Multipolar exchange interaction

Magnetic materials with strong spin-orbit interaction, such as: LaFeAsO, PrFe4P12 , YbRu2Ge2, UO2, NpO2, Ce1−xLaxB6, URu2Si2 and many other compounds, are found to have magnetic ordering constituted by high rank multipoles, e.g. quadruple, octople, etc. 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