Spin translation groups and neutron diffraction analysis

Groups that are a generalization of magnetic groups, and called 'spin groups', are defined. Among the spin groups those called 'spin translation groups' are tabulated and described in some detail. The possible magnetic reflexions of unpolarized neutrons elastically scattered from a single crystal whose spin arrangement is invariant under a spin translation group are also tabulated. It is shown how by using these tables and considering the indices of magnetic reflexions one can obtain information on the mutual orientation of non-collinear spins without making any assumptions on the rotational symmetry of the spin arrangement. As an example of this, the neutron diffraction data of the 'umbrella' spin arrangement of CrSe is reanalysed.