The objective of this contribution is a review of the principles of the continuum theory of micromagnetism and to show its applications to the main static and dynamic problems of ferromagnetic materials. Micromagnetism as a continuum theory closes the gap between quantum theory, dealing with atomic scales and the Maxwell theory dealing with macroscopic dimensions. Micromagnetism therefore corresponds to the tool to deal with nano‐ and microscales. Micromagnetism has become an indispensable theory for a fundamental understanding of magnetic domain configurations, magnetization processes and the interaction between magnetization and microstructures. After Landau–Lifshitz's wall calculations in 1935 and Brown's publication of the so‐called Brown's micromagnetic equations in 1940/1941, micromagnetism became the standard method to analyze the basic magnetic properties of ferromagnetic materials in the range of nano‐ and microscales.
The following review gives a brief presentation of the different energy terms involved in the magnetic Gibbs free energy and a derivation of the micromagnetic equilibrium conditions and of the effective field. Some characteristic applications illustrate the effectiveness of micromagnetism in the case of domain walls, nucleation problems, interaction with microstructures, domain patterns, and the dynamics of magnetization processes.
This contribution also gives a definition of the different exchange lengths related to dipolar fields, magnetocrystalline anisotropy energy, magnetostatic energy of external fields and the magnetoelastic coupling energy.
Whereas only a few cases exist where analytical solutions of the highly nonlinear micromagnetic equations are available the progress in computational micromagnetism allowed the numerical solution of many open problems, which will be treated in the following contributions by Miltat
et al.
, Schrefl
et al.
and D. Goll.