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Due to the particular geometry of the kagom\'e lattice, it is shown that antisymmetric Dzyaloshinsky-Moriya interactions are allowed and induce magnetic ordering. The symmetry of the obtained low-temperature magnetic phases are studied through mean field approximation and classical Mont\'e Carlo simulations. A phase diagram relating the geometry of the interaction and the ordering temperature has been derived. The order of magnitude of the anisotropies due to Dzyaloshinsky-Moriya interactions are more important than in nonfrustrated magnets, which enhances its appearance in real systems. Application to the jarosites compounds is proposed. In particular, the low-temperature behaviors of the Fe- and Cr-based jarosites are correctly described by this model.
Elhajal et al. (Wed,) studied this question.