  We investigate an open XXZ spin 1/2 chain driven out of equilibrium by
coupling with boundary reservoirs targeting different spin orientations in XY
plane. Symmetries of the model are revealed which appear to be different for
spin chains of odd and even sizes. As a result, spin current is found to
alternate with chain length, ruling out the possibility of ballistic transport.
Heat transport is switched off completely by virtue of another global symmetry.
Further, we investigate the model numerically and analytically. At strong
coupling, we find exact nonequilibrium steady state using a perturbation
theory. The state is determined by solving secular conditions which guarantee
self-consistency of the perturbative expansion. We find nontrivial dependence
of the magnetization current on the spin chain anisotropy $\Delta$ in the
critical region $|\Delta|<1$, and a phenomenon of tripling of the twisting
angle along the chain for narrow lacunes of $\Delta$.
