Disentanglement of Spin-Orbit Torques in Pt / Co Bilayers with the Presence of Spin Hall Effect and Rashba-Edelstein Effect

Abstract

We demonstrate a quantitative disentanglement of current-induced spin-orbit torques (SOTs) in $\mathrm{Pt}$/$\mathrm{Co}$ bilayers, where both the spin Hall effect (SHE) and the Rashba-Edelstein effect (REE) are present. The SOTs originating from the SHE in bulk $\mathrm{Pt}$ and from the REE at substrate (sub.)/$\mathrm{Pt}$ and $\mathrm{Pt}$/$\mathrm{Co}$ interfaces are successfully disentangled and quantified utilizing harmonic Hall measurements, by taking advantage of different characteristic lengths between the two effects during spin-current transport. The fieldlike (FL) torque in our samples originates from the REE, while both SHE and REE contribute to the dampinglike (DL) torque. The experimentally extracted transport characteristic lengths in bulk $\mathrm{Pt}$ (an effective spin-diffusion length) are 1.8--3.0 nm, while those at $\mathrm{Pt}$ interfaces (an effective REE thickness) are 0.2--0.6 nm. The extracted REE-induced FL torque (and DL torque) efficiencies at sub./$\mathrm{Pt}$ and $\mathrm{Pt}$/$\mathrm{Co}$ interfaces are of the same order of magnitude, but of opposite signs, which is consistent with the REE scenario. The origin of the observed temperature-dependent SOT sign reversal is clarified with our disentanglement analysis, demonstrating the significant role of the REE at both sub./$\mathrm{Pt}$ and $\mathrm{Pt}$/$\mathrm{Co}$ interfaces, in contributing to the overall SOTs, as the thickness of the heavy-metal layer is thinner than its spin-diffusion length or comparable to a REE thickness.