Direct Observation of Antiferroquadrupolar Ordering: Resonant X-Ray Scattering Study of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>DyB</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Hirota, K.; Oumi, N.; Matsumura, T.; Nakao, Hironori; Wakabayashi, Yusuke; Murakami, Youichi; Endoh, Y.

doi:10.1103/physrevlett.84.2706

Cited by 161 publications

(127 citation statements)

References 17 publications

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“…36,37,38,39,40,41,42,43 The intermediate state is created by the transition from the 2p-core to 5d states. Since the 5d states are considerably delocalized with forming energy bands, the assumption that the intermediate state preserves the rotational invariance becomes less accurate.…”

Section: Discussionmentioning

confidence: 99%

Resonant x-ray scattering spectra from multipole ordering: NpM4,5edges inNpO2

Nagao

Igarashi

2005

Phys. Rev. B

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We study resonant x-ray scattering (RXS) at Np M4,5 edges in the triple-k multipole ordering phase in NpO2, on the basis of a localized electron model. We derive an expression for RXS amplitudes to characterize the spectra under the assumption that a rotational invariance is preserved in the intermediate state of scattering process. This assumption is justified by the fact that energies of the crystal electric field and the intersite interaction is smaller than the energy of multiplet structures. This expression is found useful to calculate energy profiles with taking account of the intra-Coulomb and spin-orbit interactions. Assuming the Γ8-quartet ground state, we construct the triple-k ground state, and analyze the RXS spectra. The energy profiles are calculated in good agreement with the experiment, providing a sound basis to previous phenomenological analyses.

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Section: Discussionmentioning

confidence: 99%

Resonant x-ray scattering spectra from multipole ordering: NpM4,5edges inNpO2

Nagao

Igarashi

2005

Phys. Rev. B

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“…We make critical comparisons between our results for TmTe and the experimental ones for CeB 6 . First, we assert that the intensities expected from TmTe at several forbidden Bragg spots are sufficient enough to be experimentally detected.…”

Section: Studies On X-ray Thomson Scattering From Antiferroquadrupolamentioning

confidence: 99%

“…For example, the AFQ ordering phases in CeB 6 and DyB 2 C 2 are investigated in detail by means of RXS [3][4][5][6][7] and Thomson 1/18 scattering. 4,[8][9][10] On the other hand, the situation of TmTe may still be rudimentary.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, various experimental and theoretical studies have been devoted to clarify the nature of the ordered phase of multipole order parameters with rank higher than one. 1, 2 Among the most investigated systems, the materialization of the antiferroquadrupole (AFQ) ordering phase has been established in the materials such as CeB 6 and DyB 2 C 2 .…”

Section: Introductionmentioning

confidence: 99%

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Studies on X-ray Thomson Scattering from Antiferroquadrupolar Order in TmTe

Nagao

Shiina

2010

J. Phys. Soc. Jpn.

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We study Thomson scattering from the antiferroquadrupole ordering phase in TmTe. On the basis of the group theoretical treatment, we classify the selection rules of the scattering intensity governed by the orientation of the scattering vector G. Then, numerical verification is performed by invoking the ground states which are deduced from a J = 7 2 multiplet model. The obtained intensity varies drastically depending on the magnitude and direction of G.We also calculate the scattering intensities under the applied field for H (001) and (110).Their results behave differently when the orientation of G is changed, which is ascribed to the difference of their primary order parameters; O (110), respectively. We make critical comparisons between our results for TmTe and the experimental ones for CeB 6 . First, we assert that the intensities expected from TmTe at several forbidden Bragg spots are sufficient enough to be experimentally detected. Second, their intensities at

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“…In the last few years the investigation of resonant scattering phenomena has allowed novel studies of antiferromagnetism (through resonant magnetic xray scattering 1 ) and, more recently, of orbital 2,3,4,5 and quadrupolar order 6 . Although much progress has been made in the theory and interpretation of these effects, a large number of open questions concerning the origin of the scattering remains.…”

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confidence: 99%

Polarization analysis of K-edge resonant X-ray scattering of germanium

Detlefs

2004

Physica B: Condensed Matter

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The polarization of K-edge resonant scattering at the space group "forbidden" (0 0 6) reflection of Ge was measured as function of the azimuthal angle, ψ. The experimental results are compared to model calculations based on symmetry analysis of the resonant scattering tensors.PACS numbers: 61.10. Dp, 61.10.Eq, 78.70.Ck In the last few years the investigation of resonant scattering phenomena has allowed novel studies of antiferromagnetism (through resonant magnetic xray scattering 1 ) and, more recently, of orbital 2,3,4,5 and quadrupolar order 6 . Although much progress has been made in the theory and interpretation of these effects, a large number of open questions concerning the origin of the scattering remains.A characteristic feature of resonant scattering is its polarization dependence, which differs markedly from that of normal Thompson scattering. Indeed, polarization analysis (PA) has now been developed into a standard tool for the study of the aforementioned effects. In this communication I present a study of resonant x-ray scattering at the Ge K-edge with emphasis on the analysis of polarization effects. Anisotropic tensor susceptibility (ATS) scattering 7,8,9 and orbital/quadrupolar order resonances are intimately related as the scattering arises from the same transitions between core level and valence band electronic states 10 . Therefore systematic studies of a well-known reference system may lead to better understanding of the complex situation in compounds exhibiting orbital order.One may distinguish three different classes of ATS scattering, depending on the rank of the scattering tensor: The original experiment on NaBrO 3 may be described by second rank tensors corresponding to electric dipole (E1) transitions 7,8,9 . A later experiment on α−Fe 2 O 3 evidenced electric quadrupole (E2) transitions, which give rise to fourth rank tensors 11 . Finally, ATS scattering in Ge was attributed to rank three tensors. Two different origins of this tensor were proposed: An E1-E2 mixed resonance 12,13,14 , and an E1-E1 process combined with a displacement of the scattering atom due to thermal motion 15,16 . The subject is still under discussion 17,18 .The azimuthal dependence of the scattered beam intensity was calculated and experimentally verified by Templeton and Templeton 12 , but without polarization analysis. For some selected photon energies, the phase of the (0 0 6) and (2 2 2) resonant scattering was determined by Lee et al. 19 through the interference with Umweg reflections. Finally, Kokubun et al. 15 and Kirfel et al. 16 studied the temperature dependence of the (0 0 2) and (0 0 6) resonant scattering. They observed a strong increase of the intensity with increasing temperature, but only minor variations in the line shape of the resonance.They concluded that the dominant origin of resonant scattering lies in anisotropic thermal motion of the Ge atoms.The aim of the present experiment was to complement the existing body of experimental data to further study resonant x-ray scattering of odd-rank...

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Direct Observation of Antiferroquadrupolar Ordering: Resonant X-Ray Scattering Study ofDyB2C2

Cited by 161 publications

References 17 publications

Resonant x-ray scattering spectra from multipole ordering: NpM4,5edges inNpO2

Resonant x-ray scattering spectra from multipole ordering: NpM4,5edges inNpO2

Studies on X-ray Thomson Scattering from Antiferroquadrupolar Order in TmTe

Polarization analysis of K-edge resonant X-ray scattering of germanium

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