zero-field ordering in the intermediate phase of CeB6 observed by X-ray scattering: what orders?

Yakhou, F.; Plakhty, V.P.; Suzuki, Hiroyuki; Гаврилов, С. В.; Burlet, P.; Paolasini, L.; Vettier, C.; Kunii, S.

doi:10.1016/s0375-9601(01)00338-3

Cited by 49 publications

(73 citation statements)

References 20 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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“…For CeB 6 π−π ′ (533) ≃ 10 −2 in the experiment. 4 In a qualitative sense, we believe the difference at G = (511) is irrelevant considering the given circumstances such as a lack of information on the domain population, the weak signals at G = (511) and (711), and so on. σ−σ ′ (533) for CeB 6 , while these three quantities have nearly the same magnitudes for TmTe.…”

Section: Comparison With the Ceb 6 'S Resultsmentioning

confidence: 99%

Section: Introductionmentioning

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. This material is believed to show the AFQ order below T Q = 1.8 K. 11 Although many evidences for the AFQ order were gathered in terms of various experimental probes, [12][13][14] there remain some important issues unsettled yet.…”

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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“…2 For CeB 6 , Yakhou et al have performed resonant and non-resonant scattering experiments and found superlattice reflections in phases II and III. 3 Nakao et al have identified the boundary between phases I and II in a magnetic field by resonant scattering. 4 More recently, Tanaka et al have reported unexpected temperature and magnetic field dependences using non-resonant X-ray scattering.…”

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Theory of Coupled Multipole Moments Probed by X-ray Scattering in CeB₆

2004

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A minimal model for multipole orders in CeB 6 shows that degeneracy of the quadrupole order parameters and strong spin-orbit coupling lead to peculiar temperature and magnetic-field dependences of the X-ray reflection intensity at superlattice Bragg points. Furthermore, the intensity depends sensitively on the surface direction. These theoretical results explain naturally recent X-ray experiments in phases II and III of CeB 6 . It is predicted that under weak magnetic field perpendicular to the (111) surface, the reflection intensity should change non-monotonically as a function of temperature.KEYWORDS: X-ray scattering, CeB 6 , quadrupole order, multipole orderIn CeB 6 and related systems, presence of both orbital and magnetic degrees of freedom brings about rich structures in the phase diagram. In zero field, CeB 6 turns into the antiferro quadrupole (AFQ) ordered phase (phase II) at T Q = 3.4K and turns into antiferromagnetic (AFM) ordered phase (phase III) at T N = 2.3K.1 The order parameter in phase II is the Γ 5g -type quadrupole moment. In phase III, the non-collinear magnetic structure is described by four wave numbers:Recently, X-ray scattering has been utilized as a powerful probe to detect orbital orderings.2 For CeB 6 , Yakhou et al. have performed resonant and non-resonant scattering experiments and found superlattice reflections in phases II and III. 4 More recently, Tanaka et al. have reported unexpected temperature and magnetic field dependences using non-resonant X-ray scattering. 5,6 Although the superlattice spots emerge below T Q , the intensity of (n/2, n/2, n/2) reflections with n odd integers remains small in T N < T < T Q . The intensity increases almost stepwise below T N . 5,6 Furthermore the small intensity in phase II is suppressed by application of a magnetic field of as small as 0.1 T, while the suppression in phase III requires an order of magnitude larger magnetic field.6 These features seem strange at first sight since the staggered quadrupole moments probed by X-rays should already be present in phase II, and should not change significantly below the Néel temperature T N . In this paper we demonstrate how X-rays probe the coupling among dipole, quadrupole and octupole moments, and show that consideration of a quasi-continuous symmetry of the quadrupole order parameters provides a natural explanation of the experimental observations.In CeB 6 , a localized 4f electron of a Ce 3+ ion has the quartet crystalline electric field (CEF) ground state, which is called Γ 8 and is well below the excited CEF level Γ 7 .7 An orbital pair in the Γ 8 level are given by are written as |± ↓ , and are obtained by reversing the sign of J z in eq. (1). To describe multipole operators, we introduce two kinds of pseudo spin operators σ and τ as τ z |± ↑ = ± |± ↑ , τ z |± ↓ = ± |± ↓ ,Then the magnetic moment M is given by

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zero-field ordering in the intermediate phase of CeB6 observed by X-ray scattering: what orders?

Cited by 49 publications

References 20 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

Theory of Coupled Multipole Moments Probed by X-ray Scattering in CeB₆

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zero-field ordering in the intermediate phase of CeB6 observed by X-ray scattering: what orders?

Cited by 49 publications

References 20 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

Theory of Coupled Multipole Moments Probed by X-ray Scattering in CeB6

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Theory of Coupled Multipole Moments Probed by X-ray Scattering in CeB₆