  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.
