagnetic/nonmagnetic bilayer originated from the charge-spin conversion bythe anomalous Hall effect is presented. Analytical expressions of thelongitudinal and transverse resistivities in both nonmagnet and ferromagnet areobtained by solving the spin diffusion equation. The magnetoresistancegenerated from charge-spin conversion purely caused by the anomalous Halleffect in the ferromagnet is found to be proportional to the square of the spinpolarizations in the ferromagnet and has fixed sign. We also find additionalmagnetoresistances in both nonmagnet and ferromagnet arising from the mixing ofthe spin Hall and anomalous Hall effects. The sign of this mixing resistancedepends on those of the spin Hall angle in the nonmagnet and the spinpolarizations of the ferromagnet.