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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.
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.
This chapter presents an overview of the magnetization configurations and reversal in magnetic structures ranging from a few nanometers to a few micrometers in size that can be described using the theory of micromagnetics. A range of techniques for the characterization of magnetic structures is introduced and the theoretical micromagnetism background, including the energy terms governing the magnetic properties, are discussed. The simplest case of a single domain system with uniform magnetization is treated within the framework of the Stoner–Wohlfarth theory, and experimental examples of such systems are presented. The magnetization configurations in larger systems that exhibit nonuniform magnetization are discussed in detail with a particular emphasis on experimental examples for the geometries that have been studied most often, such as discs, rings, rectangles, wires and pillars. Theoretically, the formation of these states is explained as a result of the interplay between the different magnetic energy terms; multidomain states that occur for larger elements are also introduced. The dynamic properties of the reversal of these elements are addressed, starting with the evaluation of the Landau–Lifshitz–Gilbert equation to obtain the trajectories for single domain particles. This is then extended to cover the nonhomogeneous reversal of nonuniform states. The elementary processes occurring during nonhomogeneous reversal are introduced and used to explain the magnetization reversal in a set of instructive examples.
The objective of this contribution is to review 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 indispensible 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 1940/41, 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 treated in the contributions by Miltat et al., Schrefl et al., and D. Goll in the Handbook of Magnetism and Advanced Magnetic Materials ed. by Kronmüller and Parkin Kronmüller and Parkin (2007).
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