Multipolar exchange interaction: Difference between revisions

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Magnetic materials with strong [[spin-orbit couplinginteraction]], such as: LaFeAsO<ref name="LaFeAsO"> F. Cricchio, O. Granas, and L. Nordstrom, Phys. Rev. B. 81, 140403 (2010); R. S. Gonnelli, D. Daghero, M. Tortello, G. A. Ummarino, V. A. Stepanov, J. S. Kim, and R. K. Kremer, Phys. Rev. B 79, 184526 (2009) </ref>, PrFe4P12<ref name="PrFe4P12"> A. Kiss and Y. Kuramoto, J. Phys. Soc. Jpn. 74, 2530 (2005); H. Sato, T. Sakakibara, T. Tayama, T. Onimaru, H. Sugawara, and H. Sato, J. Phys. Soc. Jpn. 76, 064701 (2007) </ref>

, YbRu2Ge2<ref name="YbRu2Ge2"> T. Takimoto and P. Thalmeier, Phys. Rev. B 77, 045105 (2008) </ref>, UO2<ref name="UO2"> S.-T. Pi, R. Nanguneri, and S. Savrasov, Phys. Rev. Lett. 112, 077203 (2014); P. Giannozzi and P. Erdos, J. Mag. Mag Mater. 67, 75 (1987). V. S. Mironov, L. F. Chibotaru, and A. Ceulemans, Adv. Quan. Chem. 44, 599 (2003); S. Carretta, P. Santini, R. Caciuffo, and G. Amoretti, Phys. Rev. Lett. 105, 167201 (2010); R. Caciuffo, P. Santini, S. Carretta, G. Amoretti, A. Hiess, N. Magnani, L. P. Regnault, and G. H. Lander, Phys. Rev. B 84, 104409 (2011) </ref>, NpO2 <ref name="NpO2"> P. Santini and G. Amoretti, Phys. Rev. Lett 85, 2188 (2000); P. Santini, S. Carretta, N. Magnani, G. Amoretti, and R. Caciuffo, Phys. Rev. Lett. 97, 207203 (2006); K. Kubo and T. Hotta, Phys. Rev. B 71, 140404 (2005) </ref>, Ce1−xLaxB6<ref name="Ce1−xLaxB6"> D. Mannix, Y. Tanaka, D. Carbone, N. Bernhoeft, and S. Kunii, Phys. Rev. Lett. 95, 117206 (2005) </ref>, URu2Si2<ref name="URu2Si2"> P. Chandra, P. Coleman, J. A. Mydosh, and V. Tripathi, Nature (London) 417, 831 (2002); Francesco Cricchio, Fredrik Bultmark, Oscar Granas, and Lars Nordstrom, Phys. Rev. Lett. 103, 107202 (2009); Hiroaki Ikeda, Michi-To Suzuki, Ryotaro Arita, Tetsuya Takimoto, Takasada Shibauchi, and Yuji Matsuda, Nat. Phys. 8, 528 (2012); A. Kiss and P. Fazekas, Phys. Rev. B 71, 054415 (2005); J. G. Rau and H.-Y. Kee, Phys. Rev. B 85, 245112 (2012) </ref> and many other compounds, are found to have magnetic ordering constituted by high rank multipoles, e.g quadruple, octople, etc<ref name="Review"> R. Caciuffo et al., Rev. Mod. Phys. 81, 807 (2009) </ref>. Due to the strong spin-orbit coupling, multipoles are automatically introduced to the systems when the [[total angular momentmomentum 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 <ref name="NpO2"/> <ref name="Ce1−xLaxB6"/> <ref name="URu2Si2"/>