Fig. 2

Spin transport and SOT measurements in the W/TmIG bilayers. a Experimental setup for measuring resistance, SOT, and current-induced magnetization switching. b Hall resistance as a function of an out-of-plane magnetic field for the W (5 nm)/TmIG (9.6 nm), where AHE is observed as the sharp square hysteresis loop. c Hall resistance as a function of a rotating in-plane constant magnetic field (5 kOe) for the W (5 nm)/TmIG (9.6 nm), where SMR-induced PHE is observed. d Second-harmonic Hall resistance as a function of in-plane azimuthal angle for the external magnetic field 2500 Oe for the W (5 nm)/TmIG (3.2 nm), where the black curve is the fit to Eq. (1). Both cos 2φsin φ (blue curve) and sin φ (red curve) angle dependencies are revealed. e Extracted damping-like torque contribution as a function of the inverse of external magnetic field subtracting the anisotropy field. The large intercepts are the spin Seebeck resistance. f Damping-like spin-orbit torque efficiency as a function of TmIG thickness. The error bar stands for the fitting uncertainty