Spin current through a tunnel junction
  We derive an expression for the spin-current through a tunnel barrier in terms of many-body Green's functions. The spin current has two contributions. One can be associated with angular-momentum transfer by spin-polarized charge currents crossing the junction. If there are magnetic moments on both sides of the tunnel junction, due to spin accumulation or ferromagnetic ordering, then there is a second contribution related to the exchange coupling between the moments. 
Matthias Braun, J\"urgen K\"onig, Jan Martinek