Direct observation of current-induced nonlinear spin torque in Pt-Py bilayers

We experimentally observe nonlinear spin torque in metallic bilayers of platinum and permalloy by means of spin-torque ferromagnetic resonance (ST-FMR) under massive dc current injection. The observed nonlinear spin torque exerted on permalloy magnetization is attributed primarily to nonlinear spin polarization. An additional origin of the nonlinear spin torque is magnon generation (annihilation) followed by shrinkage (expansion) of effective magnetization, which is revealed by ST-FMR and unidirectional spin Hall magnetoresistance measurements. The present paper paves a way to spin Hall effect based nonlinear spintronic devices as well as time-varying nonlinear magnetic metamaterials with tailormade permeability.