Theory of Impedance Dynamics for Magnetic Multilayers

On the basis of a macroscopic spin wave-diffusion theory we study high-frequency spin transport through a junction composed of a magnetic and a nonmagnetic layer. We illustrate the consequences of the spin wave-diffusion theory for the spatio-temporal dynamics of a spin current, and apply the theory to the calculation of the dynamical impedance of the junction. For low modulation frequencies, our results are in good agreement with those from spin-diffusion theory, but the wave character of spin transport leads to different predictions for the impedance in the high-frequency regime.