Antiferroquadrupole order and magnetic field induced octupole in CeB6

We have studied the antiferroquadrupole ordered phase of CeB6 in magnetic fields by resonant x-ray diffraction. By analyzing the significant change in the energy spectrum on reversing the field direction along [(1) over bar 1 0], we have deduced field dependencies of the antiferro components of magnetic dipole, electric quadrupole, and magnetic octupole moments which are simultaneously induced in the Ce 4f orbital with a propagation vector (1/2, 1/2, 1/2). The data treatments are based on theoretically calculated spectral functions. The existence of the field-induced octupole is also concluded for other field directions. We also show direct evidence for the formation of a linear-combination-type antiferroquadrupole order parameter in magnetic fields, which is expressed as (alpha O-yz + beta O-zx + gamma O-xy) and changes continuously with the field direction (alpha, beta, gamma). A possibility of observing the quadrupolar fluctuation is also pointed out.