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Figure 1
Model for the magnetic microstructure of bulk ferromagnets. (a) Sketch of an idealized two-dimensional (nuclear) grain microstructure. The two main sources that cause a perturbation of the magnetic microstructure are identified in our magnetic SANS theory (Honecker & Michels, 2013BB23) as (i) spatial (random) variations in the direction and/or magnitude of the magnetic anisotropy field and (ii) spatial variations in the magnitude of the saturation magnetization. The characteristic length scales (correlation lengths) over which such variations occur may be related, for example, to the average particle or crystallite size D, which for bulk nanomagnets is typically of the order of 10–20 nm. In (a), the crystallographic set of easy axes for the magnetization changes randomly at each internal interface (e.g. a grain boundary); for simplicity, we have here assumed a uniaxial magnetic anisotropy ([\updownarrow]). In addition, the magnetic material's parameters (exchange constant A, anisotropy constant K and saturation magnetization Ms) may depend on the position inside the material [which is symbolized by grains (cells) with different color]. (b) Superposed (magnetic) spin microstructure in the presence of a strong applied magnetic field [{\bf H}_0]. The shown coarse-grained distribution of spins is only qualitative, but suggests the existence of continuously varying nanoscale magnetization profiles, which give rise to a strongly field-dependent magnetic SANS cross section. Note also the absence of sharp interfaces in the magnetic microstructure (b), in contrast to the grain microstructure (a).

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