Some Aspects of Scaling and Universality in Magnetocaloric Materials

The magnetocaloric effect of a magnetic material is characterized by two quantities, the isothermal entropy change and the adiabatic temperature change, both of which are functions of temperature and applied magnetic field. We discuss the scaling properties of these quantities close to a second order phase transition within the context of critical scaling theory. In the critical region the isothermal entropy change will exhibit universal scaling exponents. However, this is only true close to Tc and for small fields; we show that for finite fields the scaling exponents in general become field dependent, even at Tc. Furthermore, the scaling exponents at finite fields are not universal: Two models with the same critical exponents can exhibit markedly different scaling behaviour even at relatively low fields. Turning to the adiabatic temperature change, we argue that it is not determined exclusively by the scaling part of the free energy and its derivatives. This means that the field dependence of the adiabatic temperature change in the critical region depends on the regular part (background) of the specific heat associated with the lattice and conduction electrons. The field dependence can still be fitted to a power-law expression but with non-universal exponents as we show explicitly both within mean-field theory and using the so-called Arrott-Noakes equation of state. Finally, we discuss the implications of these observations for the interpretation of a widely used phenomenological scaling procedure.