Hysteresis and temperature-induced transitions in ferromagnetic materials

In this paper we present two basic one-dimensional models for the temperature-induced phase-changes in a ferromagnetic material. In the framework of the Ginzburg-Landau theory, we construct suitable thermodynamic potentials from which thermodynamically-consistent evolution equations for the magnetization are derived. For both soft and hard materials these models account for saturation and provide an effective description of the transition from paramagnetic to ferromagnetic regimes by displaying the onset of hysteresis loops when the temperature decreases below the Curie critical value. The temperature enters the model as a parameter by way of the magnetic susceptibility. Such a dependence is discussed in order to comply with both Bloch's law (below the critical value) and Curie-Weiss law (far above the critical value). Focusing on uniform processes, numerical simulations of the magnetic responses at different temperatures are performed.