In this thesis we investigate the magnetism of a selection of crystalline mate- rials that display fascinating macroscopic properties, largely due to the complex behaviour of rare-earth ions. The technique of choice is diffraction; shown to pro- vide the most lucid of results in this field of research. Neutron powder diffraction, a well established tool for determining magnetic structures, has been employed in order to determine two magnetic structures of the intermetallic R2CoGa8 series. This was the first such study of these materials, which are of great interest as the magnetic exchange interactions of the rare-earth ions compete with the crystal elec- tric field, giving rise to a wealth of magnetic properties tuneable by the choice of rare-earth ion. We then move on to study two of the most extreme multiferroic mate- rials, TbMn2O5 and TmMn2O5. We have developed a new technique for determin- ing electronic state specific magnetic structures through resonant x-ray diffraction, which we have successfully employed in an investigation of the terbium magnetic sub-lattice in TbMn2O5. The outstanding question in many multiferroics regards the exact microscopic mechanisms at play. Due to the huge potential in technology, this has been the subject of intense debate over that past decade. We have shown, through ab-initio computation and the simultaneous measurement of electric polar- isation and magneto-striction, that the exchange-striction model is dominant in the main ferroelectric phase of TbMn2O5 and TmMn2O5. Through ion specific resonant x-ray diffraction measurements, we have clarified the behaviour of the terbium sub- lattice upon the magnetic field induced electric polarisation reversal in TbMn2O5. Furthermore, we have made the discovery of additional incommensurate magnetic diffraction signals, believed to be indicative of the response of magnetic domains to applied magnetic fields
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