  This paper presents a micromagnetic formulation for modeling the
magnetization dynamics and thermal equilibrium in ferrimagnetic materials at
low and elevated temperatures. The formulation is based on a mean field
approximation (MFA). In this formulation, the ferrimagnet is described
micromagnetically by two coupled sublattices, including inter- and
intra-lattice micromagnetic exchange as well as four-spin interactions via an
inter-lattice molecular field and a perpendicular field with a cubic dependence
of the magnetization. The MFA is used to derive a Landau Lifshitz Bloch
equation for ferrimagnetic material, including cases with a ferromagnetic -
antiferromagnetic phase transitions. This micromagnetic formulation is used for
modeling the phase transitions in FeRh and it shown an agreement with results
presented in recent experiments and atomistic models.
