Observation of Multipole Orderings in f-Electron Systems by Resonant X-ray Diffraction

Abstract

In f-electron systems, the spin and orbital degrees of freedom are coupled through strong spin–orbit interaction to form a J-multiplet. The J-multiplet is further split into several crystalline electric field levels, where each level has its own electric and magnetic characters. In such cases, it is appropriate to describe the electronic degrees of freedom in terms of multipole moments. Actually in f-electron systems, there are cases where higher order multipole moments order by themselves and play important roles in their physical properties. In this chapter, we start by explaining the basic concept and usage of multipole moments. It is especially important to understand electric and magnetic multipole moments are coupled in magnetic fields. After explaining how the multipole moments are involved in the formalism of resonant X-ray scattering, we describe some typical experimental cases, where resonant X-ray diffraction has played a conclusive role.