Applicability of scaling behavior and power laws in the analysis of the magnetocaloric effect in second-order phase transition materials

In recent years, universal scaling has gained renewed attention in the study of magnetocaloric materials. It has been applied to a wide variety of pure elements and compounds, ranging from rare-earth-based materials to transition metal alloys, from bulk crystalline samples to nanoparticles. It is therefore necessary to quantify the limits within which the scaling laws would remain applicable for magnetocaloric research. For this purpose, a threefold approach has been followed: (a) the magnetocaloric responses of a set of materials with Curie temperatures ranging from 46 to 336 K have been modeled with a mean-field Brillouin model, (b) experimental data for Gd has been analyzed, and (c) a 3D-Ising model - which is beyond the mean-field approximation - has been studied. In this way, we can demonstrate that the conclusions extracted in this work are model-independent. It is found that universal scaling remains applicable up to applied fields, which provide a magnetic energy to the system up to 8% of the thermal energy at the Curie temperature. In this range, the predicted deviations from scaling laws remain below the experimental error margin of carefully performed experiments. Therefore, for materials whose Curie temperature is close to room temperature, scaling laws at the Curie temperature would be applicable for the magnetic field range available at conventional magnetism laboratories (∼10 T), well above the fields which are usually available for magnetocaloric devices.