A stimuli-responsive material is synthesized that combines the actuation potential of liquid-crystalline elastomers with the anisotropic magnetic properties of ellipsoidal iron oxide nanoparticles. The resulting nanocomposite exhibits unique shape-memory features with magnetic information, which can be reversibly stored and erased via parameters typical of soft materials, such as high deformations, low stresses, and liquid-crystalline smectic-isotropic transition temperatures.