The invention relates to a magnetic device (1) with thermally assisted writing, comprising at least one magnetic element including: a reference layer (2) having a stable vortex magnetisation configuration; means for creating a magnetic field for reversibly moving the core of the vortex in the plane of the reference layer; a storage layer (4) having a variable magnetisation configuration; a non-magnetic spacer (3) which separates the reference layer (2) and the storage layer (4) and magnetically decouples same; an antiferromagnetic trapping layer (5) in contact with the storage layer (4), which can trap the magnetisation configuration of the storage layer, said storage layer having at least two storage levels corresponding to two trapped magnetisation configurations; and heating means for heating the antiferromagnetic trapping layer (5) such that, during heating, the temperature of the antiferromagnetic trapping layer exceeds its blocking temperature such that, when hot, the magnetisation configuration of the storage layer (4) is no longer trapped.