We have studied the antiferroquadrupole ordered phase of CeB${}_6$ in magnetic fields by resonant x-ray diffraction. By analyzing the significant change in the energy spectrum on reversing the field direction along $\left[\overline{1}10\right]$, 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 $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$. 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 $\langle \alpha O_{yz}+\beta O_{zx}+\gamma O_{xy}\rangle$ and changes continuously with the field direction $(\alpha ,\beta ,\gamma )$. A possibility of observing the quadrupolar fluctuation is also pointed out.

• Received 1 February 2012

DOI:https://doi.org/10.1103/PhysRevB.85.174417