Multi-terminal Spin Transport: Non applicability of linear response and Equilibrium spin currents

We present generalized scattering theory for multi-terminal spin transport in systems with broken SU(2) symmetry either due to spin-orbit interaction,magnetic impurities or magnetic leads. We derive equation for spin current consistent with charge conservation. It is shown that resulting spin current equations can not be expressed as difference of potential pointing to {\it non applicability of linear response for spin currents} and as a consequence equilibrium spin currents(ESC) in the leads are non zero. We illustrate the theory by calculating ESC in two terminal normal system in presence of Rashba spin orbit coupling and show that it leads to spin rectification consistent with the non linear nature of spin transport.