Table of Contents
Physics Research International
Volume 2012 (2012), Article ID 762798, 9 pages
Research Article

Microscopic Theory of Multipole Ordering in -Electron Systems

1Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan
2Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan

Received 31 August 2011; Accepted 2 February 2012

Academic Editor: Vladimir Shavrov

Copyright © 2012 Takashi Hotta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A microscopic framework to determine multipole ordering in -electron systems is provided on the basis of the standard quantum field theory. For the construction of the framework, a seven-orbital Hubbard Hamiltonian with strong spin-orbit coupling is adopted as a prototype model. A type of multipole and ordering vector is determined from the divergence of multipole susceptibility, which is evaluated in a random phase approximation. As an example of the application of the present framework, a multipole phase diagram on a three-dimensional simple cubic lattice is discussed for the case of , where n denotes the average -electron number per site. Finally, future problems concerning multipole ordering and fluctuations are briefly discussed.