A magnetic element with thermally-assisted writing using a field or spin transfer provided, including a magnetic reference layer referred to as the “trapped layer,” the magnetization of which is in a fixed direction, and a magnetic storage layer called the “free layer” having a variable magnetization direction and consisting of a layer made of a ferromagnetic material with magnetization in the plane of the layer and magnetically coupled to a magnetization-trapping layer made of an antiferromagnetic material. A semiconductor or an insulating layer with confined-current-paths is sandwiched between the reference layer and the storage layer. At least one bilayer, consisting respectively of an amorphous or quasi-amorphous material and a material having the same structure or the same crystal lattice as the antiferromagnetic layer, is provided in the storage layer between ferromagnetic layer, which is in contact with the semiconductor or insulating layer with confined-current-paths, and antiferromagnetic layer.