Hi Qingtian, I suggest to put spin-up and spin-down on separate lattices, like in http://kwant-project.org/doc/1.0/tutorial/tutorial5#lattice-description-using-different-lattices This will split each lead into a spin-up and a spin-down lead and you can easily calculate transmission between them.
Best, Christoph PS Another, more general but also way more advanced solution would be to get the wave functions of the lead modes, and project the spin current operator on them. (Note that the object returned by kwant.smatrix contains the wave functions of the modes: http://kwant-project.org/doc/1.0/reference/generated/kwant.solvers.common.SMatrix)
