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This chapter opens with a brief description of the very wide variety of magnetically ordered structures, both commensurate (with crystal structure) and incommensurate. The concepts of magnetic Bravais lattices and magnetic space groups are introduced. For an unpolarized incident neutron beam, magnetic and nuclear scattered intensities are additive — calculation of the latter involves a magnetic form factor, a magnetic interaction vector (depending on magnetic moment relative to scattering vector), and a magnetic structure factor. Example calculations are given for anti-ferromagnetic AuMn and the incommensurate heli-magnetic Au₂Mn. Methods for solving magnetic structures, i.e., establishing the nature of the magnetic ordering, then determining the magnitude and orientation of the magnetic moments, are discussed. The solution of magnetic structures from neutron powder data is illustrated with examples taken from the recent literature.

This chapter opens with brief descriptions of neutrons, powders (polycrystalline materials), and diffraction, followed by an account of how the unique properties of neutrons and their interaction with matter define a role for neutron powder diffraction in the study of condensed matter. The concepts are refined within an historical account of the development of neutron powder diffraction and its applications. Reference are made to the earliest demonstration of neutron diffraction, to the development of neutron sources (research reactors and accelerator-based sources), and to applications ranging from early investigation of simple crystal and magnetic structures to the more recent investigations of kinetic processes and complex crystal structures (high-temperature superconductors, fullerenes).

The basic concepts of magnetic order in crystals are reviewed, including magnetic unit cells, propagation vectors and magnetic domains. Some commonly-occuring magnetic structures are discussed, such as ferromagnets, antiferromagnets, ferrimagnets, and noncollinear and incommensurate magnetic structures. The differential cross-section for neutron diffraction from a magnetic structure is derived, and the magnetic structure factor is defined. The use of neutron polarization analysis, including spherical neutron polarimetry, in the determination of magnetic structures and of the spatial distribution of magnetization is described in detail. Diffuse magnetic scattering due to magnetic frustration and magnetic phase transitions is discussed, and the relevance of the static approximation is explained. Neutron diffraction studies of nuclear spin order are described.

This chapter argues that control of magnetic domains and domain wall structures is one of the most important issues from the viewpoint of both applied and basic research in magnetism. Its discussion is however limited to static and dynamic properties of magnetic vortex structures. It has been revealed both theoretically and experimentally that for particular ranges of dimensions of cylindrical and other magnetic elements, a curling in-plane spin configuration is energetically favoured, with a small region of the out-of-plane magnetisation appearing at the core of the vortex. Such a system, which is sometimes referred to as a magnetic soliton, is characterised by two binary properties: a chirality and a polarity, each of which suggests an independent bit of information in future high-density nonvolatile recording media.

This chapter argues that control of magnetic domains and domain wall structures is one of the most important issues from the viewpoint of both applied and basic research in magnetism. Its discussion is however limited to static and dynamic properties of magnetic vortex structures. It has been revealed both theoretically and experimentally that for particular ranges of dimensions of cylindrical and other magnetic elements, a curling in-plane spin configuration is energetically favored, with a small region of the out-of-plane magnetization appearing at the core of the vortex. Such a system, which is sometimes referred to as a magnetic soliton, is characterized by two binary properties: A chirality and a polarity, each of which suggests an independent bit of information in future high-density nonvolatile recording media.