The classical two-sublattice Landau–Lifshitz–Bloch equation for all temperatures

Abstract

Micromagnetic modeling has proved itself as a widely used tool, complimentary in many respects to experimental measurements. The Landau–Lifshitz equation provides a basis for this modeling, especially where the dynamical behaviour is concerned. However, this approach is strictly valid only for zero temperature and for high temperatures must be replaced by a more thermodynamically consistent approach such as the the Landau– Lifshitz–Bloch (LLB) equation. Here we review the recently derived LLB equation for two-sublattice systems and extend its derivation for temperatures above the Curie temperature. We present comparison with many-body atomistic simulations and show that this equation can describe the ultra-fast switching in ferrimagnets, observed experimentally