Helicity-dependent resonant X-ray scattering in CuB2O4.

Exploitation of X-ray circular polarized beams to study forbidden Bragg reflections and new information that could be obtained in these experiments are discussed. It is shown that the intensities of such reflections can be different for the right- and left-circular polarizations (i.e. exhibiting circular dichroism) even for the dipole-dipole resonant transitions involved in the scattering process. This difference can be observed only in crystals having no center of inversion. Here, this approach is used to study helicity-dependent resonant diffraction in copper metaborate CuB2O4 single crystal, which is non-centrosymmetric but achiral. Nonetheless, a strong circular dichroism has been observed for hh0 forbidden reflections in the vicinity of the Cu K-edge. This effect is shown to originate from dipolar transitions in Cu atoms occupying the 8(d) Wyckoff position only.

Band Filling Control of the Dzyaloshinskii-Moriya Interaction in Weakly Ferromagnetic Insulators.

We observe and explain theoretically a dramatic evolution of the Dzyaloshinskii-Moriya interaction (DMI) in the series of isostructural weak ferromagnets, MnCO_{3}, FeBO_{3}, CoCO_{3}, and NiCO_{3}. The sign of the interaction is encoded in the phase of the x-ray magnetic diffraction amplitude, observed through interference with resonant quadrupole scattering. We find very good quantitative agreement with first-principles electronic structure calculations, reproducing both sign and magnitude through the series, and propose a simplified "toy model" to explain the change in sign with 3d shell filling. The model gives insight into the evolution of the DMI in Mott and charge transfer insulators.

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.

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

Thermal motion induced (TMI) scattering is a unique probe of changes in electronic states with atomic displacements in crystals. We show that it provides a novel approach to extract atomic correlation functions. Using numerical calculations, we are able to reproduce the temperature-dependent energy spectrum of the 115 'forbidden' Bragg reflection in ZnO. Our previous experimental studies showed that the intensity growth of such reflections over a wide range of temperatures is accompanied by a dramatic change in the resonant spectral lineshape. This is the result of the interplay between the temperature-independent (TI) and temperature-dependent TMI contributions. Here, we confirm that the TI part of the resonant structure factor can be associated with the dipole-quadrupole contribution to the structure factor and show that the temperature-dependent part arises from the zinc and oxygen vibrations, which provide additional temperature-dependent dipole-dipole tensor components to the structure factor. By fitting the experimental data at various temperatures we have determined the temperature dependences of autocorrelation and correlation functions.

Interplay of inequivalent atomic positions in resonant x-ray diffraction of Fe(3)BO(6).

'Forbidden' Bragg reflections of iron orthoborate Fe(3)BO(6) were studied theoretically and experimentally in the vicinity of the iron K edge. Their energy spectra are explained as resulting from the interference of x-rays scattered from two inequivalent crystallographic sites occupied by iron ions. This particular structure property gives rise to complex azimuthal dependences of the reflection intensities in the pre-edge region as they result from the interplay of site specific dipole-quadrupole and quadrupole-quadrupole resonant scattering. Also evidenced is an anisotropic character of the absorption spectrum. Self-absorption correction to the diffraction data, as well as possible contributions of thermal vibrations and magnetic order, are discussed. Particular care is given to extracting clean spectra from the data, and it is demonstrated that excellent results can be obtained even from measurements that appear corrupted by several effects such as poor crystal quality and multiple scattering.

Chirality-induced 'forbidden' reflections in X-ray resonant scattering.

It is shown that additional Bragg reflections can appear exclusively owing to the local chirality associated with the left-right asymmetric environment of scattering atoms in non-magnetic crystals. The structure amplitude of these reflections depends on the antisymmetric part of a third-rank tensor describing the spatial dispersion effects. It enhances for resonant near-edge scattering through a mixed multipole transition, which includes a dipole-quadrupole contribution. It is shown that this mechanism works even for centrosymmetric crystals, and some realistic examples are considered in detail (alpha-Fe2O3, LiNbO3 etc.). For instance, the interference between the dipole-quadrupole and quadrupole-quadrupole terms may be responsible for the threefold symmetry of the azimuthal dependence of the hhh, h = 2n + 1, reflections observed recently in hematite.

Resonant X-ray scattering in the presence of several anisotropic factors.

The general form of the X-ray susceptibility tensor near absorption edges is found when several anisotropic factors, such as the anisotropy of local atomic environment, magnetic ordering and orbital ordering, simultaneously exist in a crystal. Different phenomenological approaches are used to obtain the explicit form of the susceptibility tensor and to find the contributions from each anisotropic factor separately as well as 'combined' terms owing to their simultaneous existence. The results of the theoretical treatment are applied to the resonant diffraction by La0.5Sr1.5MnO4 below the Neel temperature, where charge and orbital ordering coexist with anisotropy of local atomic environment and magnetic ordering.