The present invention relates to a process for separating at least one first material from a mixture comprising this at least one first material and at least one second material, which comprises the following steps: (A) contacting of the mixture comprising the at least one first material and at least one second material with at least one selective hydrophobicizing agent in the presence of a suspension medium so that an adduct is formed from the at least one hydrophobicizing agent and the at least one first material but not with the at least one second material, (B) contacting of the adduct from step (A) with at least one magnetic particle which is functionalized on the surface with at least one polymeric compound having a transition temperature LCST (lower critical solution temperature) at a temperature at which the polymeric compound has hydrophobic character so that the adduct from step (A) and the at least one functionalized magnetic particle agglomerate, (C) if appropriate addition of further suspension medium to the mixture obtained in step (B), (D) separation of the agglomerate present in the suspension from step (B) or (C) from the suspension by application of a magnetic field, (E) dissociation of the agglomerate separated off in step (D) by setting of a temperature at which the polymeric compound has hydrophilic character in order to obtain the at least one first material.