Dynamic Feedback in Ferromagnet/Spin Hall Metal Heterostructures

In ferromagnet/normal metal heterostructures, spin pumping and spin-transfer torques are two reciprocal processes that occur concomitantly. Their interplay introduces a dynamic feedback effect interconnecting energy dissipation channels of both magnetization and current. By solving the spin diffusion process in the presence of the spin Hall effect in the normal metal, we show that the dynamic feedback gives rise to: (i) a nonlinear magnetic damping that is crucial to sustain uniform steady-state oscillations of a spin Hall oscillator at large angles. (ii) a frequency dependent spin Hall magnetoimpedance that reduces to the spin Hall magnetoresistance in the dc limit.