Direct spin accumulation quantification in ferromagnetic heterostructures using DC bias harmonic Hall measurement

Abstract

A technique for spin accumulation quantification, specifically in the ferromagnetic layer of spin-orbit torque inducing heterostructures has been elusive. Here, we demonstrate an easy-to-implement technique to achieve this quantification by applying an additional DC bias during the harmonic Hall measurement in Si/${\mathrm{SiO}}_{2}$/Ta/Co/Pt. The spin accumulation arising from the DC bias generates an amplitude offset detectable in the first harmonic Hall magnetoresistance. By performing the first harmonic Hall magnetoresistance measurement under a fixed DC bias for two oppositely magnetized states, spin accumulation polarity set by the DC bias enhances the magnetoresistance if it aligns with the magnetization, and vice versa. Thus, the difference in the magnetoresistance amplitude provides the quantitative magnitude of spin accumulation relative to the ferromagnet's saturation magnetization, measured to be up to 0.29% in Si/${\mathrm{SiO}}_{2}$/Ta/Co/Pt. The strength of both spin accumulation and dampinglike efficiency increased with Ta thickness, further verifying our experimental technique.