Criticality of Domains in Ferromagnets described by the Landau Functional

The distribution of magnetic moments in finite ferromagnetic bodies was first investigated by Landau an Lifshitz in a famous paper, where they obtained the domain structure of a ferromagnetic crystal at low temperatures, in the regime of saturated magnetization. We propose a generalization of the above approach, using from the start the Landau theory of phase transitions, where the free energy of the system is written as a functional with the magnetic permeability as the order-parameter density. We obtain more general field solutions, allowing nonhomogeneous regimes, which are used to describe the ferromagnetic phase transition at Tc. We find that domain sizes and walls are enlarged when the temperature is increased in direction of Tc. Very close to Tc however, the walls tend to suppress the layers, leading to a continuous vanishing of the domain structure. We discuss the validity of the model in the critical region.