The azimuthal angle dependence observed in the resonant X-ray scattering in phase IV of Ce 0.7 La 0.3 B 6 is analyzed theoretically. It is shown that the peculiar angle dependence observed in the E2 channel is consistent with the Γ 5u -type octupole order with principal axis along (111) and equivalent directions. Under the assumption that the four equivalent octupole domains are nearly equally populated in the sample, the observed angle dependences are reproduced by calculation for both σσ ′ and σπ ′ polarizations. The calculation for various symmetries of order parameters excludes unambiguously other order parameters than the Γ 5u -type octupole. and Ce x La 1−x B 6 . [5][6][7] In particular, Ce x La 1−x B 6 exhibits a rich variety of the H-T phase diagram, called I-IV. 8,9 The importance of the octupole degrees of freedom was first recognized by Sakai and co-workers 10,11 in resolving the inconsistency between NMR and the neutron scattering measurements in the antiferro-quadrupole phase II. Soon after their work, possible relevance of the Γ 5u -type octupole to the magnetic phase III and III' was pointed out. 6 For consistent understanding of the overall phase diagram, this type of octupole was also suggested as a hidden order parameter of phase IV. 6 The prediction of the accompanied lattice distortion along the [111] axis is indeed observed.
KEYWORDS12 The model of the Γ 5u -type octupole order explains most of the characteristic behaviors in phase IV, 7 such as the cusp-like behavior in the uniform susceptibility, 9 no significant magnetic reflection in neutron scattering, 13 and the huge softening of C 44 mode in the strain susceptibility 14 as well as the spontaneous lattice distortion along [111].12 However, there has been no direct evidence from diffraction experiment.Resonant X-ray scattering (RXS) measurement has been performed recently to obtain a direct evidence of the order parameter symmetry in phase IV. 19 The RXS has already proven its efficiency in various systems such as LaMnO 3 , 15 DyB 2 C 2 16-18 and NpO 2 . 2, 3 The measurement was done for Ce 0.7 La 0.3 B 6 below T IV = 1.5 K, using the L 2 absorption edge in the Ce atom. 19 They measured the azimuthal angle dependences of the superlattice Bragg reflections at q = (3/2, 3/2, 3/2) with the rotation axis normal to the [111] surface. Both the non-rotated (σ-σ ′ ), and the rotated (σ-π ′ ) polarization channels have been measured at the electric quadrupole (E2) resonance. In the σ-σ ′ channel, the scattering intensity exhibits six-fold oscillation, which indicates the occurrence of the electronic order with three-fold symmetry along [111]. In contrast, the σ-π ′ channel shows three-fold oscillation, which remains to be clarified. It is not clear to us how the fitting in ref.19 is justfied microscopically.In this Letter, we demonstrate that the Γ 5u -type octupole order can reproduce the azimuthal angle dependences both in the σ-σ ′ and σ-π ′ channels. The three-fold oscillation is explained in terms of domains whose principal axis is other ...