Magnetically ordered quasicrystals: enumeration of spin groups and calculation of magnetic selection rules

Details are given of the theory of magnetic symmetry in quasicrystals, which has previously only been outlined. A practical formalism is developed for the enumeration of spin point groups and spin space groups, and for the calculation of selection rules for neutron scattering experiments. The formalism is demonstrated using the simple, yet non-trivial, example of magnetically ordered octagonal quasicrystals in two dimensions. In a companion paper [Even-Dar Mandel & Lifshitz (2004). Acta Cryst. A60, 179-194], complete results are provided for octagonal quasicrystals in three dimensions.