  In XXZ chains, spin transport can be significantly suppressed when the
interactions in the chain and the bias of the dissipative driving are large
enough. This phenomenon of negative differential conductance is caused by the
formation of two oppositely polarized ferromagnetic domains at the edges of the
chain. Here we show that this many-body effect, combined with a non-uniform
magnetic field, can allow a high degree of control of the spin current. In
particular, by studying all the possible combinations of a dichotomous local
magnetic field, we found that a configuration in which the magnetic field
points up for half of the chain and down for the other half, can result in
giant spin-current rectification, for example up to $10^8$ for a system with
$8$ spins. Our results show clear indications that the rectification can
increase with the system size.
