  The conventional definition of spin-current, namely spin density multiplied
by the group velocity, is not a conserved quantity due to possible spin
rotations caused by spin-orbit (SO) interaction. However, in a model with
spin-spin interactions, rotation of a spin causes a dynamic response of
surrounding spins that opposes the rotation. Such a many-body effect restores
the spin-current conservation. Here we prove that the non-conservation problem
of spin-current can be resolved if a self-consistent spin-spin interaction is
included in the analysis. We further derive a spin-conductance formula which
partitions spin-current into different leads of a multi-lead conductor.
