Domain Theory

Abstract

Domain observation and domain theory must go together in the study of magnetic microstructure. This chapter introduces domain theory. The focus is on applicationoriented procedures rather than on the well-established fundamentals. A more detailed analysis is offered where it illustrates characteristic mechanisms. In this case intermediate steps are presented as a guideline to encourage the reader to reproduce the line of arguments. In Sect. 3.2 the free energy of a magnet is presented. The principle that this energy must be a minimum leads to the micromagnetic equations and their dynamic generalizations. A discussion of the origin of domains from the viewpoint of theory (Sect. 3.3) is followed by two sections, which deal with cases for which no knowledge of domain walls is necessary. Phase theory (Sect. 3.4) is adequate for the calculation of the reversible magnetization curve of large, bulk crystals. Small particle switching theory (Sect. 3.5) applies to small particles that are too small to contain regular domain walls. For all intermediate cases domain walls become important. Their properties are summarized in Sect. 3.6, which also includes a discussion of substructures of domain walls and of wall dynamics. In the last part of the chapter (Sect. 3.7) a number of commonly occurring domain features-like domain branching or dense stripe domains-are discussed from a theoretical point of view. This section ends with a thorough discussion of a seemingly simple, but actually rather complex model case: the Néel block.Sketch 3.12.

Magnetic Characterization in the Rayleigh Region of Nanocrystalline Magnetic Cores

“…Additionally, research on the magnetic behavior of soft magnetic materials with amorphous and nanocrystalline structure in the Rayleigh region can provide useful information regarding these applications. In this context, previous works (see for example [10,11,12]) analyzed the magnetization process in the Rayleigh region of these materials as one part of the complete magnetization process until the magnetic saturation state, a few of these focused only on the deep analysis of such a region [13].…”

Strong and ductile high temperature soft magnets through Widmanstätten precipitates

“…3d, right-bottom, II-IV). The observed surface domain structure is typical for bulk SMMs with cubic anisotropy (for example, Fe-Ni and Fe-Si alloys 28 ). The slight variations are derived from the individual crystallographic orientations of the constituting grains.…”

Correlation between perpendicular magnetic anisotropy and microstructure in TbFeCo and TbFeCo–SiO2films

“…For the TbFeCo-SiO 2 films, the areal density of domains is higher, compared with the TbFeCo films. As is well known, the domain size is determined by a competition between the domain wall energy (proportional to K u L/D) and the demagnetizing energy (proportional to M 2 S D) and the domain width at equilibrium is proportional to √ LK u /M S [16][17][18], where L is the film thickness, D is the domain width and K u is the intrinsic perpendicular anisotropy. Since the domain size increases as the PMA is increased, the difference in the domain size between the TbFeCo and TbFeCo-SiO 2 films cannot be explained well if only the PMA energy and the demagnetization energy are considered.…”