  We show that, when a finite anisotropic Heisenberg spin-1/2 chain in the
gapped regime is driven far from equilibrium, oppositely polarized
ferromagnetic domains build up at the edges of the chain, thus suppressing
quantum spin transport. As a consequence, a negative differential conductivity
regime arises, where increasing the driving decreases the current. The above
results are explained in terms of magnon localization and are shown to be
structurally stable against breaking of integrability.
