Decoupling of spin–orbit torque components in Py/W bilayers unveiled through variation of W-resistivity

Abstract

Harmonic Hall measurements were performed on a series of ferromagnetic metal/heavy metal (FM/HM) bilayers consisting of Permalloy (Py) as the FM and β-tungsten (W) as the HM, and the efficiencies of the two orthogonal components of the spin–orbit torque were extracted. Two sets of Hall bar-shaped devices, differing in the aspect ratio of the voltage pickup linewidth and the current channel width, were studied. Within each set, the resistivity of the W layer was systematically varied over a wide range (approximately 150–1000 μΩ cm). To account for geometry-induced variations in current distribution, numerical simulations were performed, and a correction protocol was developed to normalize the torque efficiencies obtained from the conventional analysis. After applying the correction, the Slonczewski-like (anti-damping, in-plane) torque efficiency exhibited a consistent dependence on W-resistivity across both device sets. In contrast, the field-like (out-of-plane) torque efficiency remained largely independent of W-resistivity, reinforcing its interfacial character.