Dielectric permittivity in the x-ray region

In order to determine types of the orbital ordering in manganites, we study theoretically the polarization dependence of the anomalous x-ray scattering, which is caused by the anisotropy of the scattering factor. The general formula of the scattering intensity in the experimental optical system is derived and the atomic scattering factor is calculated in the microscopic electronic model. By using the results, the x-ray scattering intensity in several types of the orbital ordering is numerically calculated as a function of azimuthal and analyzer angles. ͓S0163-1829͑98͒09443-0͔

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“…The anomalous one is derived by the interaction between electronic current and photon and is expressed as follows: 34,35 ⌬ f i␣␤ ͑kЈ,kЉ͒ϭ m…”

Section: Atomic Scattering Factormentioning

confidence: 99%

Polarization dependence of anomalous x-ray scattering in orbital-ordered manganites

Ishihara

Maekawa

1998

Phys. Rev. B

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“…In the x-ray scattering process, the structure factor is defined by the scattering amplitude divided by ͑e 2 ͞mc 2 ͒. By the second-order perturbational calculation with respect to the electron-photon interaction, the anomalous part of the scattering factor for the ith ion in the unit cell is given by [11,12] Df i ͑k 0 , k 00 ͒ ab m e 2 …”

mentioning

confidence: 99%

Theory of Anomalous X-Ray Scattering in Orbital-Ordered Manganites

1998

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We study the theory of the anomalous x-ray scattering in relation to its role as a detector of the orbital orderings and excitations in perovskite manganites. The scattering matrix is given by virtual electron excitations in Mn from the 1s level to the unoccupied 4p level. We find that the orbital dependence of the Coulomb interaction between 3d and 4p electrons is essential to the anisotropy of the scattering factor near the K edge. The calculated results in MnO 6 clusters explain the forbidden reflections observed in La 0.5 Sr 1.5 MnO 4 and LaMnO 3 . The possibility of observing orbital waves with x-ray scattering is discussed as well. [S0031-9007(98)05782-2] PACS numbers: 71.10. -w, 71.90. + q, 75.90. + w, 78.70.CkThe discovery of high T c cuprates has stimulated intensive study of transition-metal oxides (TMO) from the new theoretical and experimental viewpoints. One of the key factors in studying the electronic structures in TMO is the orbital degrees of freedom in 3d transitionmetal ions. In particular, the orbital degrees in perovskite manganites and related compounds bring about a lot of fruitful and dramatic phenomena [1][2][3][4][5]. The electron configuration in a Mn 31 ion is ͑e g ͒ 1 ͑t 2g ͒ 3 with parallel spins due to the strong Hund coupling. In the cubic oxygen octahedral cage, the two e g levels are degenerate. Thus, an e g electron has the orbital degrees of freedom as well as charge and spin. In order to reveal the unique magnetotransport phenomena in manganites, it is essential to study the nature of the orbital degrees and their correlation with spin and lattice. However, the experimental techniques directly detecting the orbital ordering have been limited [6].Recently, Murakami et al. have applied the anomalous x-ray scattering in order to observe the orbital ordering in the single layered manganites La 0.5 Sr 1.5 MnO 4 [7]. By studying a ͑3͞4, 3͞4, 0͒ reflection, which would be forbidden were the anomalous part of the scattering factor isotropic [8,9], they observed a sharp reflection near the Mn 31 K edge. This experimental result implies the following [7]: (i) There exist two nonequivalent Mn 31 ions in the MnO 2 plane, which exhibit an alter-nating orbital ordering. The ordering is called "antiferrotype" hereafter. (ii) The electric dipole ͑E1͒ transition in Mn from the 1s core level to the unoccupied 4p level causes the anomalous scattering. This method was also applied to the undoped manganite LaMnO 3 [10] where the ͑3, 0, 0͒ forbidden reflection suggesting the antiferrotype orbital ordering was observed. The new experimental technique not only confirms the orbital ordering in the two manganites, but has a great potential for applications to study the nature of the orbital in a variety of TMO.In this Letter, we study theoretically the anomalous x-ray scattering in relation to its role as a detector of the orbital ordering in manganites. We identify the origin of the anisotropy of the scattering factor in the orbital ordered state. The orbital dependence of the Coulomb interactions bet...

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“…Kolpakov et al . and later Dmitrienko extended the dielectric tensor formalism to the X‐ray energy regime to account for the polarization dependence of resonant X‐ray scattering. A concept for the calculation of dynamic electron excitations into several intermediate states within the frame of the Multiple Scattering Theory is discussed by Natoli et al .…”

Section: History and Present Statusmentioning

confidence: 99%

Probing a crystal's short‐range structure and local orbitals by Resonant X‐ray Diffraction methods

Zschornak

Richter

Nentwich

et al. 2014

Crystal Research and Technology

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Diffraction Anomalous Fine Structure (DAFS) combines the long‐range, crystallographic sensitivity of X‐ray diffraction with the short‐range sensitivity of X‐ray Absorption Spectroscopy (XAS). In comparison to other spectroscopic methods, DAFS can additionally distinguish phases of different translational symmetry by choice of momentum transfer, or isolate spectra from chemically identical atoms on various Wyckoff sites of a crystal's structure using crystallographic weights. The Anisotropy of Anomalous Scattering (AAS) extends the concept of isotropically scattering atoms to a more general case, where the atom's scattering characteristics depend on the polarization as well as the wavevector of the incident and scattered X‐rays. These can be written as tensors that reflect the local site symmetries of the resonant atom. Forbidden Reflection Near‐Edge Diffraction (FRED) is an elegant way to measure AAS by using reflections that are extinguished in the special case of isotropically scattering atoms. They can only be observed due to the non‐isotropic contributions at photon energies in the vicinity of an absorption edge where electronic transitions occur. Combining the site selectivity of DAFS with the information accessible through AAS allows probing the short‐range order and local orbitals of selected atoms in a crystal structure of a chosen phase. The present condensed review gives a brief overview on the pioneer work, the theory and sensitivities as well as selected recent applications of these powerful and promising Resonant X‐ray Diffraction (RXD) methods. Additionally, some recent work of the authors is included exemplarily for the model structure rutile TiO2 presenting the progress in measurement and interpretation.

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Dielectric permittivity in the x-ray region

Cited by 18 publications

References 6 publications

Polarization dependence of anomalous x-ray scattering in orbital-ordered manganites

Polarization dependence of anomalous x-ray scattering in orbital-ordered manganites

Theory of Anomalous X-Ray Scattering in Orbital-Ordered Manganites

Probing a crystal's short‐range structure and local orbitals by Resonant X‐ray Diffraction methods

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