Microscopic Theory of Multipole Ordering in -Electron Systems

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 =2, where n denotes the average -electron number per site. Finally, future problems concerning multipole ordering and fluctuations are briefly discussed.