Octupole moment as a hidden order parameter in orbitally degenerate f-electron systems

Possibility of a novel pseudoscalar (octupole) order is studied theoretically for orbitally degenerate systems with strong spin-orbit coupling such as Ce_xLa_1-xB₆. We argue that coexistence of an octupole order parameter and antiferromagnetic fluctuation should lead to marked 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 a path integral.