  We study by extensive Monte Carlo simulations the transport of itinerant
spins travelling inside a multilayer composed of three ferromagnetic films
antiferromagnetically coupled to each other in a sandwich structure. The two
exterior films interact with the middle one through non magnetic spacers. The
spin model is the Ising one and the in-plane transport is considered. Various
interactions are taken into account. We show that the current of the itinerant
spins going through this system depends strongly on the magnetic ordering of
the multilayer: at temperatures $T$ below (above) the transition temperature
$T_c$, a strong (weak) current is observed. This results in a strong jump of
the resistance across $T_c$. Moreover, we observe an anomalous variation,
namely a peak, of the spin current in the critical region just above $T_c$. We
show that this peak is due to the formation of domains in the temperature
region between the low-$T$ ordered phase and the true paramagnetic disordered
phase. The existence of such domains is known in the theory of critical
phenomena. The behavior of the resistance obtained here is compared to a recent
experiment. An excellent agreement with our physical interpretation is
observed. We also show and discuss effects of various physical parameters
entering our model such as interaction range, strength of electric and magnetic
fields and magnetic film and non magnetic spacer thicknesses.
