Thickness dependence of unidirectional spin-Hall magnetoresistance in metallic bilayers

A nonlinear magnetoresistance - called unidirectional spin-Hall magnetoresistance - is recently experimentally discovered in metallic bilayers consisting of a heavy metal and a ferromagnetic metal. To study the fundamental mechanism of the USMR, both ferromagnetic and heavy metallic layer thickness dependence of the USMR are presented in a Pt/Co/AlOx trilayer at room temperature. To avoid ambiguities, second harmonic Hall measurements are used for separating spin-Hall and thermal contributions to the non-linear magnetoresistance. The experimental results are fitted by using a drift-diffusion theory, with parameters extracted from an analysis of longitudinal resistivity of the Co layer within the framework of the Fuchs-Sondheimer model. A good agreement with the theory is found, demonstrating that the USMR is governed by both the spin-Hall effect in the heavy metallic layer and the metallic diffusion process in the ferromagnetic layer.