Alternative harmonic detection approach for quantitative determination of spin and orbital torques

Abstract

In this study, the spin–orbit torque (SOT) in light metal oxide systems is investigated using an experimental approach based on harmonic Hall voltage techniques in out-of-plane (OOP) angular geometry for samples with in-plane magnetic anisotropy. In parallel, an analytical derivation of this alternative OOP harmonic Hall detection geometry has been developed, followed by experimental validation to extract SOT effective fields. In addition to accurately quantifying SOT, this method allows complete characterization of thermoelectric effects, opening promising avenues for accurate SOT characterization in related systems. In particular, this study corroborates the critical role of naturally oxidized copper interfaced with metallic Cu in the generation of orbital current in Co(2)|Pt(4)|CuOx(3), demonstrating a twofold increase in damping-like torques compared to a reference sample with an oxidized Al capping layer. These findings offer promising directions for future research on the application aspect of nonequilibrium orbital angular momentum.