  We present 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 with corresponding interactions, including inter- and
intra-sublattice micromagnetic exchange as well as four-spin interactions
described as an inter-sublattice molecular field with a cubic dependence of the
magnetization. The MFA is used to derive a Landau Lifshitz Bloch type equation
for ferrimagnetic material, including cases with a ferromagnetic -
antiferromagnetic phase transitions. For validation, the results obtained via
the presented model are compared with recent experimental data for phase
transitions in FeRh.
