# Magnetic Structure

## Magnetic Structure

(atomic magnetic structure), the periodic spatial arrangement and orientation of atomic magnetic moments in a magnetically ordered crystal (ferromagnet, ferri-magnet, or antiferromagnet). Atomic magnetic structure should be distinguished from domain magnetic structure, which is determined by the nature and relative position of domains. The periodicity of the spatial arrangement of atomic magnetic moments is determined by the crystal structure of the substance. An exchange interaction of an electrical nature is responsible for the relative orientation of the moments; forces of magnetic anisotropy are responsible for their overall orientation with respect to the crystallographic axes. More complex (and weak) types of magnetic interaction may complicate the atomic magnetic structure.

A distinction is made between two main classes of magnetic substances, which are related to specific atomic molecular structure: substances with a nonzero total macroscopic magnetic moment M (M *≠* 0) and substances with M = 0. A ferromagnetic structure (Figure 1, a) corresponds to the first case; here the magnetic moments of all atoms are aligned in the same direction (the direction of easy magnetization), which may be different in different crystals. An antiferromagnetic structure (Figure 1, b) corresponds to the second case: each magnetic moment in the immediate vicinity has a compensating moment of strictly anti-parallel orientation. Various antiferromagnetic magnetic structures may exist, depending on the nature of the immediate vicinity (for example, the structures shown in Figure 1, b, 1, c, and 1, d). The periods of antiferromagnetic structures may be an integral multiple of the periods of the atomic structure. Antiferromagnetic structures with magnetic moments oriented along two or three axes and still more complicated structures—umbellate,

triangular, and so on (Figure 1, e and 1, 0—are sometimes achieved.

Ferrimagnetic structures with M ≠ 0 are close to the antiferromagnetic structure. They occur when an antiferromagnetic structure is formed by atoms or ions having different magnetic moments (Figure 1, f) Here the value of M is determined by the magnitude of the difference between the moments of the two magnetic sublattices (systems of identically oriented magnetic moments). Another case is found in weak ferromagnets: the presence of additional interatomic forces leads to the noncol-linearity of magnetic moments and to the appearance of an aggregate ferromagnetic component (Figure 1, g).

In some cases the more complex (long-range) nature of atomic interaction leads to the establishment of spiral magnetic structures, in which the magnetic moments of adjacent atoms are rotated with respect to one another in such a way that the ends of the vectors that represent them lie on the same spiral. A distinction is made among several types of spiral magnetic structures, depending on the magnitude of projection of magnetic moments onto the direction of the spiral axis (Figure 2). The essential difference between spiral magnetic structures and other magnetic structures is that in the general case the pitch of the spiral is incommensurable with the corresponding period of the crystal lattice and, in addition, is temperature-dependent.

The complete classification of magnetic structure is based on the theory of magnetic symmetry, which takes into account not only the arrangement but also the orientation of atomic magnetic moments in a crystal. In addition to ordinary rotations about the axes of symmetry, reflections in planes of symmetry, and translations, the transformation *R*, which reverses the directions of magnetic moments, is also a transformation of magnetic symmetry. Introduction of the transformation *R* increases the number of symmetry classes from 32 to 122 and the number of spatial symmetry groups from 230 to 1,651. Substances that have a magnetic structure are described by the groups of magnetic symmetry in which *R* appears in the form of products with the ordinary elements of crystal symmetry.

The magnetic structure of a crystal and its physical (above all magnetic) properties are closely interrelated. Therefore, indirect assessments of magnetic structure may be made on the basis of data concerning these physical properties of a substance. Direct data on the magnetic structure of crystals may be obtained through magnetic neutron-diffraction research. Since the appearance of the first work in this field (1949), the magnetic structure of more than 1,000 metals, alloys, and chemical compounds has been established by neutron diffraction. Nuclear gamma resonance (the Mossbauer effect) may also be used to establish the magnetic symmetry.

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R. P. OZEROV