1. A magnetic device comprising a magnetoresistive tunnel junction, including: a reference magnetic layer having magnetization in a direction that is fixed; a storage magnetic layer having magnetization in a direction that is variable; and an intermediate layer acting as a tunnel barrier that is essentially semiconductor or electrically insulating and that separates the reference magnetic layer from the storage magnetic layer; the device being characterized in that the potential profile of the intermediate layer is asymmetrical across a thickness of said intermediate layer this asymmetry being caused by the creation of a potential well that is localized in an asymmetrical position within the thickness of the tunnel barrier, this asymmetry producing a current response that is asymmetrical as a function of the applied voltage, and in that the potential well that is localized in an asymmetrical position within the thickness of the tunnel barrier is created through either a first creating means or a second creating means, wherein according to the first creating means, the intermediate layer acting as a tunnel barrier includes in its thickness, at a first distance (e 1 ) from the storage magnetic layer and at a second (e 2 ) distance from the reference magnetic layer, a very thin layer of a metallic or semiconductive material other than that or those constituting the remainder of the intermediate layer, the second distance (e 2 ) presenting value that is different from that of the first distance (e 1 ), said very thin layer presenting a thickness either of one to two planes of atoms or of a fraction of a plane of atoms, and according to the second creating means, said intermediate layer acting as a tunnel barrier includes a doped region within its thickness at a first distance (e 1 ) from the storage magnetic layer and at a second distance (e 2 ) from the reference magnetic layer, where the second distance presents a value different from that of the first distance (e 1 ), the doped region being doped by inserting a material other than that constituting the remainder of the intermediate layer so as to create in the doped region said potential well.