Conversion of spin and charge currents in magnetic and non-magnetic systems

We formulate the law of conversion between spin current and charge current in several classes of materials including ferromagnetic, paramagnetic and spin-orbit coupled systems. We find that the interpretation of spin current is highly non-trivial, and we have identified pure and composite spin currents. For an interfacial Rashba spin-orbit coupled Hamiltonian, we show that the spin transport is much closer to that in ferromagnets than in non-magnetic materials. In particular, we show that an in-plane charge current in layered structures will generate a pure spin current flowing perpendicular to the Rashba spin-orbit coupled interface, and vice versa. Application of the spin-charge current conversion in several experimental realizations is discussed.