  We consider an open isotropic Heisenberg quantum spin chain, coupled at the
ends to boundary reservoirs polarized in different directions, which sets up a
twisting gradient across the chain. Using a matrix product ansatz, we calculate
the exact magnetization profiles and magnetization currents in the
nonequilibrium steady steady state of a chain with N sites. The magnetization
profiles are harmonic functions with a frequency proportional to the twisting
angle {\theta}. The currents of the magnetization components lying in the
twisting plane and in the orthogonal direction behave qualitatively
differently: In-plane steady state currents scale as 1/N^2 for fixed and
sufficiently large boundary coupling, and vanish as the coupling increases,
while the transversal current increases with the coupling and saturates to
2{\theta}/N.
