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The present invention relates to a method for preparing solid or thin-film single-crystals of cubic sesquioxides (space group no. 206, Ia-3) of scandium, yttrium or rare earth elements optionally doped with lanthanide ions with a valence of +III, using a high-temperature flux growth technique, and to the uses of the non-doped single-crystals obtained according to said method, in particular in the field of optics.