Superspace symmetry has been for many years the standard approach for the analysis of non-magnetic modulated crystals because of its robust and efficient treatment of the structural constraints present in incommensurate phases. For incommensurate magnetic phases, this generalized symmetry formalism can play a similar role. In this context we review from a practical viewpoint the superspace formalism particularized to magnetic incommensurate phases. We analyse in detail the relation between the description using superspace symmetry and the representation method. Important general rules on the symmetry of magnetic incommensurate modulations with a single propagation vector are derived. The power and efficiency of the method is illustrated with various examples, including some multiferroic materials. We show that the concept of superspace symmetry provides a simple, efficient and systematic way to characterize the symmetry and rationalize the structural and physical properties of incommensurate magnetic materials. This is especially relevant when the properties of incommensurate multiferroics are investigated.
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 stu...
Microsymposia C209MS complicated, like determining the electron density of states from the band structure, instructors tend to skip the long tedious calculations needed since there is not enough time for this during lectures. The online student presentations have no such limitation and can explain how to do a long calculation step-by-step. This can be a valuable resource for those trying to perform similar calculations but for whom the scientific literature is still to difficult to digest. Students teach at the right level for their fellow students to understand. The production of a collection of long and detailed calculations that go into more detail than the lectures but are written in a style that is accessible to students was an unexpected outcome of this experiment. An important factor for the success of this model is the sheer volume of material produced. The students produce much more material than a single instructor could. The students are also more likely to try new approaches. Not all material that the students produce is useful but the less useful material gets displaced by other student projects as the students continuously try to improve the course. The students of our solid state physics course have created some wonderful material that has enriched the course. The biggest challenge for the instructor is managing the influx of material that is produced.
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