Magnetic materials with strong spin-orbit interaction, such as: LaFeAsO,[1][2] PrFe4P12,[3][4] YbRu2Ge2,[5] UO2,[6][7][8][9][10] NpO2,[11][12][13] Ce1−xLaxB6,[14]URu2Si2[15][16][17][18][19] and many other compounds, are found to have magnetic ordering constituted by high rank multipoles, e.g. quadruple, octople, etc.[20] Due to the strong spin-orbit coupling, multipoles are automatically introduced to the systems when the total angular momentum quantum number J is larger than 1/2. If those multipoles are coupled by some exchange mechanisms, those multipoles could tend to have some ordering as conventional spin 1/2 Heisenberg problem. Except the multipolar ordering, many hidden order phenomena are believed closely related to the multipolar interactions [11][14][15]
https://en.wikipedia.org/wiki/Multipolar_exchange_interaction
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