  We present a general formulation of spin-dependent transport through a clean
one-dimensional interacting quantum wire or carbon nanotube, connected to
non-collinear ferromagnets via tunnel junctions. We show that the low energy
description of each junction is given by a conformally-invariant boundary
condition representing *exchange coupling*, in addition to a pair of electron
tunneling operators. The effects of the exchange coupling are strongly enhanced
by interactions, leading to a dramatic suppression of spin accumulation. This
is a direct signature of spin-charge separation in a Luttinger liquid.
Furthermore, we demonstrate that magnetic polarization can lead to oscillations
in the non-linear current-voltage relation. This phenomena is a surprising
purely nonequilibrium effect due to backscattering interactions, which are thus
dangerously marginally irrelevant in the repulsively-interacting Luttinger
liquid.
