the low-temperature phase of breaking time-reversal symmetry.[@Kopmann98]

A natural way to reconcile with the above observations is to introduce the higher-rank multipole ordering rather than the dipole moment. Actually, Santini and Amoretti proposed a octupole ordering of $\Gamma_{2}(xyz)$ symmetry.[@Santini00; @Santini02] However, this phase can be ruled out because it gives rise to no RXS intensity. Recently, Paixão *et al*. have reported that a longitudinal triple-**k** octupole ordering accounts well for their RXS experiment.[@Paixao02] The reason for anticipating triple-**k** orderings is that it excludes a crystal distortion or a shift of oxygen positions, which is consistent with the experiment. Experimental data obtained from the $^{17}$O NMR spectrum, which indicate the existence of two inequivalent oxygen sites, support the occurrence of the triple-**k** octupole ordering phase.[@Tokunaga05] Some theoretical works also have lent support to realization of this type of the phase.[@Kiss03; @Kubo05]

Assuming the $\Gamma_8$-quartet ground state, we explicitly construct a triple-**k** octupole ordering state. This state is found to simultaneously carry a finite quadrupole moment, which generates the RXS intensity. Since the RXS amplitudes are characterized by three terms, the scalar, dipole, and quadrupole ones, it is not necessary to assume the existence of the hexadecapole moment instead of the quadrupole 