Fundamentals and applications of the Landau-Lifshitz-Bloch equation

The influence of thermal excitations on magnetic materials is a topic of increasing relevance in the theory of magnetism. The Landau-Lifshitz-Bloch equation describes magnetisation dynamics at finite temperatures. It can be considered as an extension of already established micromagnetic methods with a comparable numerical effort. This review is a brief summary of this new field of research, with a focus on the fundamentals of the Landau-Lifshitz-Bloch equation, its connection with the stochastic Landau-Lifshitz equation, and its applications in modern magnetism.