  In solid state physics, giant magnetoresistance is the large change in
electrical resistance due to an external magnetic field. Here we show that
giant magnetoresistance is possible in a spin chain composed of weakly
interacting layers of strongly coupled spins. This is found for all system
sizes even down to a minimal system of four spins. The mechanism driving the
effect is a mismatch in the energy spectrum resulting in spin excitations being
reflected at the boundaries between layers. This mismatch, and thus the
current, can be controlled by external magnetic fields resulting in giant
magnetoresistance. A simple rule for determining the behavior of the spin
transport under the influence of a magnetic field is presented based on the
energy levels of the strongly coupled spins.
