Theory of Orbital Ordering, Fluctuation and Resonant X-ray Scattering in Manganites

A theory of resonant x-ray scattering in perovskite manganites is developed by applying the group theory to the correlation functions of the pseudospin operators for the orbital degree of freedom. It is shown that static and dynamical informations of the orbital state are directly obtained from the elastic, diffuse and inelastic scatterings due to the tensor character of the scattering factor. We propose that the interaction and its anisotropy between orbitals are directly identified by the intensity contour of the diffuse scattering in the momentum space.Comment: 4 pages, 1 figur

Multi-k⃗\vec{k} Configurations

Using resonant x-ray scattering to perform diffraction experiments at the U M$_{4}$ edge novel reflections of the generic form have been observed in UAs$_{0.8}$Se$_{0.2}$ where $\vec{k} = $, with $k = {1/2}$ reciprocal lattice units, is the wave vector of the primary (magnetic) order parameter. The reflections, with $10^{-4}$ of the magnetic intensities, cannot be explained on the basis of the primary order parameter within standard scattering theory. A full experimental characterisation of these reflections is presented including their energy, azimuthal and temperature dependencies. On this basis we establish that the reflections most likely arise from the electric dipole operator involving transitions between the core 3d and partially filled $5f$ states. The temperature dependence couples the peak to the triple-$\vec{k}$ region of the phase diagram: Below $\sim 50$ K, where previous studies have suggested a transition to a double-$\vec{k}$ state, the intensity of the $$ is dramatically reduced. Whilst we are unable to give a definite explanation of how these novel reflections appear, this paper concludes with a discussion of possible ideas for these reflections in terms of the coherent superposition of the 3 primary (magnetic) order parameters

Resonant x-ray diffraction study of the magnetoresistant perovskite Pr0.6Ca0.4MnO3

We report a x-ray resonant diffraction study of the perovskite Pr0.6Ca0.4MnO3. At the Mn K-edge, this technique is sensitive to details of the electronic structure of the Mn atoms. We discuss the resonant x-ray spectra measured above and below the charge and orbital ordering phase transition temperature (TCOO = 232 K), and present a detailed analysis of the energy and polarization dependence of the resonant scattering. The analysis confirms that the structural transition is a transition to an orbitally ordered phase in which inequivalent Mn atoms are ordered in a CE-type pattern. The Mn atoms differ mostly by their 3d orbital occupation. We find that the charge disproportionation is incomplete, 3d^{3.5-\delta} and 3d^{3.5+\delta} with \delta\ll0.5 . A revised CE-type model is considered in which there are two Mn sublattices, each with partial e_{g} occupancy. One sublattice consists of Mn atoms with the 3x^{2}-r^{2} or 3y^{2}-r^{2} orbitals partially occupied, the other sublattice with the x^{2}-y^{2} orbital partially occupied.Comment: 15 pages, 15 figure

Cubic approximants in quasicrystal structures

The regular deviations from the exact icosahedral symmetry, usually observed at the diffraction patterns of quasicrystal alloys, are analyzed. It is shown that shifting, splitting and asymmetric broadening of reflections can be attributed to crystalline phases with the cubic symmetry very close to the icosahedral one (such pseudo-icosahedral cubic approximants may be called the Fibonacci crystals). The Fibonacci crystal is labelled as , if in this crystal the most intense vertex reflections have the Miller indices {0, Fn, Fn + 1} where Fi are the Fibonacci numbers (Fi = 1, 1, 2, 3, 5, 8, 13, 21, 34...). The deviations of x-ray and electron reflections from their icosahedral positions are calculated. The comparison with available experimental data shows that at least four different Fibonacci crystals have been observed in Al-Mn and Al-Mn-Si alloys : (MnSi structure), (α-Al-Mn-Si), , and with the lattice constants 4.6 Å, 12.6 Å, 33.1 Å, 86.6 Å respectively. It is interesting to note that there are no experimental evidences for the intermediate approximants , and . The possible space groups of the Fibonacci crystals and their relationships with quasicrystallographic space groups are discussed

Anisotropic resonant X-ray scattering: Beauty of forbidden reflections

Experimental results and their theoretical explanation are reviewed for fundamentals of anisotropic resonant X-ray scattering. Resonant scattering depends on X-ray polarization, i.e. the scattering reflects anisotropic environment of atoms in crystal. The polarization anisotropy in atomic scattering can excite the forbidden Bragg reflections. Studying this type of forbidden reflections we can distinguish electronic orbitals of specific symmetry. This method is very useful for studying local electronic states in crystal. We reveal detailed property of the anisotropic scattering, effect of quadrupole transition, thermal motion, magnetic scattering and so on. Especially successful examples are given in detail: observation of phase of the scattering factor, the hybridization of states with different parity, local chirality of atom in centrosymmetric crystals, thermal-motion-induced resonant reflections, etc

Intensity and width of bragg reflections from imperfect icosahedral quasicrystals obtained by simulating atomic growth.

International audienceThe Bragg reflections from icosahedral quasicrystals obtained in the course of a computer experiment on the simulation of crystal growth have been studied. The computer experiments based on the theory developed earlier allow one to “grow” in a computer the imperfect quasicrystals of nanometer dimensions. It is shown that the absolute value of the structure factor can be close to the maximum possible one for crystals, i.e., to the structure factor in the case where all the atoms scatter in phase. The spectral width of Bragg reflections is studied, and it is shown that the reflection width depends not only on the quasicrystal dimensions in the physical space but, also, on the perpendicular component of the reciprocal-lattice vectors. The data obtained are compared with the known experimental data

Thermal motion induced resonant forbidden reflections in wurtzite GaN

International audienceWe 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

Numerical simulation of the forbidden Bragg reflection spectra observed in ZnO.

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