The polarizing spectroscopy techniques in visible range optics have been used since the beginning of the 20th century to study the anisotropy of crystals based on birefringence and optical activity phenomena. On the other hand, the phenomenon of X-ray optical activity has been demonstrated only relatively recently. It is a selective probe for the element-specific properties of individual atoms in non-centrosymmetric materials. We report the X-ray Natural Circular Dichroism (XNCD) imaging technique which enables spatially resolved mapping of X-ray optical activity in non-centrosymmetric materials. As an example, we present the results of combining micro-focusing X-ray optics with circularly polarized hard X-rays to make a map of enantiomorphous twinning in a multiferroic SmFe${}_3$(BO${}_3$)${}_4$ crystal. Our results demonstrate the utility and potential of polarization-contrast imaging with XNCD as a sensitive technique for multiferroic crystals where the local enantiomorphous properties are especially important. In perspective, this brings a novel high-performance method for the characterization of structural changes associated with phase transitions and identification of the size and spatial distribution of twin domains.

We propose a new method to determine the absolute structure of chiral crystals, which is based on the chiral asymmetry of multiple scattering diffraction. It manifests as a difference in the azimuthal dependence of the forbidden Bragg reflection intensity measured with left and right circularly polarized X-ray beams. Contrary to the existing ones, the suggested method does not use X-ray anomalous dispersion. The difference between the Renninger scans with circularly polarized X-rays has been experimentally demonstrated for the 001 reflection intensities in the right- and left-handed quartz single crystals. A Jmulti-based code on model-independent three-wave-diffraction approach has been developed for quantitative description of our experimental results. The proposed method can be applied to various structures including opaque, organic and monoatomic crystals, even with only light elements. To determine the type of isomer, the Renninger plot of a single forbidden reflection is sufficient.

Examining forbidden reflections provides valuable information on electronic states and the local environment of resonant atoms in crystals. Experimental studies of two forbidden reflections 002 and 100 in TeO${}_2$ single crystals were performed at photon energies close to the $L_1$ tellurium absorption edge. It was found that the spectral form corresponding to these two reflections looks almost identical, which is completely unexpected for a highly anisotropic material. Theoretical consideration shows that only one component $f_{xy}$ of the tensor describing dipole-dipole resonance scattering contributes to the 002 reflection, while two components $f_{xy}$ and $f_{xz}$ correspond to the 100 reflection. Numerical calculations show that the latter tensor component is comparable to the first one, but the combination of several geometric factors leads to the fact that its contribution to the spectrum is negligible. This explains the experimentally observed results. The finding shows a way for targeted investigation of single tensor components and makes it possible to compare different spectra and use them the study the physical phenomena in functional materials.

Absorption spectra of two orthogonal linearly polarized X-rays in a single CeCoGe₃ crystal were measured at the ID12 beamline of the ESRF for the energies near the K-edges of Ge, Co and near the L₂₃ edges of Ce. The X-ray natural linear dichroism (XNLD) was revealed in the vicinity of all the absorption edges, which indicates a splitting of electronic states in a crystalline field. Mathematical modelling in comparison with experimental data allowed the isotropic and anisotropic parts of atomic absorption cross section in CeCoGe₃ to be determined near all measured absorption edges. The calculations also show that the “average” anisotropy of the cross section close to the Ge K-edge revealed in the experiment is less than the partial anisotropic contributions corresponding to Ge atoms in two different Wyckoff positions.