Octupole Moment as a Hidden Order Parameter in Orbitally Degenerate   f-Electron Systems
  Possibility of a novel pseudo-scalar (octupole) order is studied theoretically for orbitally degenerate systems with strong spin-orbit coupling such as Ce$_x$La$_{1-x}$B$_6$. It is discussed that coexistence of an octupole order parameter and antiferromagnetic fluctuation should lead to drastic softening of the elastic constant by a mode-mixing effect. Nonlinear coupling between dipole, quadrupole and octupole fluctuations is taken into account in terms of a Ginzburg-Landau-type functional which is derived microscopically through path integral. 
Yoshio Kuramoto and Hiroaki Kusunose