  We demonstrate possible scenarios for production of pure spin current and
large tunnelling magnetoresistance ratios from elastic co-tunnelling and
crossed Andreev reflection across a superconducting junction comprising of
normal metal-superconductor-normal metal, where, the normal metal is a
one-dimensional interacting quantum wire. We show that there are fixed points
in the theory which correspond to the case of pure spin current. We analyze the
influence of electron-electron interaction and see how it stabilizes or
de-stabilizes the production of pure spin current. These fixed points can be of
direct experimental relevance for spintronics application of normal
metal-superconductor-normal metal junctions of one-dimensional quantum wires.
We also calculate the power law temperature dependence of the crossed Andreev
reflection enhanced tunnelling magnetoresistance ratio for the normal
metal-superconductor-normal metal junction.

Mesoscale and Nanoscale Physics