## International Tables for Crystallography

Magnetic properties International Tables for Crystallography (2013). Vol. D, ch. 1.5, pp. 106-153 [ doi:10.1107/97809553602060000904 ] Abstract This chapter gives a short review of the structure and some properties of magnetic substances that depend mainly on the symmetry of these substances. Aspects related to the magnetic symmetry receive the most emphasis. The magnetic symmetry takes into account the fact that it is necessary to consider time inversion in addition to the usual spatial transformations in order to describe the invariance of the thermodynamic equilibrium states of a body. The first part of the chapter is devoted to a brief classification of disordered and ordered magnetics. The classification of ferromagnets according to the type of the magnetic structure is given in Section 1.5.1.2.1. In Section 1.5.1.2.2, the antiferromagnets are classified by the types of their magnetic structures: collinear, weakly non-collinear and strongly non-collinear antiferromagnets. Incommensurate structures are briefly mentioned in Section 1.5.1.2.3. Section 1.5.2 is devoted to magnetic symmetry. Different types of magnetic point (Section 1.5.2.1) and magnetic space (Section 1.5.2.3) groups are defined. The 22 magnetic Bravais lattices are displayed in Section 1.5.2.2. The transition from the paramagnetic state into the magnetically ordered state entails a transition from one magnetic group into another. These transitions are considered in Section 1.5.3. The domain structure of ferromagnets and antiferromagnets is considered in Section 1.5.4, where 180° and T-domains are described. Non-collinear antiferromagnetic structures (weakly ferromagnetic, non-collinear and non-coplanar antiferromagnetic structures) are described in Section 1.5.5. Besides the magnetic phase transition from the disordered into the ordered state, there exist transitions from one magnetic structure into another. Those of these that are obtained by a rotation of the ferromagnetic or antiferromagnetic vector relative to the crystallographic axis are called reorientation transitions and are analysed in Section 1.5.6. Sections 1.5.7 and 1.5.8 are devoted to phenomena that can be (and were) predicted only on the basis of magnetic symmetry. These are piezomagnetism (Section 1.5.7) and the magnetoelectric effect (Section 1.5.8). In Section 1.5.9, the magnetostriction in ferromagnets is briefly discussed. |

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## About **International Tables for Crystallography**

**International Tables for Crystallography**is the definitive resource and reference work for crystallography. The series consists of nine volumes and comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.