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

Abstract

Spin-orbit torque (SOT), arising from spin-orbit coupling-induced spin currents, provides efficient control of magnetization. SOT characterization involving harmonic Hall resistances is typically done in low-current regimes, distinct from high-current regimes, where SOT-induced magnetization switching occurs. In this study, we investigate 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 2ϕ behavior and the second harmonic Hall resistance comprises cos ϕ and cos 3ϕ terms. Interestingly, with increasing current, higher-order angular-dependent terms become non-negligible, referring to the sin 4ϕ and sin 6ϕ terms for the first harmonic and the cos 5ϕ and cos 7ϕ terms for the second harmonic Hall resistances. We attribute this unconventional angular dependence to the nonlinear response of magnetization direction to SOT, emphasizing its relevance to understanding the magnetization dynamics during SOT-induced switching under large currents.