Theory of Coupled Multipole Moments Probed by X-ray Scattering in   CeB$_6$
  A minimal model for multipole orders in CeB$_6$ shows that degeneracy of the quadrupole order parameters and strong spin-orbit coupling lead to peculiar temperature and magnetic-field dependences of the X-ray reflection intensity at superlattice Bragg points. Furthermore, the intensity depends sensitively on the surface direction. These theoretical results explain naturally recent X-ray experiments in phases II and III of CeB$_6$. It is predicted that under weak magnetic field perpendicular to the (111) surface, the reflection intensity should change non-monotonically as a function of temperature. 
Hiroshi N. Kono, Katsunori Kubo and Yoshio Kuramoto