Samuel V. Gallego

Magnetic symmetry in the Bilbao Crystallographic Server: a computer program to provide systematic absences of magnetic neutron diffraction

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.

MAGNDATA: towards a database of magnetic structures. I. The commensurate case

A free web page under the name MAGNDATA, which provides detailed quantitative information on more than 400 published magnetic structures, has been made available at the Bilbao Crystallographic Server (http://www.cryst.ehu.es). It includes both commensurate and incommensurate structures. In the first article in this series, the information available on commensurate magnetic structures was presented [Gallego, Perez-Mato, Elcoro, Tasci, Hanson, Momma, Aroyo & Madariaga (2016). J. Appl. Cryst. 49, 1750–1776]. In this second article, the subset of the database devoted to incommensurate magnetic structures is discussed. These structures are described using magnetic superspace groups, i.e. a direct extension of the non-magnetic superspace groups, which is the standard approach in the description of aperiodic crystals. The use of magnetic superspace symmetry ensures a robust and unambiguous description of both atomic positions and magnetic moments within a common unique formalism. The point-group symmetry of each structure is derived from its magnetic superspace group, and any macroscopic tensor property of interest governed by this point-group symmetry can be retrieved through direct links to other programs of the Bilbao Crystallographic Server. The fact that incommensurate magnetic structures are often reported with ambiguous or incomplete information has made it impossible to include in this collection a good number of the published structures which were initially considered. However, as a proof of concept, the published data of about 30 structures have been re-interpreted and transformed, and together with ten structures where the superspace formalism was directly employed, they form this section of MAGNDATA. The relevant symmetry of most of the structures could be identified with an epikernel or isotropy subgroup of one irreducible representation of the space group of the parent phase, but in some cases several irreducible representations are active. Any entry of the collection can be visualized using the online tools available on the Bilbao server or can be retrieved as a magCIF file, a file format under development by the International Union of Crystallography. These CIF-like files are supported by visualization programs like Jmol and by analysis programs like JANA and ISODISTORT.

Symmetry conditions for type II multiferroicity in commensurate magnetic structures

Type II multiferroics are magnetically ordered phases that exhibit ferroelectricity as a magnetic induced effect. We show that in single-k magnetic phases the presence in the paramagnetic phase of non-symmorphic symmetry combined with some specific type of magnetic propagation vector can be sufficient for the occurrence of this type of multiferroic behaviour. Other symmetry scenarios especially favourable for spin driven multiferroicity are also presented. We review and classify known type II multiferroics under this viewpoint. In addition, some other magnetic phases which due to their symmetry properties can exhibit type II multiferroicity are pointed out.

Materials studies by the Bilbao Crystallographic Server

The Bilbao Crystallographic Server (www.cryst.ehu.es) is a free web site with an access to crystallographic data of space and point groups, magnetic space groups, subperiodic groups, their representations and group-subgroup relations [1]. Wide range of complex solid-state physics and structure-chemistry aspects of materials studies are facilitated by the specialized software provided by the server. The server offers a set of structure-utility programs including basic tools for transformations between different structure descriptions or transformations compatible with a specific symmetry reduction. There is an online tool (COMPSTRU) for a quantitative analysis of the similarity of two structure models, also helpful for the recognition of identical or nearly identical atomic arrangements of different compounds. The program STRUCTURE RELATIONS for the analysis of structure relations between two phases of the same compound with group-subgroup related space groups is of great utility for the construction of family trees of homeotypic crystal structures, known as Baernighausen trees.
 The program AMPLIMODES performs the decomposition of the global distortion into symmetry-mode contributions and classifies the correlated atomic displacements separating the so-called primary modes (fundamental for the phase stability), from the weaker distortions of limited relevance for the transition mechanism [2]. The server also offers online tools for the evaluation of the pseudosymmetry of a given structure with respect to a supergroup of its space group, which could serve as a powerful method for the prediction of new ferroic materials. Of special interest is the program SUBGROUPS which extends further the capabilities of the server in the symmetry characterization of distorted structures by providing their possible subgroup symmetries given the relationship of the distorted to the parent undistorted lattice. Recently implemented computational tools and databases in the server allow the systematic application of symmetry arguments in the study of magnetic structures [3]. There is an online access to basic crystallographic data of magnetic space groups in different settings (MGENPOS, MWYCKPOS), to the systematic absences for non-polarized neutron magnetic diffraction and also to the symmetry-adapted forms of the corresponding structure factors (MAGNEXT). The user can identify a magnetic space group from its symmetry operations given in an arbitrary setting (IDENTIFY MAGNETIC GROUP), derive the possible magnetic space groups for a given set of propagation vectors (MAXMAGN, k-SUBGROUPSMAG) or generate a magnetic structure model complying with a chosen magnetic space group (MAGMODELIZE). The server offers an access to a database of more than 400 published magnetic structures (MAGNDATA) described using magnetic space groups for commensurate structures, and magnetic superspace groups for incommensurate structures. The presentation of the databases and programs offered by the Bilbao Crystallographic Server will be accompanied by case studies illustrating the capacity and efficiency of the online tools in material studies.

A collection of magnetic structures with cif-like files as a database seed

We report the release within the Bilbao Crystallographic server [1] of a webpage providing detailed quantitative information on a representative set of published magnetic structures. Under the name of MAGNDATA (www.cryst.ehu.es/magndata) more than 140 entries are available. Each magnetic structure has been saved making use of magnetic symmetry, i.e. Shubnikov magnetic groups for commensurate structures, and magnetic superspace groups for incommensurate ones. This ensures a unified communication method and a robust and unambiguous description of both atomic positions and magnetic moments. The origin and main crystallographic axes of the parent phase are usually kept, with the cost of often using a non-standard setting for the magnetic symmetry. The magnetic point group is also given, so that the allowed macroscopic tensor properties can be derived. The fact that magnetic structures are being described according to various methods, often with ambiguous information, has forced an elaborate interpretation and transformation of the original data. For this purpose the freely available internet tools MAXMAGN [1] and ISODISTORT [2] have been our essential tools. Most of the analyzed structures happen to possess maximal magnetic symmetries within the constraints imposed by the magnetic propagation vector, and the relevant model could be derived in a straightforward manner using MAXMAGN [1]. In a few cases a lower symmetry is realized, but then it corresponded to one isotropy subgroup of one or several irreducible representations (irreps) of the paramagnetic grey space group, and ISODISTORT [2] could be applied to model the structure. Although the structure description is done using magnetic groups, the active irrep(s) are also given in most cases. The entries of the collection can be retrieved in a cif-like format, which is supported by internet tools as STRCONVERT [1] and ISOCIF [2], the visualization program VESTA [3], and some refinement programs (JANA2006, FULLPROF). Each entry also includes Vesta files that allow the visualization of a single magnetic unit cell.

Phase-transition studies at the Bilbao Crystallographic Server

The Bilbao Crystallographic Server (www.cryst.ehu.es) is a free web site with crystallographic databases and programs. The server is built on a core of databases that contain crystallographic data of space groups, magnetic space groups, subperiodic groups and their symmetry relations. Parallel to the crystallographic software we have developed specialized tools for the analysis of complex solid-state physics and structural chemistry problems. The aim of this contribution is to report on databases and computer programs of the server that facilitate complete and thorough phase-transition studies. Starting from the experimental structures of the high- and low-symmetry phases the program STRUCTURE RELATIONS studies the crystal-structure relationship between two phases. It is characterized by a global distortion that, in general, can be decomposed into homogeneous strain and atomic displacement field. The program AMPLIMODES [2] performs the decomposition of the global distortion into symmetry-mode contributions, and the determination of the corresponding polarization vectors. This type of analysis separates the correlated atomic displacements that are fundamental for the phase stability, the so-called primary modes, from the weaker distortions of limited relevance for the transition mechanism. The server also offers online tools for the evaluation of the pseudosymmetry of a given structure with respect to a supergroup of its space group [3]. The detection of structural pseudosymmetry as the consequence of a small distortion of a higher symmetry is a powerful method for the prediction of new ferroic materials. Recently, computer databases and tools for the analysis of magnetic phase transitions have been implemented. Case studies will accompany the presentation of the programs offered by the Bilbao Crystallographic Server and will illustrate their capacities and efficiency in phase-transition studies.

Bilbao Crystallographic Server: new tools and improvements

The Bilbao Crystallographic Server (http://www. cryst.ehu.es) website offers crystallographic databases and programs [1,2]. It can be used free of charge from any computer with a web browser via Internet. The server has been operating for more than ten years, and new programs and applications are constantly being developed. The aim of the present contribution is to report on the current state of the server emphasizing on the newly developed computer tools and the underlying crystallographic algorithms. The utility of the available applications will be demonstrated by illustrative examples. The server is built on a core of databases that include data from International Tables, Vol. A: Space-group symmetry, Vol. A1: Symmetry Relations between Space Groups and Vol. E: Subperiodic groups. A k-vector database with Brillouin-zone figures and classification tables of the wave vectors for all 230 space groups is also available. Recently, a Magnetic Space Groups database with general positions and Wyckoff positions in both OG and BNS notations, alongside with a new tool for the calculation of systematic absences have also been incorporated into the server [3]. There are a number of online applications essential for problems involving group-subgroup relations between space groups and their irreducible representations. The database of incommensurate structures, hosted by the server, contains both single-modulated structures and composites. A set of recently developed structure-utility programs includes basic tools for transformations between different structure descriptions as for example, switching between different settings or structure transformations compatible with a specific symmetry reduction. The server offers an online tool for a quantitative analysis of the similarity of two structure models, also helpful for the recognition of identical or nearly identical atomic arrangements of different compounds. There is a program for the study of structure relations between two phases of the same compound with group-subgroup related space groups. The tool is of great utility for the construction of family trees of homeotypic crystal structures, known as Baernighausen trees. Parallel to the crystallographic software there are a number of programs facilitating the study of specific problems related to solid-state physics, structural chemistry and crystallography. There are online tools for evaluation of the pseudosymmetry of a given structure, for group-theoretical analysis of structural phase transitions or for the determination of phonon extinction rules in inelastic neutron scattering and diffuse scattering experiments. Of special interest is a set of newly developed tools for the analysis of the infrared and Raman activity of phonon modes at the Brillouin-zone centre, including the calculation of selection rules of infrared, Raman, hyper-Raman and second-order processes, or the polarization selection rules for different configurations of the scattering experiment. The available data on group-subgroup relations between point and space groups and the corresponding correlations between their irreducible representations permit the analysis of the behaviour of the phonon modes during a symmetry break. One of the authors (EST) would like to thank TUBITAK for financial support through 2232 fellowship program.