Spin-transport in multi-terminal normal metal - ferromagnet systems with   non-collinear magnetizations
  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 parameters. Microscopic expression for these conductances are derived in terms of scattering matrices and explicitly calculated for simple models. The circuit theory is applied to 2-terminal and 3-terminal devices attached to ferromagnetic reservoirs. 
Arne Brataas, Yu. V. Nazarov, and G. E. W. Bauer