A. Brataas et al., Spin-transport in multi-terminal normal metal-ferromagnet systems with non-collinear magnetizations, EUR PHY J B, 22(1), 2001, pp. 99-110
A theory of spin-transport in hybrid normal metal-ferromagnetic electronic
circuits is developed, taking into account non-collinear spin-accumulation.
Spin-transport through resistive elements is described by 4 conductance pa
rameters. Microscopic expression for these conductances are derived in term
s of scattering matrices and explicitly calculated for simple models. The c
ircuit theory is applied to 2-terminal and 3-terminal devices attached to f
erromagnetic reservoirs.