In rare-earth cage compounds, the guest 4f ion cannot be considered as fixed at the centre of its cage. As result of the electronic degeneracy of the 4f shell, single-ion or collective mechanisms can redistribute the ion inside the cage, which can be described in terms of multipolar components. These mechanisms and their influence are here discussed and illustrated in relation with the rare-earth hexaboride series. Warning: Following our oral presentation, this manuscript should have appeared in the Proceedings of SCES 2014 (SCES 2014, International Conference on Strongly Correlated Electron Systems, held 7 - 11 July 2014 in Grenoble). An infuriated referee decided otherwise stating, in substance, that ... it could corrupt the youth ... (the very few interested in this particular the subject). The casual reader is here free to appreciate how far this corruption goes...
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