A magnetoresistive memory element has a stacked structure including: a tunneling barrier made of non-magnetic material, a first magnetic system with a ferromagnetic tunneling junction reference layer barrier having a fixed magnetic moment vector on one side of the tunneling adjacent to the non-magnetic material, and a second magnetic system with a ferromagnetic tunneling junction free layer on an opposite side of the tunneling barrier having a free magnetic moment vector adjacent to the non-magnetic material and forming a magnetoresistive tunneling junction. The tunneling junction free layer is one of a plurality of N ferromagnetic free layers which are antiferromagnetically coupled. The first magnetic system is sandwiched in between the tunneling junction free layer and at least one of the ferromagnetic free layers that are anti-ferromagnetically coupled therewith.