Unconventional angular dependence of spin-orbit torque-induced harmonic Hall resistance in Pt/YIG bilayers

Spin orbit torque (SOT), arising from spin-orbit coupling-induced spin currents, provides efficient control of the magnetization direction. SOT characterization that involves analyzing the first and second harmonic Hall resistances are typically done in a low-current regime, distinct from a high-current regime, where SOT-induced magnetization switching occurs. In this study, we investigate the azimuthal angle ( ϕ )-dependent harmonic Hall resistances of a Pt/yttrium iron garnet (YIG) layer across a wide range of measurement currents. Under low-current conditions, conventional ϕ-dependent Hall resistances are observed; the first harmonic Hall resistance exhibits sin⁡2 ϕ behavior and the second harmonic Hall resistance comprises cos⁡ ϕ and cos⁡3 ϕ terms, associated with damping-like and field-like SOT, respectively. Interestingly, with an increase in the current, higher-order angular-dependent terms become non-negligible, referring to the sin⁡4 ϕ and sin⁡6 ϕ terms for the first harmonic and the cos⁡5 ϕ and cos⁡7 ϕ terms for the second harmonic Hall resistances. We attribute this unconventional angular dependence to the nonlinear current dependence of SOT, emphasizing its relevance to understand the magnetization dynamics during SOT-induced switching under large currents.