Tetrahedral anisotropy of x-ray anomalous scattering

Templeton, David H.; Templeton, L. K.

doi:10.1103/physrevb.49.14850

Cited by 121 publications

(105 citation statements)

References 15 publications

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“…The experiments were performed utilizing resonant x-ray diffraction which involve measuring the intensity of a reflection as a function of the incident photon energy [26,27,28,29,30]. By tuning the incident energy to the Mn absorption K-edge, 1s electrons are promoted to an intermediate unoc- Figure 3: The diffraction geometry.…”

Section: Materials and Experimental Methodsmentioning

confidence: 99%

“…In order to quantify the resonant x-ray cross-section of this distorted structure one has to take into account the resulting anisotropy of the crystal field around the Mn sites. The scattering amplitude is then described as a tensor of rank two within the dipolar approximation (E1) [26]. In the following x, y and z are defined along the crystallographic axes (see Fig.…”

Section: A High Temperature Phase (T > Tcoo)mentioning

confidence: 99%

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Resonant x-ray diffraction of the magnetoresistant perovskitePr0.6Ca0.4MnO
Grenier
¹
,
Hill
²
,
Gibbs
³

et al. 2004
Phys. Rev. B
102
5
71
1
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We report a resonant x-ray diffraction study of the magnetoresistant perovskite Pr0.6Ca0.4MnO3. We discuss the spectra measured above and below the semiconductor-insulator transition temperature with aid of a detailed formal analysis of the energy and polarization dependences of the structure factors and ab initio calculations of the spectra. In the low temperature insulating phase, we find that inequivalent Mn atoms order in a CE-type pattern and that the crystallographic structure of La0.5Ca0.5MnO3, (Radaelli et al., Phys. Rev. B 55, 3015 (1997)) can also describe this system in fine details. Instead, the alternative structure proposed for the so-called Zener polaron model (Daoud-Aladine et al., Phys. Rev. Lett. 89, 097205 (2002)) is ruled out by crystallographic and spectroscopic evidences. Our analysis supports a model involving orbital ordering. However, we confirm that there is no direct evidence of charge disproportionation in the Mn K-edge resonant spectra. Therefore, we consider a CE-type model in which there are two Mn sublattices, each with partial eg occupancy. One sublattice consists of Mn atoms with the 3x 2 − r 2 or 3y 2 − r 2 orbitals partially occupied in a alternating pattern, the other sublattice with the x 2 − y 2 orbital partially occupied.

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Section: Materials and Experimental Methodsmentioning

confidence: 99%

Section: A High Temperature Phase (T > Tcoo)mentioning

confidence: 99%

Resonant x-ray diffraction of the magnetoresistant perovskitePr0.6Ca0.4MnO
Grenier
¹
,
Hill
²
,
Gibbs
³

et al. 2004
Phys. Rev. B
102
5
71
1
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“…Then, ATS re¯ections are also absent when resonant atoms are in special positions with high point symmetry (for instance cubic) and for which the dipole anisotropy vanishes. If the re¯ections are nevertheless observed, the high-rank dipole±quadrupole (Templeton & Templeton, 1994) and quadrupole±quadrupole (Finkelstein et al, 1992) terms are supposed to be relevant. In optics, similar terms are associated with the ®rst-and secondorder spatial dispersion correspondingly.…”

Section: Introductionmentioning

confidence: 99%

Chirality-induced `forbidden' reflections in X-ray resonant scattering

Дмитриенко

Овчинникова

2001

Acta Cryst Sect A

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It is shown that additional Bragg re¯ections can appear exclusively owing to the local chirality associated with the left±right asymmetric environment of scattering atoms in non-magnetic crystals. The structure amplitude of these re¯ections depends on the antisymmetric part of a third-rank tensor describing the spatial dispersion effects. It enhances for resonant near-edge scattering through a mixed multipole transition, which includes a dipole±quadrupole contribution. It is shown that this mechanism works even for centrosymmetric crystals, and some realistic examples are considered in detail ( -Fe 2 O 3 , LiNbO 3 etc.). For instance, the interference between the dipole±quadrupole and quadrupole±quadrupole terms may be responsible for the threefold symmetry of the azimuthal dependence of the hhh, h = 2n + 1, re¯ections observed recently in hematite.

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“…In general, this contribution is much smaller than the Thompson scattering. For practical purposes this term is therefore significant only when the Thompson contribution vanishes, i.e., at reflections which are "forbidden" due to glide plane or screw axis extinction rules, or structure factor arithmetic 12 .…”

mentioning

confidence: 99%

“…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 .…”

mentioning

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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Tetrahedral anisotropy of x-ray anomalous scattering

Cited by 121 publications

References 15 publications

Resonant x-ray diffraction of the magnetoresistant perovskitePr0.6Ca0.4MnO
Grenier
¹
,
Hill
²
,
Gibbs
³

et al. 2004
Phys. Rev. B
102
5
71
1
View full text Add to dashboard Cite

Resonant x-ray diffraction of the magnetoresistant perovskitePr0.6Ca0.4MnO
Grenier
¹
,
Hill
²
,
Gibbs
³

et al. 2004
Phys. Rev. B
102
5
71
1
View full text Add to dashboard Cite

Chirality-induced `forbidden' reflections in X-ray resonant scattering

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

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Tetrahedral anisotropy of x-ray anomalous scattering

Cited by 121 publications

References 15 publications

Resonant x-ray diffraction of the magnetoresistant perovskitePr0.6Ca0.4MnOGrenier1, Hill2, Gibbs3 et al. 2004Phys. Rev. B1025711View full textAdd to dashboardCite

Resonant x-ray diffraction of the magnetoresistant perovskitePr0.6Ca0.4MnOGrenier1, Hill2, Gibbs3 et al. 2004Phys. Rev. B1025711View full textAdd to dashboardCite

Chirality-induced `forbidden' reflections in X-ray resonant scattering

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

Contact Info

Product

Resources

About

Resonant x-ray diffraction of the magnetoresistant perovskitePr0.6Ca0.4MnO
Grenier
¹
,
Hill
²
,
Gibbs
³

et al. 2004
Phys. Rev. B
102
5
71
1
View full text Add to dashboard Cite

Resonant x-ray diffraction of the magnetoresistant perovskitePr0.6Ca0.4MnO
Grenier
¹
,
Hill
²
,
Gibbs
³

et al. 2004
Phys. Rev. B
102
5
71
1
View full text Add to dashboard Cite