  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.
