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A heterogeneous medium (HM) for writing optical data is discussed. It consists of a binder, which is a transparent material which can make an aggregative solid-liquid transition, and a filler of magnetic particles, which can absorb the writing radiation. The particles in the binder are randomly oriented and the HM film is practically opaque. Writing occurs as a result of the partial melting of the binder under the action of radiation heating and the pulling of the particles into threads parallel to an external magnetic field applied perpendicular to the HM film. This thus increases its transparency, in agreement with the spatial distribution of the power of the writing radiation. The writing becomes fixed upon solidification of the binder. The erasure of the writing occurs when the binder is melted in an alternating magnetic field. After erasure the HM can be used for repeated writing, i.e. it is reversible.