Energy Line Shape Research Articles

Low-energy quasi-one-dimensional spin dynamics in charge-ordered La2−xSrxNiO4

The low-energy spin excitations of La${}_{2\ensuremath{-}x}$Sr${}_{x}$NiO${}_{4}$, $x=0.275$ and $1/3$, have been investigated by unpolarized- and polarized-inelastic neutron scattering from single crystals. A pattern of magnetic diffuse scattering is observed in both compositions and is consistent with quasi-one-dimensional AFM spin correlations along the charge stripes. Analysis of the energy line shape for $x=1/3$ indicates that the diffuse scattering is inelastic with a characteristic energy of $1.40\ifmmode\pm\else\textpm\fi{}0.07$ meV. There is no discernible difference between the diffuse scattering from $x=0.275$ and $x=1/3$, suggesting that it is an intrinsic property of the charge stripes.

E1 and E2 contributions to the L3 resonance line shape in antiferromagnetic holmium

A detailed study of the angular, energy and polarization dependences of the electric dipolar (E1: 2p→5d) and quadrupolar (E2: 2p→4f) contributions to the x-ray scattering cross-section is presented for holmium in its basal plane spiral antiferromagnetic phase at the L3 edge. The corresponding E1 and E2 scattering factors have been extracted from fits to the experimental energy line shapes, taking into account for the first time a split dipole resonance. Using the imaginary part of the resonant scattering factors to retrieve the XMCD spectrum, we find qualitative agreement with the dichroic spectrum measured in transmission through a holmium foil.

Resonant x-ray scattering at the forbidden reflections in Mn3+ perovskites REMnO3 (RE:La and Tb)

We here report a combined experimental and theoretical resonant x-ray scattering study in two isomorphous compounds, LaMnO3 and TbMnO3. The two samples show an orthorhombic Pbnm structure with four Mn3+ atoms at equivalent positions. The Mn sites have a local inversion symmetry and they are surrounded by nearly tetragonal-distorted oxygen octahedron. The tetragonal distortion is larger in TbMnO3 than in LaMnO3. Resonances were measured at the Mn K-edge of the (h,0,0), (0,k,0) and (0,0,1) (h,k,1=3,5) reflections. All the reflections show a resonance only in the σ-π' polarization channel. The observed resonant intensities exhibit a sin2ϕ dependence on the azimuth angle ϕ. The (h,0,0) and (0,k,0) reflections have identical energy dependence but markedly different than the (0,0,1) reflections. Differences in the energy line shape and width of these resonant reflections between La and Tb samples are explained in terms of the different tetragonal distortion and the different ionic radius of the rare-earth. The origin of the two types of reflections (related to two different nonzero non-diagonal elements of the scattering tensor) is explained within the multiple scattering theory considering long-range order of structural distortions in a cluster up to 63 atoms without invoking any d-orbital order.

Magnetic structure ofSm2IrIn8determined by x-ray resonant magnetic scattering

The magnetic structure of the intermetallic antiferromagnet ${\mathrm{Sm}}_{2}\mathrm{Ir}{\mathrm{In}}_{8}$ was determined using x-ray resonant magnetic scattering. Below ${T}_{N}=14.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, ${\mathrm{Sm}}_{2}\mathrm{Ir}{\mathrm{In}}_{8}$ has a commensurate antiferromagnetic structure with a propagation vector $\stackrel{P\vec}{\ensuremath{\eta}}=(1∕2,0,0)$. The Sm magnetic moments lie in the $ab$ plane and are rotated roughly 18\ifmmode^\circ\else\textdegree\fi{} away from the $a$ axis. The magnetic structure of this compound was obtained by measuring the strong dipolar resonant peak whose enhancement was of over 2 orders of magnitude at the ${L}_{2}$ edge. At the ${L}_{3}$ edge, both quadrupolar and dipolar features were observed in the energy line shape. The magnetic structure and properties of ${\mathrm{Sm}}_{2}\mathrm{Ir}{\mathrm{In}}_{8}$ are found to be consistent with the general trend already seen for the Nd-, Tb-, and the Ce-based compounds from the ${R}_{m}{M}_{n}{\mathrm{In}}_{3m+2n}$ family ($R=\text{rare}$ earth; $M=\mathrm{Rh}$ or Ir; $m=1,2$; $n=0,1$), where the crystalline electrical field effects determine the direction of magnetic moments and the ${T}_{N}$ evolution in the series. The measured N\'eel temperature for ${\mathrm{Sm}}_{2}\mathrm{Ir}{\mathrm{In}}_{8}$ is slightly suppressed when compared to the ${T}_{N}$ of the parent cubic compound $\mathrm{Sm}{\mathrm{In}}_{3}$.

Origin of the resonant x-ray scattering inLaMnO3

We have performed a detailed resonant x-ray scattering (RXS) study at the Mn K edge of LaMnO{sub 3} by measuring the (h,0,0) (0,k,0) and (0,0,l) forbidden reflections (h,k,l=3,5) between 10 and 300 K in the {sigma}-{pi} channel. For all three types of reflections we observed strong resonant peaks presenting the sin{sup 2} {phi} intensity modulation as a function of the azimuth scanning angle {phi}, characteristic of dipolar transitions. Their origin was ascribed to anisotropic tensor scattering, since no change either in energy line shape or in intensity was observed when crossing the Neel temperature at {approx}140 K. Integrated intensities were roughly constant up to 300 K, contrary to previous reports found in the literature. The energy dependence of the scattered intensity for the (h,0,0) and (0,k,0) reflections was identical but different from the (0,0,l) reflection. All reflections have been explained within multiple scattering theory in terms of long-range structural distortions around Mn atoms, without invoking any kind of 3d orbital ordering. We also studied the energy dependence of the principal axes of the anomalous-scattering tensor in a case, like the present one, where the scattering atoms do not possess any point-symmetry axes. We found that they are not constant withmore » the photon energy, implying the absence of a direct correlation between RXS and quadrupolar charge distribution in the ground state.« less

X-ray resonant scattering of(004n+2)forbidden reflections in spinel ferrites

The origin of the x-ray resonant scattering of (002) and (006) forbidden reflections in the spinel ferrites has been investigated. Resonant features were previously observed in ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ at the pre-edge and main-edge energies of the $\mathrm{Fe}\phantom{\rule{0.2em}{0ex}}K$-absorption edge. They were ascribed to dipole--quadrupole and dipole transitions at the tetrahedral and pseudo-octahedral Fe ions, respectively. To corroborate this origin and to differentiate between effects at the different metal sites, we have studied the energy and azimuthal dependencies of these reflections at the Fe, Co, and $\mathrm{Mn}\phantom{\rule{0.2em}{0ex}}K$ edges in $\mathrm{Mn}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ and $\mathrm{Co}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ spinels. ${\mathrm{Mn}}^{2+}$ mainly replaces Fe in the tetrahedral site whereas ${\mathrm{Co}}^{2+}$ occupies the octahedral site. No pre-edge peak is observed either at the $\mathrm{Fe}\phantom{\rule{0.2em}{0ex}}K$-edge in $\mathrm{Mn}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ or at the $\mathrm{Co}\phantom{\rule{0.2em}{0ex}}K$ edge in $\mathrm{Co}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$. On the other hand, the peak at the absorption edge and the oscillations at energies beyond the edge are observed at the $\mathrm{Fe}\phantom{\rule{0.2em}{0ex}}K$ edge in $\mathrm{Mn}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ and $\mathrm{Co}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ and at the $\mathrm{Co}\phantom{\rule{0.2em}{0ex}}K$ edge in $\mathrm{Co}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$. Therefore, the pre-edge peak comes from the metal ions at the tetrahedral site while the main-edge peak arises from the metal ions at the pseudo-octahedral site of the spinel structure. The azimuthal dependence and the energy line shape confirm the dipole--quadrupole and dipole characters of these pre-edge and main-edge resonances, respectively. The energy-dependence spectra of ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ above and below the N\'eel temperature are alike, discarding any magnetic effect on the resonant spectra. Finally, the fine structure at energies beyond the absorption edge has been theoretically simulated considering only the local anisotropy of the dipolar atomic scattering factor of the pseudo-octahedral metal atom. These results demonstrate that $(004n+2)$ resonant reflections arise from the anisotropy of the local structure around the transition-metal atom without contributions of charge or $d$-orbital ordering.

Continuous Outflow Variation along Irrigation Laterals: Effect of the Number of Outlets

Previous continuous-uniform outlet discharge approaches for the hydraulic analysis of irrigation laterals are generally valid for large (theoretically) infinite number of outlets. For a finite number of outlets, however, these approaches may lead to errors in hydraulic computation. A new continuous-uniform outflow approach that takes into account the effect of the number of outlets on the lateral hydraulics is presented. A new analytical equation describing the energy line shape along uniform sprinkle and trickle irrigation laterals and manifolds is developed. The effect of ground slope and velocity head on hydraulic computation is also considered. The method is however restricted by the simplified assumption of equal outlet discharge. An alternate improved analytical method considering the effect of non-uniform outflow distribution along the lateral is also included. Analytical expressions for determining the inlet pressure head and global statistical parameters characterizing the outflow distribution (Christiansen uniformity coefficient, pressure head variation) are developed for design and evaluation purposes. Comparison tests with an accurate numerical stepwise method indicated that the proposed simplified approach is more accurate than other previous works particularly when the number of outlets is relatively small. The improved method is the most accurate method for all cases examined even for low levels of uniformity.

Resonant X-ray magnetic scattering: antiferromagnetic metals

Resonant X-ray magnetic scattering is a recognized tool for the investigation of new magnetic phases and phase transitions. Many experiments on antiferromagnetic materials involve excitation to valence (band) states for which the density of levels extends over a large interval in comparison with Γ, where Γ/ h is the inverse core hole lifetime. A simple model, for the analysis of resonant magnetic scattering from antiferromagnetic materials, is put forward in two stages. First, the antiferromagnetic narrow-band limit is treated and the suggested framework illustrated with an elementary, parametric, analysis of the anomalous resonant energy line shapes observed at the Dy L 2,3 edges in the intermetallic compound DyFe 4Al 8. The method is then extended to deal with intermediate levels which have a bandwidth significant on the scale of Γ.

Spin dynamics in the metallic state of the high- Tc superconducting system YBa 2Cu 3O 6 + x

The spin dynamics in single crystals of YBa 2Cu 3O 6 + x has been successfully investigated, by inelastic neutron scattering (INS) experiments, as a function of temperature in the metallic state over the whole doping range from the weakly doped ( x = 0.45, 0.51) to the heavily doped ( x = 0.69, 0.83, 0.92) and the overdoped ( x = 0.97, 1) regimes. Dynamical AF-correlations persist in all the metallic state. Actually, the imaginary part of the magnetic susceptibility χ″ consists of two contributions which have different doping and temperature dependences. At low temperature, χ″ exhibits an energy gap in any superconducting samples which becomes much weaker close to the insulating-metallic transition. To emphasize the characteristic features of the spin dynamics in YBCO, INS results obtained by other groups are compared with our experiments. Several theoretical approaches, which intend to describe the energy line shape of the dynamical magnetic susceptibility, are also discussed.