Description of Multipole in f-Electron Systems

A systematic description of multipole degrees of freedom is discussed on the basis of the Stevens' operator-equivalent technique. The generalized Stevens' multiplicative factors are derived for all of the electric and the magnetic multipoles relevant to f-electron systems. With extensive use of the Stevens' factors, we express the spatial dependences of the electric and the magnetic fields, and the electric and the magnetic charge densities of localized f electrons. The latter is utilized to draw wave functions including their magnetic profile in addition to their shape with the charge density. The definite relation between the operators as quantum-mechanical variables in a multipole exchange model and the multipole moments in expansion of electromagnetic fields is given. The general treatments for the exchange model with the RPA susceptibility and the Ginzburg-Landau free-energy expansion are discussed, using CexLa1-xB6 as a typical example. The representative formula of the vector spherical harmonics are summarized, which are suitable basis for vector fields in the spherical expansion.