Spin groups

Suggestions of Naish, Kitz, and Brinkman and Elliot to introduce groups that are more general than magnetic space groups for describing spin arrangements in magnetic crystals have not been carried out by these authors in a general and mathematically rigorous way. These deficiencies are removed in this paper by defining such more general groups, which we call spin groups (and of which magnetic groups are a special case), starting out from first principles and deducing some fundamental properties of these groups: in particular, the structure of the most general symmetry spin group of a spin arrangement is derived. The principles of constructing all spin groups and using spin groups to classify all spin arrangements are described. Also the effect of such spin-group symmetries on elastic magnetic neutron diffraction is briefly discussed.