Signal propagation in time-dependent spin transport

Signal propagation in magnetic multilayers is studied using a macroscopic theory of time-dependent spin transport. Our analysis shows that time-dependent spin transport possesses a wave-diffusion duality, i.e., it is wave like for fast signal modulation and reduces to the diffusion equation for slow modulation [1]. The wave-like characteristics allow us to extract a finite spin signal-propagation velocity, which cannot be done using the spin diffusion equation. Applications to different switching scenarios for collinear and noncollinear spin transport through magnetic multilayers will be discussed.\newline [1] Y.-H. Zhu, B. Hillebrands, H. C. Schneider, Phys.\ Rev.\ B \textbf{78}, 054429 (2008)