I saw this sentence "The spin structure of the Fe sites is of the GxAyFz type in Bertaut's notation" in the literature(DOI: 10.1038/NMAT2469). Does anybody has the illustration of GxAyFz ??
Do you understand the classification of Bravais lattices through crystallographic point groups and the associated space groups (and in particular Fedorov groups)? That might be a good starting point to get somewhat familiar with the notations for finite groups. Then, you can start to look at spin structures and so-called magnetic space groups and their classification. Basically, magnetic space groups extend crystallographic space groups with the time-reversal operator. You might like to look at http://stokes.byu.edu/iso/magneticspacegroupshelp.php for explanations and some simple illustrations.
@Maxime Bagnoud: Thank you. The classification of Bravais lattices through crystallographic point groups and the associated space groups is in my knowledge. It is very useful for the site:http://stokes.byu.edu/iso/magneticspacegroupshelp.php. By the way, is there any visual software for magnetic space groups? It is hard to imagine the map of spin structure.
You're welcome. Take a look at the article from http://www.iucr.org/__data/assets/pdf_file/0006/13929/final_23.pdf
Besides having nice visualizations, he seems to put his graphical routines at public disposal. His author, de Baer also wrote a book with McHenry: Introduction to Crystallography, Diffraction and Symmetry (see https://books.google.ch/books?id=NMUgAwAAQBAJ&pg=PA223&lpg=PA223&dq=visualization+of+magnetic+groups&source=bl&ots=VQ3MagtpF8&sig=oEbp78MRrjxPfdt2D1WUpDY5cwM&hl=en&sa=X&ei=ucjTVIjrFI3SaJjLgKgB&ved=0CEwQ6AEwBw#v=onepage&q=visualization%20of%20magnetic%20groups&f=false). You might also want to look at http://www.cryst.ehu.es/
Good luck!
http://iopscience.iop.org/article/10.1088/0953-8984/28/12/123001
in this paper you can find a nice visualization of the Bertaut's notaion including GxAyFz
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