Resonant X-ray Scattering Research Articles

Checkerboard-ordered pattern ofBi0.5Sr0.5MnO3low-temperature phase probed by x-ray resonant scattering

Resonant x-ray scattering (RXS) at the Mn $K$ edge has been used to characterize the low temperature ordered phase of ${\mathrm{Bi}}_{0.5}{\mathrm{Sr}}_{0.5}\mathrm{Mn}{\mathrm{O}}_{3}$. Strong resonances were observed for the (030), (050), $(05∕20)$, $(0\phantom{\rule{0.3em}{0ex}}7∕2\phantom{\rule{0.3em}{0ex}}0)$, $(4\phantom{\rule{0.3em}{0ex}}\frac{1}{2}\phantom{\rule{0.3em}{0ex}}0)$, and $(3\phantom{\rule{0.3em}{0ex}}\frac{1}{2}\phantom{\rule{0.3em}{0ex}}0)$ reflections as the photon energy is tuned through the Mn $K$ edge. The reported azimuthal and polarization dependence of the resonant intensities indicates that the low temperature phase is described as a checkerboard ordering of two types of Mn sites with different local geometrical structures. One of the sites is anisotropic, a tetragonal distorted oxygen octahedron and the other one is isotropic, a nearly undistorted oxygen octahedron. The distinction of these two Mn sites is accompanied by a displacement of the Mn atoms transverse to the $b$ axis. We conclude that this checkerboard-ordered pattern is a common ground state in half-doped manganites. Intermediate valence states according to fractional charge segregation were deduced for the two nonequivalent Mn atoms, far from the localized ${\mathrm{Mn}}^{3+}$ and ${\mathrm{Mn}}^{4+}$ ionic species. Hence, the experimental data discard the ionic model of charge and orbital ordering of localized $3d$ (or $3d$-like) states at the Mn site (or the $\mathrm{Mn}{\mathrm{O}}_{6}$ cluster). We suggest a description of the RXS in terms of band structure effects and lattice dynamics.

Interplay between orbital ordering and magnetism in the Mott insulator Ti oxides

We have revealed the relationship between the orbital ordering and the magnetism in the perovskite Ti oxides RTiO 3 (R; rare earth elements) by using resonant X-ray scattering (RXS) near the K absorption edge of Ti. We observed the temperature dependence of the resonant signal in SmTiO 3. The resonant signal hardly changed at the magnetic phase transition. Besides, the energy spectra at Q = ( 0 0 3 ) and the full width at half maximum (FWHM) for the 2 θ - ω scan are unchanged. Combining with the behavior that the periodicities of the azimuthal angle dependence for GdTiO 3 and SmTiO 3 are identical at each scattering vector, it is concluded that the change of the magnetism from ferromagnetic (FM) to antiferromagnetic (AFM) has little effect on the orbital ordering in RTiO 3.

New findings in Resonant X-ray Scattering investigation of KCuF 3 orbital model system

KCuF 3 single crystals grown by Bridgman method were investigated by means of Resonant X-ray Scattering: we report on both magnetic and orbital Bragg forbidden reflections. A comparison with previously obtained results on samples grown by aqueous solution method evidences strong differences in spectra: some considerations on related theoretical works are reported.

Resonant X-Ray Scattering on theM-Edge Spectra from Triple-kStructure Phase in U0.75Np0.25O2and UO2

We derive an expression for the scattering amplitude of resonant x-ray scattering under the assumption that the Hamiltonian describing the intermediate state preserves spherical symmetry. On the basis of this expression, we demonstrate that the energy profile of the RXS spectra expected near U and Np M_4 edges from the triple-k antiferromagnetic ordering phase in UO_{2} and U_{0.75}Np_{0.25}O_{2} agree well with those from the experiments. We demonstrate that the spectra in the \sigma-\sigma' and \sigma-\pi' channels exhibit quadrupole and dipole natures, respectively.

Coupling between Orbital and Lattice Degrees of Freedom in Y1-xCaxTiO3 (0 < x ≤0.75): A Resonant X-ray Scattering Study

We have studied the orbitally ordered states in Y 1- x Ca x TiO 3 (0 < x ≤0.75) by resonant X-ray scattering (RXS) near the Ti K -edge ( E ∼5 keV) and by powder X-ray diffraction measurements. The ...

Resonant x-ray scattering spectra from multipole ordering: NpM4,5edges inNpO2

We study resonant x-ray scattering (RXS) at Np M_{4,5} edges in the triple-\textbf{k} multipole ordering phase in NpO_{2}, 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 \Gamma_{8}-quartet ground state, we construct the triple-\textbf{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.

Anomalous scattering in structural chemistry and biology¶

The uses of X-ray anomalous scattering in crystal structure analysis have undergone a major expansion due to the refinement and ease of availability of the necessary X-ray instrumentation and methods. The structural chemistry and biology fields span a similar suite of technical needs but with widely differing molecular systems. The innate synergies between the two research fields brought two of the authors (JRH and VK) together at an Erice Summer School on Synchrotron Radiation in Crystallography in 1985 and took them into a collaboration spanning already 20 years. The authors’ wide perspectives are therefore, if not unique, perhaps rather rare. Thus the breadth of coverage of this review is unusual. However, there are two excellent books on anomalous scattering and its uses that have been published covering the periods up to 1975 and 1994 [S. Ramaseshan, S.C. Abrahams (Eds). Anomalous Scattering, Munksgaard, Copenhagen (1975); G. Materlik, C.J. Sparks, K. Fischer (Eds). Resonant Anomalous X-ray Scattering: Theory and Applications, North Holland, Amsterdam (1994)]. As the number of examples of applications in structural biology are now so many it has only been possible to select some illustrative examples but with surveys of trends. In addition though, the development of the methodologies is described in more detail. The structural chemistry applications in, for example, microporous materials, superconductors and magnetic materials is expanding fast but still at a stage where we could attempt to provide a detailed coverage of results, which we have done. Anomalous scattering results on locating metal atoms can also be compared with other technique results and so sections on X-ray Absorption Spectroscopy (XAS), Diffraction Anomalous Fine Structure (DAFS), neutron diffraction and Nuclear Magnetic Resonance (NMR) applications are described where they relate to metal atom location and local structure. Finally anomalous scattering has also been very useful to help develop the modern synchrotron Laue method for quantitative crystal structure analysis, which is also briefly described. ¶Dedicated to Professor Durward W. J. Cruickshank, FRS, Emeritus Professor of Chemistry, The University of Manchester, on the occasion of his 82nd Birthday, 7 March 2006. Durward is an inspiration to us all as a scientist with many fine contributions spanning nearly 60 years, as well as a friend, mentor and colleague to several of us for many years. Contents Introduction 246 1. Brief resume of anomalous scattering 252 1.1.Principles 252 1.2.Different nomenclatures in use for the anomalous scattering coefficients 255 1.3.Some crystal symmetry and diffraction data measurement key facts 258 1.4.Absolute structure: the key definitions 260 2. Some historical notes: the absolute configuration of (R, R)-(1)-tartaric acid was determined by J. M. Bijvoet and colleagues (1951) 262 3. The use of anomalous scattering in structural chemistry 264 3.1.Introduction to site-specific, neighbouring element and valence contrast experiments 264 3.2.Overview of neighbouring element and valence contrast experiments 265 3.3.Applications of anomalous scattering to particular classes of materials 277 3.4.Potential applications of anomalous dispersion in powder diffraction structure solution de novo 290 3.5.The determination of the absolute configuration or hand of smaller molecules using crystallography 292 4. The use of anomalous scattering in structural biology 293 4.1.Previous reviews of the uses of anomalous scattering in protein crystallography especially SR 293 4.2.The location of the anomalous scatterers 296 4.3.MIR, SIROAS and MAD phasing 296 4.4.The recent growth of Single-wavelength Anomalous Dispersion(SAD) phasing 299 4.5.Identification of metals in metalloproteins (Mn, Zn, Cu, Ca) and ions (Cl − ,) in proteins including case studies 307 4.6.Instrumentation case study: line 10 at the SRS 309 5. Use of anomalous scattering derived structural details to help develop the Laue method 311 6. Complementary methods 314 6.1.XAS 314 6.2.Diffraction Anomalous Fine Structure Analysis (The DAFS method) 317 6.3.Neighbouring atom contrast by neutron diffraction methods 319 6.4.Magnetic resonance spectroscopy 320 7. Concluding remarks 323 Acknowledgements 324 References 325 Subject index 333

Quadrupolar Frustration in Shastry–Sutherland Lattice of DyB4Studied by Resonant X-ray Scattering

We have observed geometrical frustration of quadrupolar and magnetic moments in dysprosium tetraboride, DyB4, where the rare-earth sites form a Shastry-Sutherland lattice. Resonant x-ray scattering at the LIII absorption edge of Dy was utilized. Analysis of the energy, polarization, temperature, and azimuthal-angle dependences of the E1 resonance of the (1 0 0) forbidden reflection show that the magnetic and quadrupolar components within the frustrated c plane have a short-range correlation, suggesting that the moments are fluctuating. By contrast, the basic antiferromagnetic component along the c axis has a long-range order.

Evidence for Octupole Order in Ce0.7La0.3B6 from Resonant X-ray Scattering

The azimuthal angle dependence observed in the resonant X-ray scattering in phase IV of Ce$_{0.7}$La$_{0.3}$B$_6$ is analyzed theoretically. It is shown that the peculiar angle dependence observed in the E2 channel is consistent with the Gamma_{5u}-type octupole order with principal axis along (111) and equivalent directions. Under the assumption that the four equivalent octupole domains are nearly equally populated in the sample, the observed angle dependences are reproduced by calculation for both sigma-sigma' and sigma-pi' polarizations. The calculation for various symmetries of order parameters excludes unambiguously other order parameters than the Gamma_{5u}-type octupole.

Structural properties and phase transition of hole-orbital-ordered(C2H5NH3)2CuCl4studied by resonant and non-resonant x-ray scatterings under high pressure

The effects of hydrostatic pressure on a structure and the corresponding resonant x-ray scattering (RXS) spectrum have been investigated for the hole-orbital-ordered compound ${({\mathrm{C}}_{2}{\mathrm{H}}_{5}\mathrm{N}{\mathrm{H}}_{3})}_{2}\mathrm{Cu}{\mathrm{Cl}}_{4}$. We have found a structural phase transition at ${P}_{\mathrm{c}}\ensuremath{\sim}4\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, as suggested by the Raman scattering measurement, by observing a peak splitting resulting from an orthorhombic-to-monoclinic symmetry breaking. The reduction of the Jahn-Teller distortion (JTD) toward ${P}_{\mathrm{c}}$ is also ascertained by structural analyses. The gradual change in the color of the crystal is also observed in connection with the structural change near ${P}_{\mathrm{c}}$. The red-colored transparency of the crystal indicates that the system is still insulative above ${P}_{\mathrm{c}}$. The observed RXS and fluorescence spectrum at ambient pressure were precisely analyzed. We experimentally confirmed that the RXS intensity comes from the polarization of the density of states of ${p}_{\mathrm{x}}$ and ${p}_{\mathrm{y}}$ symmetries, which is mainly dominated not by the on-site $3d\text{\ensuremath{-}}4p$ Coulomb interaction but by the JTD of the $\mathrm{Cu}{\mathrm{Cl}}_{6}$ octahedron. charged Cl ions neighboring the Cu site. It is also expected that the RXS intensity is proportional to JTD; however, our RXS study under a high pressure shows no striking change as JTD is suppressed by the application of pressure. On the other hand, the RXS intensity becomes zero above ${P}_{\mathrm{c}}$. The results indicate that the local environment of the ${\mathrm{Cu}}^{2+}$ ion markedly changes. Two possible structures of ${\mathit{EA}}_{2}\mathrm{Cu}{\mathrm{Cl}}_{4}$ above ${P}_{\mathrm{c}}$ are proposed.

Multipole Tensor Analysis of the Resonant X-ray Scattering by Quadrupolar and Magnetic Order in DyB2C2

Resonant x-ray scattering (RXS) experiment has been performed for the (3 0 1.5) superlattice reflection in the antiferroquadrupolar and antiferromagnetic phase of DyB 2 C 2 . Azimuthal-angle dependence of the resonance enhanced intensities for both dipolar ( E 1) and quadrupolar ( E 2) resonant processes has been measured precisely with polarization analysis. Every scattering channel exhibits distinctive azimuthal dependence, differently from the symmetric reflection at (0 0 0.5) which was studied previously. We have analyzed the results using a theory developed by Lovesey et al. [J. Phys.: Condens. Matter 8 (1996) 10983], which directly connects atomic tensors with the cross-section of RXS. The fitting results indicate that the azimuthal dependences can be explained well by the atomic tensors up to rank 2. Rank 4 tensor is not reflected in the RXS data. In addition, the coupling scheme among the 4 f quadrupolar moment, 5 d ortital, and the lattice has been determined from the interference among the Thomson scattering from the lattice distortion and the resonant scatterings of E 1 and E 2 processes. It has also been established from the RXS of the (3 0 1.5) reflection that the canting of the 4 f quadrupolar moments exists up to T Q . We also discuss a possible wavefunction of the ground state and the existence of the rank 4 moment.

Periodic Arrangement of Quadrupolar Moments Induced by the Antiferromagnetic Order in TbB2C2: Observation by Resonant X-ray Scattering

We have investigated the antiferromagnetic ground state, phase IV, of TbB 2 C 2 by resonant X-ray scattering to study the background of its anomalous magnetic structure. Polarization analysis was carried out to clarify the origin of the superlattice and forbidden reflections that appear below the Neel temperature. We observed magnetic reflections of (1 0 0.5) and (0 0 0.5), consistently with the neutron diffraction experiment by Kaneko et al. In addition, we have detected the (1 0 0) forbidden reflection in the unrotated σ–σ' channel, which was not observed by neutron diffraction. From the detailed analysis of the resonant X-ray scattering, we conclude that this reflection originates from the ordering of the quadrupolar moment that accompany the canted antiferromagnetic structure of TbB 2 C 2 because of the strong spin-orbit coupling. No lattice distortion was detected.

Resonant Magnetoelectric X-ray Scattering in GaFeO3: Observation of Ordering of Toroidal Moments

We report on the first observation of magnetoelectric X-ray scattering (MEXS), i.e., incident- k -direction-dependent scattering, for a polar ferrimagnet GaFeO 3 . Near the K edge of Fe, the magnetic component of the (040) X-ray reflection shows a larger enhancement than that of the (020) X-ray reflection, which cannot be attributed to the genuine magnetic scattering, but to the MEXS of Fe 3+ ions. Toroidal moments as defined by the outer product of the Fe off-center displacement and the magnetic moment show ferroic ordering, which causes the resonant MEXS at the Fe 1 s –3 d excitation energy.

Octupolar order in [formula omitted]: A specific heat investigation

Resonant X-ray scattering (RXS) experiments on NpO 2 provide indications for a low-temperature phase where magnetic octupole order is established in absence of magnetic dipole order. The interpretation of the RXS findings has led to a controversy about the symmetry of the primary order parameter, which has been identified either with Γ 2 or with Γ 5 octupoles. A consequence of long-range octupole order is that the degeneracy of the Γ 8 crystal field ground state is removed. Γ 8 would be split into two doublets if Γ 2 octupoles order, and into two singlets and one doublet if the order parameter has Γ 5 symmetry. Here we present specific heat measurements between 0.7 K and 300 K supporting a singlet ground state in the ordered phase below 25.5 K.

Resonant X-ray Scattering from URu2Si2

Based on a localized crystal electric field model for the U^{4+} in the (5f)^2-configuration, we analyze the resonant x-ray scattering spectra around U M_{IV} and M_{V} edges in URu_{2}Si_{2}, taking full Coulomb and spin-orbit interactions into account. We consider two level schemes, a singlet model of Santini and Amoretti and a doublet model of Ohkawa and Shimizu, and assume the antiferroquadrupolar order and the antiferromagnetic order as candidates for the ambient pressure phase and the high pressure phase. It is found that the spectral shapes as a function of photon energy are independent of the assumed level scheme, but are quite different between the antiferroquadrupole and antiferromagnetic phases, This may be useful to determine the character of the ordered phase.

Ordering of Toroidal Moments Studied by Resonant X-ray Scattering

Ordering of Toroidal Moments Studied by Resonant X-ray Scattering

D−fCoulomb and quadrupole-strain interactions inDyB2C2observed by resonant x-ray scattering

Experimental evidence of the d-f Coulomb interaction responsible for the resonant x-ray scattering (RXS) from antiferroquadrupolar order in DyB2C2 is presented. The energy dependences of the RXS intensity with polarization analysis are analyzed by considering the interference between the resonances of dipolar (E1) and quadrupolar (E2) transition processes. It is found that the structure factors for the E1 and E2 processes have the same sign for sigma-pi' but the opposite sign for sigma-sigma' channel. This result, when compared with the calculated structure factors, means that the quadrupolar moments of the 4f and 5d electrons have opposite signs to each other. Interference between nonresonant Thomson scattering from the lattice distortion and the resonant scatterings is also studied and a direct coupling between 4f and the lattice is concluded.

4p States and X-Ray Spectroscopy

The 4p states in transition metals and their compounds usually play minor roles on their physical quantities. Recent development of resonant x-ray scattering (RXS) at the K-edge of transition metals, however, casts light on the 4p states, because the signals on orbital and magnetic superlattice spots are brought about by the modulation in the 4p states. The 4p states are extending in solids and thereby sensitive to electronic states at neighboring sites. This characteristic determines the mechanism of RXS that the intensity on orbital superlattice spots are mainly generated by the lattice distortion and those on magnetic superlattice spots by the coupling of the 4p states with the orbital polarization in the 3d states at neighboring sites. Taking up typical examples for orbital and magnetic RXS, we demonstrate these mechanisms on the basis of the band structure calculation. Finally, we study the magnetic circular dichroism spectra at the K-edge, demonstrating that the same mechanism as the magnetic RXS is working.

Orbital ordering near a Mott transition: Resonant x-ray scattering study of the perovskite Ti oxidesRTiO3andLaTiO3.02(R=Gd, Sm, Nd, and La)

We investigated orbital ordering states in the vicinity of the Mott transition in $R\mathrm{Ti}{\mathrm{O}}_{3}$ and $\mathrm{La}\mathrm{Ti}{\mathrm{O}}_{3.02}$ ($R=\mathrm{Gd}$,Sm,Nd,La) using resonant x-ray scattering (RXS) at the $1s\ensuremath{\rightarrow}3d$ transition energy of the $K$ absorption edge of Ti. We measured the energy and azimuthal angle dependences of the resonant signal at the reflections of $Q=(1\phantom{\rule{0.3em}{0ex}}0\phantom{\rule{0.3em}{0ex}}0)$, (0 1 1), and (0 0 1). The RXS intensity gradually decreased with decreasing the $\mathrm{Gd}\mathrm{Fe}{\mathrm{O}}_{3}$-type distortion. Although there is a magnetic phase boundary between $\mathrm{Gd}\mathrm{Ti}{\mathrm{O}}_{3}$ (ferromagnet) and $\mathrm{Sm}\mathrm{Ti}{\mathrm{O}}_{3}$ (antiferromagnet), the ratio among the magnitudes at those reflections was almost the same. The azimuthal angle dependence also showed an identical periodicity at each scattering vector. With further decreasing the $\mathrm{Gd}\mathrm{Fe}{\mathrm{O}}_{3}$-type distortion, the magnitude of the RXS in $\mathrm{La}\mathrm{Ti}{\mathrm{O}}_{3}$ became small and almost isotropic. This means that the orbital state of $\mathrm{La}\mathrm{Ti}{\mathrm{O}}_{3}$ is different from those of $R\mathrm{Ti}{\mathrm{O}}_{3}$ ($R=\mathrm{Y}$,Gd,Sm). Furthermore, when we approached the Mott transition by hole doping, the signal of the RXS disappeared in $\mathrm{La}\mathrm{Ti}{\mathrm{O}}_{3.02}$, which is just located on the metal-insulator boundary. This indicates a disappearance of the orbital ordering at the Mott transition.

Resonant x-ray scattering as a probe of toroidal moments in centrosymmetric systems

The aim of this paper is to show that it is possible to detect, by means of resonant x-ray scattering (RXS), the magnetic toroidal moment and/or higher order time-reversal and parity-odd multipoles in centrosymmetric systems, where absorption-dichroic techniques are ineffective. We have found a material, ${\mathrm{Li}}_{2}\mathrm{V}\mathrm{O}\mathrm{Si}{\mathrm{O}}_{4}$, whose magnetic space group allows such a measurement. We then performed an ab initio numerical simulation based on a relativistic extension of the multiple scattering theory to show that the intensity of the RXS signal can be detected in modern third generation synchrotron radiation sources. Finally, we stress that RXS, unlike dichroism in absorption, allows a complete separation of toroidal dipole moment and higher order multipoles, due to the possibility of exploiting the extra degrees of freedom related to the incoming and outgoing polarizations.