The invention concerns a magnetic memory, whereof each memory point consists of a magnetic tunnel junction (60), comprising: a magnetic layer, called trapped layer (61), whereof the magnetization is rigid; a magnetic layer, called free layer (63), whereof the magnetization may be inverse; and insulating layer (62), interposed between the free layer (73) and the trapped layer (71) and respectively in contact with said two layers. The free layer (63) is made with an amorphous or nanocrytallized alloy based on rare earth or a transition metal, the magnetic order of said alloy being of the ferromagnetic type, said free layer having a substantially planar magnetization.