Derivation of the Landau–Lifshitz–Bloch equation from continuum thermodynamics

Within the continuum thermodynamic framework, we derive the evolution equation for the magnetization vector in a ferromagnetic body. This procedure leads to an evolution equation that generalizes the well-known Landau–Lifshitz model for magnetically saturated bodies and looks very similar to the Landau–Lifshitz–Bloch equation which was obtained by Garanin in 1997 from statistical mechanics. As a by product, we also obtain a generalization of the Gilbert equation when the magnetic field is far from saturation. By virtue of a suitable choice of the Gibbs free energy, this phenomenological model is able to describe the phase transition occurring from the paramagnetic to the ferromagnetic regime in anisotropic ferromagnets.