Long-range ordering and representational analysis of the jarosites

The jarosites are the most studied family of kagomé antiferromagnets. Despite these works little is still known about the detailed causes of the observed magnetic structures. In this article representational analysis is used to determine the possible symmetry-allowed magnetic structures for the observed propagation vectors, and to examine their stability conditions. Refinements are presented of the magnetic structures of ${\mathrm{AgFe}}_3\left({\mathrm{SO}}_4{)}_2\right(\mathrm{OD}{)}_6$ and $\left({\mathrm{H}}_3\mathrm{O}\right){\mathrm{V}}_3\left({\mathrm{SO}}_4{)}_2\right(\mathrm{OH}{)}_6.$ The steps required for these calculations and the refinement of the models against the neutron-diffraction data are detailed.