Phonon-electron interaction and vibration correlations in germanium within a broad temperature interval

Kirfel, Α.; Grybos, J.; Дмитриенко, В. Е.

doi:10.1103/physrevb.66.165202

Cited by 38 publications

(57 citation statements)

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“…Low-temperature measurements have been reported for cuprite (Kirfel & Krane, 1999) and magnetite (Hagiwara et al, 1999;Kirfel et al, 2002a) but, as shown in x8, studies at elevated temperatures may also make an essential contribution.…”

Section: Acta Cryst (2005) A61 481-493mentioning

confidence: 99%

“…in hematite, -Fe 2 O 3 (Finkelstein et al, 1992;Watanabe et al, 2001;Kokubun, Watanabe et al, 2005), and in magnetite, Fe 3 O 4 (Kirfel et al, 1995a;Hagiwara et al, 1999;García et al, 2000;Kanazawa et al, 2002;, where the polarization and spectral analysis of the scattered radiation revealed site-specific dq transitions for the pre-edge peak. The latter type was also assumed to cause the 'forbidden' hk0 ðh þ k ¼ 4n þ 2Þ reflections in the diamond structure of germanium (Templeton, 1994;Templeton & Templeton, 1994) but later it was found Kirfel et al, 2002b) that a thermal-motion-induced dd contribution is the reason for this class of reflections, at least at ambient and elevated temperatures (see x8 below). This paper presents a survey of the observations of the pure crystalline 'forbidden' reflections with emphasis on the experimental features; their theoretical treatment has been reviewed before by Belyakov & Dmitrienko (1989), Carra & Thole (1994) and .…”

Section: Introductionmentioning

confidence: 99%

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Polarization anisotropy of X-ray atomic factors and `forbidden' resonant reflections

et al. 2005

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Symmetry and physical aspects of 'forbidden' reflections excited by a local polarization anisotropy of the X-ray susceptibility are surveyed. Such reflections are observed near absorption edges where the anisotropy is caused by distortions of the atomic electronic states owing to interaction with neighbouring atoms. As a consequence, they allow for extracting nontrivial information about the resonant atom's local environment and their physical conditions. The unusual polarization properties of the considered reflections are helpful to distinguish them from other types of 'forbidden' reflections. When such reflections are excited, it is, for example, possible to determine not only the intrinsic anisotropy of an atomic form factor but also additional anisotropy induced by thermal motion, point defects and/or incommensurate modulations. Even the local 'chirality' of atoms in centrosymmetric crystals is accessible. Unsolved key problems and possible future developments are addressed.

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Section: Acta Cryst (2005) A61 481-493mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Polarization anisotropy of X-ray atomic factors and `forbidden' resonant reflections

et al. 2005

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“…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.…”

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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 .…”

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confidence: 99%

“…The resulting tensor is A αβγ = DT αβγ , where D is a complex number depending of the matrix elements, the resonant denominators, the densities of state, etc, but not on the scattering geometry, and the photon polarization and wave vectors. T αβγ is symmetric over all its indices, i.e., T xyz = T xzy = T yzx = T yxz = T zxy = T zyx = 1 and 0 otherwise 16 . In particular, A αβγ is symmetric in α and β, so that the second term in eq.…”

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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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Phonon effects in resonant “forbidden” reflections

Дмитриенко

Овчинникова

Ishida

et al. 2004

phys. stat. sol. (c)

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The influence of atomic vibrations on the "forbidden" Bragg reflections, excited near absorption edges owing to anisotropic resonant X-ray scattering, is discussed. It is shown that in spite of the difference of Xrays and phonons energies the "forbidden" reflections can be extremely sensitive to the atomic vibrations and their correlations. The numerical calculations are performed taking into account the correlations of atomic thermal displacements, which give an adequate description of the thermal growth of the 600 forbidden reflection in Ge and describe drastic changes of the "forbidden" reflections spectra in ZnO.1 Introduction In view of the very different x-ray and phonon energies, it is rather surprising that phonons can drastically affect both the intensity and the spectrum of resonant x-ray scattering in crystals. The reason is that resonant scattering is extremely sensitive even to very small atomic displacements distorting the electronic states. Moreover, phonon vibrations permanently change the symmetry of atomic sites, induce an additional anisotropy of the atomic scattering factors (ASF) and therefore give rise to extra Bragg reflections, otherwise forbidden (see [1][2][3][4][5] and references therein). It was shown that this effect is sensitive mainly to optical phonon modes (even at zero temperature). It allows to observe vibrations of selected resonant atoms because the anisotropy of ASF is significant only near the X-ray absorption edges where ASF becomes a tensor.In the beginning of this studies, the phenomenological expressions describing a scattering amplitude of thermal motion induced (TMI) forbidden reflections in Ge were obtained supposing independent atomic motion [1], and the microscopic calculations, using such a model, gave a satisfactory description of the phenomenon [3,6,7]. Later it was shown for Ge [4] that the description becomes better, if one takes into account the correlation of atomic displacements, i.e. a cooperative type of atomic movements. Recently the spectral intensity of "forbidden" reflections in ZnO was calculated [8] supposing a special character of the phonon modes, which contributed to atomic displacements. In the present paper we discuss what information about phonons in crystals could be obtained from the energy spectra and simulate the contribution of different phonon modes into the "forbidden" reflections.

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Phonon-electron interaction and vibration correlations in germanium within a broad temperature interval

Cited by 38 publications

References 25 publications

Polarization anisotropy of X-ray atomic factors and `forbidden' resonant reflections

Polarization anisotropy of X-ray atomic factors and `forbidden' resonant reflections

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

Phonon effects in resonant “forbidden” reflections

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