Interplay between orbital and magnetic long range order by resonant X-ray scattering in (V1−xCrx)2O3

Resonant X-ray scattering experiments have been performed in 2.8% Cr-doped V₂O₃ single crystal at the Vanadium K-photoabsorption edge. Using linear polarization analysis and comparing the angular dependence of scattered photons with structure factor calculations we can discriminate the nature of the different resonant X-ray processes involved in forbidden lattice reflections enhanced by resonances. We present an experimental method to extract information on local properties of edge-atom such as the anisotropy of the local atomic environment, the atomic magnetic moment orientation and orbital ordering.     

Thermal motion induced resonant forbidden reflections in wurtzite GaN

We report on an experimental study of forbidden reflections in GaN (wurtzite structure) by resonant X-ray scattering at the Gallium K edge. Resonant reflections are explained by the coherent sum of a Thermal Motion Induced (TMI) scattering amplitude and a temperature independent term. We show that the shape of the TMI energy spectrum is the same for a number of reflections that are exactly forbidden by spacegroup symmetry, as well as one that relies on approximate cancellation due to special atomic sites. In addition to demonstrating new selection rules, several non-trivial aspects of the theory of TMI scattering in wurtzite crystals are quantitatively verified, including dependence on temperature, energy, azimuthal angle and polarization. The temperature-dependent and temperature independent spectra of GaN are very similar to those found in ZnO, suggesting strong similarities in the anisotropy of their electronic states. This is also supported by the strong linear dichroism observed in GaN. TMI spectra are determined by the evolution of the electronic anisotropy with nuclear position, and are likely to be extremely valuable for developing theories of electronic properties at elevated temperatures.     

Low energy electronic excitations in the layered cuprates studied by copper L3 resonant inelastic x-ray scattering

We have measured the resonant inelastic x-ray scattering (RIXS) spectra at the Cu L3 edge in a variety of cuprates. Exploiting a considerably improved energy resolution (0.8 eV) we recorded significant dependencies on the sample composition and orientation, on the scattering geometry, and on the incident photon polarization. The RIXS final states correspond to two families of electronic excitations, having local (dd excitations) and nonlocal (charge-transfer) character. The dd energy splitting can be estimated with a simple crystal field model. The RIXS at the L3 edge demonstrates here a great potential, thanks to the resonance strength and to the large 2p spin-orbit splitting.     

Resonant scattering of X-ray radiation in magnetic crystals with non-cubic local anisotropy

Features of resonant diffraction of synchrotron radiation in magnetic crystals in which the local symmetry of resonant atom positions is lower than cubic are considered. It was shown that the simultaneous presence of two anisotropic factors can cause asymmetry of the azimuthal dependence of purely resonant reflections. The observed azimuthal dependence of the 002 reflection in the HoFe₂ crystal was numerically simulated.     

Polarization Analysis to Separate the Resonance Contribution to the Allowed X-Ray Reflections

JETP Letters - It has been shown that channels of resonant X-ray scattering with a change in polarization can be present in allowed Bragg reflections. The measurement of the energy and azimuthal...     

Resonant diffraction in stishovite near the <Emphasis Type="Italic">K</Emphasis> absorption edge of silicon

The X-ray resonant diffraction in a stishovite crystal near the K absorption edge of silicon (E _K = 1839 eV) is studied theoretically. For such a long wavelength, the only possible Bragg reflection is the 100 reflection, which is forbidden by the space group of the crystal. It can be excited solely due to anisotropy of the X-ray scattering amplitude. The crystal symmetry is used to determine the polarization and azimuthal dependence of the reflection intensity. Since this reflection is single, it can be detected upon diffraction from a powder, which substantially widens the possibilities of investigations. The numerical calculations of the energy dependences of the forbidden reflection intensity and the absorption coefficient demonstrate that the dipole-quadrupole, quadrupole-quadrupole, and dipole-octupole contributions to the resonant diffraction and absorption are small and that the dipole-dipole contribution is the most important one.     

Application of X-ray resonant diffraction to structural studies of liquid crystals

Liquid crystals are soft materials that combine the fluidity of disordered liquids and the long range orientational or positional order of crystalline solids along one or two directions of space. X-ray scattering is widely and generally successfully used to investigate and characterize the microscopic structure of most liquid crystals. In many cases however, the Bragg reflections are forbidden by special symmetries of the unit cell and the low dimensional structure of the liquid crystalline phases are out of reach of conventional X-ray experiments. We show in this paper that this problem can be overcome by resonant scattering of X-rays as it reveals the anisotropy of the tensor structure factor. We review various examples in which the restored forbidden reflections reveal unambiguously the hidden structure of liquid crystalline phases. Moreover, we show that in some cases, a fine analysis of the polarization of the Bragg reflections enables one to discriminate between different structural models. These studies solved long standing questions about biaxial liquid crystal structures and provided new insights into physical phenomena such as supercritical behaviour or commensurate-incommensurate transitions.     

Interaction induced light scattering in orientationally disordered crystals: the translational phonon region

We have derived an expression for the light scattering spectrum of a crystal in which the mechanically regular sites are occupied by point polarizable orientationally disordered molecules when the polarizabilities are assumed to depend on the positions of the surrounding atoms (interaction induced polarizability fluctuations).

Owing to the ‘electrical’ disorder properties of the system all phonons can contribute to the anisotropic scattering measured in all polarization configuration with wavevector, branch index and polarization dependent coefficients. Assuming short range interaction induced polarizabilities we show that the temperature reduced intensity I(ω)/[n(ω) + 1] is given by a superposition of the Brillouin zone centre symmetry ‘projected’ density of states with polarization dependent coefficients. These coefficients are found to be essentially frequency independent for all the projections, exception made for those corresponding to the acoustic phonons. For the acoustic branches the coefficients vanish in a first approximation. They can however be treated on more rigorous grounds and, as already found by other authors, their contribution is proportional to the density of states multiplied by ω².

In addition zone centre (k?0) totally symmetric phonons can also be present in the ‘isotropic’ term (which appears only in the polarized VV configuration).

A procedure is suggested to obtain the total density of states from the spectra measured in different polarization configurations.     

Structural distortion,charge modulation and local anisotropies in magnetite below the Verwey transition using resonant X‐ray scattering

The pattern of charge modulations and local anisotropies below the Verwey transition has been determined and quantified in high‐quality Fe₃O₄ single crystals and thin films grown on MgO by using resonant X‐ray scattering at the Fe K‐edge. The energy, polarization and azimuthal angle dependencies of an extensive set of reflections with potential sensitivity to charge or local anisotropy orderings have been analyzed to explore their origins. A charge disproportion on octahedral B sites of 0.20 ± 0.05 e^? with [0 0 1] and cubic periodicities has been confirmed, while no significant charge disproportion has been obtained with [0 0 1/2] cubic periodicity. Additional charge modulations in the monoclinic a–b plane are also present. In addition, the occurrence of new forbidden (1, 1, 0) and (0, 0, 2n + 1/2) cubic reflections that arise from the anisotropy of the local structure around different tetrahedral and octahedral Fe atoms is shown. This complex pattern of weak charge modulations and local anisotropies is fully compatible with the low‐temperature crystal structure refined in the non‐polar C2/c space group and disproves any bimodal charge disproportion of the octahedral Fe atoms.     

Studies of nuclear resonant scattering at TRISTAN-AR

Studies of nuclear resonant scattering of synchrotron radiation undertaken with the X-ray undulator installed in the TRISTAN Accumulation Ring at the National Laboratory for High Energy Physics, KEK, are reported. These studies have evaluated the effect of fast magnetic switching on the nuclear collective decay in an FeBO₃ crystal, the change in the polarization state of nuclear Bragg scattering by fast magnetic switching, and the influence of this switching on the time evolution of the nuclear forward scattering. The phenomenon of interferometric nuclear forward scattering has also been studied.     

Direct observation of charge order in triangular metallic AgNiO2 by single-crystal resonant X-ray scattering

We report resonant x-ray scattering measurements on a single crystal of the orbitally degenerate triangular metallic antiferromagnet 2H-AgNiO2 to probe the spontaneous transition to a triple-cell superstructure at temperatures below T(S)=365 K. We observe a strong resonant enhancement of the supercell reflections through the Ni K edge. The empirically extracted K-edge shift between the crystallographically distinct Ni sites of 2.5(3) eV is much larger than the value expected from the shift in final states, and implies a core-level shift of ～1 eV, thus providing direct evidence for the onset of spontaneous honeycomb charge order in the triangular Ni layers. We also provide band-structure calculations that explain quantitatively the observed edge shifts in terms of changes in the Ni electronic energy levels due to charge order and hybridization with the surrounding oxygens.     

Scattering properties of an individual metallic nano-spheroid by the incident polarized light wave

The scattering properties of a metallic nano-spheroid under the illumination of different polarized light waves are investigated using 3D boundary element method. The influences of different geometrical sizes of the nano-spheroid and incident directions of the illuminating light wave on the scattering spectrum are studied for different incident polarized light waves. The results show that the metallic nano-spheroid has two intrinsic resonant modes, corresponding to different polarization states and resonant wavelengths. The scattering enhancement, the resonant wavelength, and the location of the enhanced optical field are strongly dependent on the polarization properties of the illuminating light waves, and they can be modulated by appropriately choosing the polarization directions of the incident light wave.     

Soft X-ray resonant magnetic scattering of magnetic nanostructures

Soft X-ray resonant magnetic scattering offers a unique element-, site- and valence-specific probe to study magnetic structures on the nanoscopic length scale. This new technique, which combines X-ray scattering with X-ray magnetic circular and linear dichroism, is ideally suited to investigate magnetic superlattices and magnetic domain structures. The theoretical analysis of the polarization dependence to determine the vector magnetization profile is presented. This is illustrated with examples studying the closure domains in self-organising magnetic domain structures, the magnetic order in patterned samples, and the local configuration of magnetic nano-objects using coherent X-rays. To cite this article: G. van der Laan, C. R. Physique 9 (2008).     

The resonant secondary emission of the F center in alkali halides

The secondary radiation after resonant excitation of F center and its linear polarization P correlated to the polarization of resonant light have been measured for five alkali halides at low temperatures. In KC1, the spectrum of P over the whole Stokes region is divided into three successive regions, the depolarization range at the one-phonon Raman scattering, the near plateau range, and the depolarization range down to vanishing. The former two have common relevance to resonant energy and symmetries of coupled phonons. These relevances are interpreted adopting a configuration coordinate model for 2s- and 2p-like excited states.     

The chromium spin density wave: magnetic X-ray scattering studies with polarisation analysis

We report on X-ray magnetic diffraction studies of the spin density wave antiferromagnetism formed in the conduction electron band of chromium. Non-resonant X-ray magnetic scattering was used to directly determine that chromium has zero orbital magnetisation. Furthermore, the azimuthal dependence of this scattering provides unique evidence that chromium forms a linearly polarised wave. In the vicinity of the K absorption edge, resonant X-ray magnetic scattering was observed. A consistent model of the magnetic scattering has been derived from the resonant and non-resonant magnetic amplitudes. The enhancement of the magnetic intensity arises primarily from dipole transitions from the core 1s level to 4p states. Quadrupole transitions to the magnetic 3d states are essentially non-existent due to their sensitivity to (and the absence of) orbital moment. This effect is predicted from atomic considerations of the 3d⁵ ( = 0) transition metal ions. Received 22 September 2000     

Ab initio calculations of the forbidden Bragg reflections energy spectra in wurtzites versus temperature

Thermal-motion induced (TMI) scattering is caused by the influence of atomic displacements on electronic states in crystals and strongly depends on temperature. It corresponds to dipole-dipole resonant x-ray scattering, but is usually accompanied by dipole-quadrupole scattering. The phenomenological theory supposes the dipole-quadrupole term to be temperature independent (TI). As a result, the transformation of the energy spectra with temperature observed experimentally in ZnO and GaN corresponds to the interference between the TMI and TI terms. In the present paper the direct confirmation of this theoretical prediction is given. Ab initio molecular dynamics was used to simulate the sets of atomic sites at various temperatures followed by quantum mechanical calculation of resonant Bragg reflection energy spectra. The results of simulation are in excellent coincidence with experimental energy spectra of forbidden reflections and confirm the earlier phenomenological conjecture about the interference between the TI dipole-quadrupole and TMI dipole-dipole contributions to the resonant atomic factor.     

A three-beam case X-ray interferometer

A new type of X-ray interferometer is described in which total reflection is established in the process of beam splitting, beam deflection and beam recombination by making essential use of simultaneous Bragg case diffraction from two different sets of net planes.The amplitudes of the interfering beams are calculated along the lines of the dynamical theory of X-ray diffraction. It is found that in the general non-planar three-beam case a complicated interaction of polarization states occurs which results in a destruction of interference contrast. On the other hand, in the planar case the polarization states stay separated and interference contrast can reach 100%.A monolithic interferometer using coplanar (440) and (404) reflections was made from a perfect silicon crystal and operated successfully. The degree of interference contrast was investigated experimentally with NiK radiation of an ordinary X-ray tube and with synchrotron X-rays from DESY.Focusing requirements and source properties influencing the coherence conditions are discussed.Part of doctorate thesis (University of Dortmund, 1976)     

Ce 5d and Fe 3d magnetic profiles in CeH2/Fe multilayers probed by XRMS

The element and electronic shell specificities of X-ray resonant magnetic scattering have been used to investigate the magnetization of Ce 5d and Fe 3d states in [CeH₂(19.6 ?)/Fe(25.4 ?)]*38 a multilayer. We show that the measurement of the magnetic contribution to the intensities reflected at low angles at the Ce L₂ and Fe L_2,3 edges allows us to investigate the profile of the Ce 5d and Fe 3d magnetic polarization. The Fe 3d polarization is found to be uniform across the Fe layer and the Ce 5d polarization appears to be restricted close to the interface with Fe. Received: 22 May 2001 / Accepted: 4 July 2001 / Published online: 5 October 2001     

Luminescence spectra produced by exciton relaxation at local magnetization fluctuations in semimagnetic semiconductors

An analysis is made of the exciton angular-momentum alignment along a fluctuation in local magnetization, which is the first stage in evolution of the localized-exciton spin state in a semimagnetic semiconductor. It is shown that spin relaxation of localized excitons subjected to resonant optical excitation is accompanied by their relaxation in energy. When excited by polarized light, this process gives rise to an anisotropic angular-momentum distribution in the spectrum of final exciton states and, hence, to polarization of the secondary luminescence. Luminescence spectra of a cubic crystal are calculated, and the possibility of their experimental observation discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 2156–2160 (December 1998)     

Resonant Inelastic X-ray Scattering: From band mapping to inter-orbital excitations

Resonant inelastic X-ray scattering (also known as resonant X-ray Raman spectroscopy when only valence and conduction states are involved in the final state excitation) has developed into a major tool for understanding the electronic properties of complex materials. Presently it provides access to electron excitations in the few hundred meV range with element and bulk selectivity. Recent progress in X-ray optics and synchrotron radiation engineering have opened up new perspectives for this powerful technique to improve resolving power and efficiency. We briefly present the basics of the method and illustrate its potential with examples chosen from the literature. To cite this article: J. Lüning, C.F. Hague, C. R. Physique 9 (2008).