page_title: Multipolar exchange interaction
section_title: Antiferromagnetism of Multipolar Moments
hierarchical_section_title: Multipolar exchange interaction / Antiferromagnetism of Multipolar Moments
caption_attribution_description: English: Flipping the phases of multipoles Ref: Phys. Rev. B 90, 045148 (2014)
context_page_description: 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
context_section_description: Unlike magnetic spin ordering where the antiferromagnetism can be defined by flipping the magnetization axis of two neighbor sites from a ferromagnetic configuration, flipping of the magnetization axis of a multipole is usually meaningless. Taking a  moment as an example, if one flips the z-axis by making a  rotation toward the y-axis, it just changes nothing. Therefore, a suggested definition of antiferromagnetic multipolar ordering is to flip their phases by , i.e. . In this regard, the antiferromagnetic spin ordering is just a special case of this definition, i.e. flipping the phase of a dipole moment is equivalent to flipping its magnetization axis. As for high rank multipoles, e.g. , it actually becomes a  rotation and for  it is even not any kind of rotation.
caption: Flipping the phases of multipoles [21]
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