This magnetic memory with a thermally-assisted write, every storage cell of which consists of at least one magnetic tunnel junction, said tunnel junction comprising at least:one magnetic reference layer, the magnetization of which is always oriented in the same direction at the time of the read of the storage cell;one so-called “free” magnetic storage layer, the magnetization direction of which is variable;one insulating layer sandwiched between the reference layer and the storage layer.The magnetization direction of the reference layer is polarized in a direction that is substantially always the same at the time of a read due to magnetostatic interaction with another fixed-magnetization layer called the “polarizing layer”.