Landau-Lifshitz-Bloch equation for ferrimagnets with higher-order interaction

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.