A magnetic element for writing by thermally assisted magnetic field or thermally assisted spin transfer comprises a stack consisting of a free magnetic layer, also called storage layer or switchable magnetization layer, of which the magnetization direction is switchable between two nonwrite stable states, both directed out-of-plane and substantially perpendicular to the plane of said layer, and of which the magnetization is spontaneously reoriented from substantially perpendicular to the plane to substantially in the plane under the effect of the rise in temperature during the writing, at least one reference magnetic layer, called pinned layer, of which the magnetization is oriented substantially perpendicular to the plane of said layer, a nonmagnetic spacer inserted between the two layers and means for making an electric current flow perpendicular to the plane of said layers.