In recent years, two important advances have opened new doors for the characterization and determination of magnetic structures. Firstly, researchers have produced computer-readable listings of the magnetic or Shubnikov space groups. Secondly, they have extended and applied the superspace formalism, which is presently the standard approach for the description of nonmagnetic incommensurate structures and their symmetry, to magnetic structures. These breakthroughs have been the basis for the subsequent development of a series of computer tools that allow a more efficient and comprehensive application of magnetic symmetry, both commensurate and incommensurate. Here we briefly review the capabilities of these computation instruments and present the fundamental concepts on which they are based, providing various examples. We show how these tools facilitate the use of symmetry arguments expressed as either a magnetic space group or a magnetic superspace group and allow the exploration of the possible magnetic orderings associated with one or more propagation vectors in a form that complements and goes beyond the traditional representation method. Special focus is placed on the programs available online at the Bilbao Crystallographic Server ( http://www.cryst.ehu.es ).

The Brillouin-zone database of the Bilbao Crystallographic Server (http://www.cryst.ehu.es) offers k-vector tables and figures which form the background of a classification of the irreducible representations of all 230 space groups. The symmetry properties of the wavevectors are described by the so-called reciprocal-space groups and this classification scheme is compared with the classification of Cracknell et al. [Kronecker Product Tables, Vol. 1, General Introduction and Tables of Irreducible Representations of Space Groups (1979). New York: IFI/Plenum]. The compilation provides a solution to the problems of uniqueness and completeness of space-group representations by specifying the independent parameter ranges of general and special k vectors. Guides to the k-vector tables and figures explain the content and arrangement of the data. Recent improvements and modifications of the Brillouin-zone database, including new tables and figures for the trigonal, hexagonal and monoclinic space groups, are discussed in detail and illustrated by several examples.

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A free web page under the name MAGNDATA, which provides detailed quantitative information on more than 400 published magnetic structures, has been developed and is available at the Bilbao Crystallographic Server (http://www.cryst.ehu.es). It includes both commensurate and incommensurate structures. This first article is devoted to explaining the information available on commensurate magnetic structures. Each magnetic structure is described using magnetic symmetry, i.e. a magnetic space group (or Shubnikov group). This ensures a robust and unambiguous description of both atomic positions and magnetic moments within a common unique formalism. A non‐standard setting of the magnetic space group is often used in order to keep the origin and unit‐cell orientation of the paramagnetic phase, but a description in any desired setting is possible. Domain‐related equivalent structures can also be downloaded. For each structure its magnetic point group is given, and the resulting constraints on any macroscopic tensor property of interest can be consulted. Any entry can be retrieved as a magCIF file, a file format under development by the International Union of Crystallography. An online visualization tool using Jmol is available, and the latest versions of VESTA and Jmol support the magCIF format, such that these programs can be used locally for visualization and analysis of any of the entries in the collection. The fact that magnetic structures are often reported without identifying their symmetry and/or with ambiguous information has in many cases forced a reinterpretation and transformation of the published data. Most of the structures in the collection possess a maximal magnetic symmetry within the constraints imposed by the magnetic propagation vector(s). When a lower symmetry is realized, it usually corresponds to an epikernel (isotropy subgroup) of one irreducible representation of the space group of the parent phase. Various examples of the structures present in this collection are discussed.

MAGNEXT is a new computer program available from the Bilbao Crystallographic Server (http://www.cryst.ehu.es) that provides symmetry‐forced systematic absences or extinction rules of magnetic nonpolarized neutron diffraction. For any chosen Shubnikov magnetic space group, the program lists all systematic absences, and it can also be used to obtain the list of the magnetic space groups compatible with a particular set of observed systematic absences. Absences corresponding to specific ordering modes can be derived by introducing effective symmetry operations associated with them. Although systematic extinctions in neutron diffraction do not possess the strong symmetry‐resolving power of those in nonmagnetic crystallography, they can be important for the determination of some magnetic structures. In addition, MAGNEXT provides the symmetry‐adapted form of the magnetic structure factor for different types of diffraction vectors, which can then be used to predict additional extinctions caused by some prevailing orientation of the atomic magnetic moments. This program, together with a database containing comprehensive general information on the symmetry operations and the Wyckoff positions of the 1651 magnetic space groups, is the starting point of a new section in the Bilbao Crystallographic Server devoted to magnetic symmetry and its applications.