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 beta-Tungsten (W) as the HM, and the efficiencies of the two orthogonal components of the spin-orbit torque (SOT) were extracted. Two sets of Hall bar-shaped devices, differing in the aspect ratio of the voltage pickup line width 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 micro-Ohm-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.

Figures (4)

• Figure 1: Schematic diagram of (a) SOT in FM/HM bilayer and (b) HH measurement setup overlaid with an SEM image of a typical device (top view). (c) Variation of second harmonic Hall resistance $R_{xy}^{2\omega}=V_y^{2\omega}/I_0$ for two devices at $B_{ext}=0.1T$.
• Figure 2: Variation of spin–orbit torque (SOT) efficiencies with resistivity for devices in Set 1 (aspect ratio 0.26, blue spheres) and Set 2 (aspect ratio 0.71, green squares): (a) Damping-like torque efficiency $\xi_{SL}$ and (b) Field-like torque efficiency $\xi_{FL}$.
• Figure 3: (a) SL torque efficiency $\xi_{SL}$ and (b) FL torque efficiency $\xi_{FL}$ as a function of aspect ratio ($l/w$). The red curves represent the predicted $\xi_{SL/FL}$ values obtained by scaling the value at the lowest aspect ratio using the simulated current density reduction (Eq. \ref{['eq:scaled zeta']}) for each corresponding device. The blue curve in (b) represents the simulated $\xi_{SL}$ including corrections due to the Oersted field. (c) and (d) Simulated current distribution in Hall bars with aspect ratios of 0.25 and 0.75, respectively, using the GETDP solver.
• Figure 4: (a) Variation of scaled spin–orbit torque (SOT) efficiency $\xi^\prime_{SL}$ (Eq.\ref{['eq:scaled zeta']}) for Sets 1 and 2 as a function of $\rho_W$ (in log scale), showing a consistent trend across devices, except for the one with the lowest $\rho_W$. Inset: Scaled field-like (FL) torque efficiency $\xi^\prime_{FL}$ normalized by the thickness of the FM layer. (b) Fit of the magnitude of $\xi^\prime_{SL}$ versus $\rho_W$ using Eq. \ref{['eq:zetaSlvsthetaSH']}, excluding the device with the lowest $\rho_W$.