Single-crystal Fe/MgO multilayers are model systems in which to study magnetic tunnel junctions. We find that the interfacial roughness leads to the loss of coherence of the crystal structure. For thick MgO layers ferromagnetic (FM) ordering is found using polarized neutron reflectivity (PNR). For thin MgO layers magnetization measurements reveal the presence of antiferromagnetic (AF) interactions, but no long-range AF order is found using PNR. After cycling in a hysteresis loop, FM correlations are found at the coercive point, and this will limit the maximum tunnelling magnetoresistance.