  This article discusses two dual approaches to spin transport in magnetic
multilayers: a direct, purely quantum, approach based on a Tight-Biding model
(TB) and a semiclassical approach (Continuous Random Matrix Theory, CRMT). The
combination of both approaches provides a systematic way to perform
multi-scales simulations of systems that contain relevant physics at scales
larger (spin accumulation, spin diffusion...) and smaller (specular reflexions,
tunneling...) than the elastic mean free paths of the layers. We show
explicitly that CRMT and TB give consistent results in their common domain of
applicability.
