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Journal Articles

Large ferroquadrupole moment induced in the octupole-ordered Ce$$_{0.7}$$La$$_{0.3}$$B$$_6$$ revealed by high-resolution X-ray diffraction

Inami, Toshiya; Michimura, Shinji*; Hayashi, Yuya*; Matsumura, Takeshi*; Sera, Masafumi*; Iga, Fumitoshi*

Physical Review B, 90(4), p.041108_1 - 041108_5, 2014/07

 Times Cited Count:9 Percentile:42.22(Materials Science, Multidisciplinary)

We carried out a high-resolution X-ray diffraction experiment on Ce$$_{0.7}$$La$$_{0.3}$$B$$_6$$. This compound exhibits antiferro-octupole order (AFO) below $$T_O$$ = 1.4 K, and it is theoretically suggested that ferroquadrupole moments and a resultant rhombohedral deformation are induced in the AFO phase. We observe the splitting of Bragg reflections below $$T_O$$ and find that the unit cell is rhombohedral with the elongated [111] axis. We also precisely evaluate the magnitude of the induced quadrupole moments from the obtained shear strain and find that the quadrupole moments are not reduced in the AFO phase.

Journal Articles

Multipole ordering in $$f$$-electron systems on the basis of a $$j$$-$$j$$ coupling scheme

Kubo, Katsunori; Hotta, Takashi

Physical Review B, 72(14), p.144401_1 - 144401_12, 2005/10

 Times Cited Count:30 Percentile:73.99(Materials Science, Multidisciplinary)

We investigate microscopic aspects of multipole ordering in $$f$$-electron systems with emphasis on the effect of lattice structure. For the purpose, we construct $$f$$-electron models on three kinds of lattices, simple cubic (sc), bcc, and fcc, in a tight-binding approximation on the basis of a $$j$$-$$j$$ coupling scheme. Then, an effective model is derived in the strong-coupling limit for each lattice with the use of second-order perturbation theory with respect to $$(ffsigma)$$. By applying mean-field theory to such effective models, we find multipole ordered states depending on the lattice structure. For the sc lattice, a $$Gamma_{3g}$$ antiferro-quadrupole transition occurs at a finite temperature and at further lowering temperature, we find another transition to a ferromagnetic state. For the bcc lattice, a $$Gamma_{2u}$$ antiferro-octupole ordering occurs first, and then, a ferromagnetic phase transition follows it. Finally, for the fcc lattice, we find a single phase transition to the longitudinal triple-$$q$$ $$Gamma_{5u}$$ octupole ordering.

Journal Articles

Quadrupole and hexadecapole ordering in DyB$$_2$$C$$_2$$; Direct observation with resonant X-ray diffraction

Tanaka, Yoshikazu*; Inami, Toshiya; Lovesey, S. W.*; Knight, K. S.*; Yakhou, F.*; Mannix, D.*; Kokubun, Jun*; Kanazawa, Masayuki*; Ishida, Kotaro*; Nanao, Susumu*; et al.

Physical Review B, 69(2), p.024417_1 - 024417_11, 2004/01

 Times Cited Count:35 Percentile:79.89(Materials Science, Multidisciplinary)

Direct evidence of the spatial ordering of Dy 4$$f$$ quadrupole and hexadecapole moments in DyB$$_2$$C$$_2$$ is demonstrated by resonant X-ray diffraction enhanced by an electric quadrupole event ($$E$$2 resonance) at the Dy L$$_{III}$$ absorption edge. The diffraction data show that the structural phase transition at $$T$$$$_{Q}$$ = 24.7 K is accompanied by a reduction in the symmetry of the Dy site to 2/$$m$$, from 4/$$m$$, and the spatial ordering of the time-even Dy multipoles with A$$_{g}$$ character. Below $$T$$$$_{Q}$$ the crystal structure is described by the space group $$P$$4$$_2$$/$$mnm$$ and Dy ions occupy sites (4$$c$$). The distortion at T$$_{Q}$$ involves the lattice occupied by B and C ions, and it amounts to a buckling of B-C planes that are normal to the two-fold rotation axis of 2/$$m$$. An immediately plausible model of low-energy Dy states correlates data on the specific heat, our X-ray diffraction signals, and magnetic ordering below 15.3 K which has been observed in magnetic neutron diffraction.

Journal Articles

Interference between thomson scattering and resonant scattering in X-ray diffraction from CeB$$_{6}$$

Nagao, Tatsuya*; Igarashi, Junichi

Journal of the Physical Society of Japan, 72(9), p.2381 - 2384, 2003/09

 Times Cited Count:10 Percentile:55.8(Physics, Multidisciplinary)

We examine the mechanism of the X-ray diffraction process by including the Thomson scattering (TS) term in addition to the resonant X-ray scattering (RXS) term near the Ce L absorption edge in the antiferroquadrupole (AFQ) ordering phase of CeB$$_{6}$$. Assuming the AFQ order in the 4f states but without any lattice distortion, we obtain the TS intensity comparable to the RXS intensity, owing to the anisotropic charge distribution of 4f states. The present calculation reproduces well the interference pattern between the TS and RXS terms for the (5/2,3/2,3/2) spot observed in the recent experiment. The result suggests that the TS signal as well as the main peak of the RXS signal are a direct reflection of the AFQ order in CeB$$_{6}$$.

Journal Articles

Mechanism of resonant X-ray scattering in DyB$$_{2}$$C$$_{2}$$

Nagao, Tatsuya*; Igarashi, Junichi

Physica B; Condensed Matter, 329-333(Part2), p.628 - 630, 2003/05

 Times Cited Count:5 Percentile:32.08(Physics, Condensed Matter)

For elucidating the relation between the resonant X-ray scattering (RXS) signal and the orbital order, we calculate the RXS spectra near the Dy L$$_{III}$$ absorption edge in DyB$$_{2}$$C$$_{2}$$, in the antiferro-quadrupole (AFQ) ordering phase. Using a microscopic model that the 4f states of Dy are atomic while the 5d states form an energy band with a reasonable density of states, we obtain sufficient RXS intensities on the AFQ superlattice spot assuming the quadrupole order in the 4f states but without any lattice distortion, in good agreement with the recent experiment. The present result demonstrates the mechanism that the intensity is brought about by the modulation of 5d states through the anisotropic term of the 5d-4f Coulomb interaction.

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