Magnetic space and superspace groups, representation analysis: competing or friendly concepts?

Although encoded in theoretical works, relationships between the diffraction symmetry of magnetic structures and magnetic space/superspace groups are often ignored in practical applications. It is shown that magnetic symmetry operations have a direct impact through the rotation parts in the diffraction symmetry of the crystal and can be used to simplify calculations of magnetic structure factors. Besides, the translation parts can introduce specific systematic extinctions of magnetic reflections. Another point is that the efficiency and stability of refinement of magnetic crystal structures, in analogy with the refinement of nuclear structures, depend on direct application of the magnetic symmetry in the structure-factor formula. Magnetic symmetry also allows diffractionally independent magnetic domains and their mutual spatial orientations to be recognized. The selection of one irreducible representation can provide extra relationships between magnetic moments which do not directly affect diffraction symmetry. Thus the combination of both methods seems to be the most effective way to analyze and refine magnetic structures.