Resonant X-ray scattering in low quartz to characterize the polarization light

The variation with energy of the diffracted peak intensities around the absorption edges has been known for very long time. It is only very recently that resonant elastic x-ray scattering (REXS) experiments were performed on enantiomers [1], showing the sensitivity of this technique to study tiny features in these materials. In right and left low quartz, azimuthal scans of the (001) reflection intensity show the angular anisotropy by presenting a 3 fold periodicity. These scans are shifted and their amplitude oscillations vary when changing from right to left the enantiomer or when changing the light helicity. Our purpose is to show that azimuthal scans recording the (001) reflection intensity in right and left low quartz can be completely explained by the proper taking into account of the polarization characteristics of the incoming electromagnetic wave. More importantly, we show that such experiments are an excellent way to fully determine the light properties, when this one is not perfectly known. From these scans, we get 3 equations giving their relative shift, the ratio between their amplitude oscillations and the polarization rate. Consequently, without need of simulations because these equations only depend on the symmetry and the geometry, we are able to get the three unknowns which are the Stokes parameter values. Such characterization does not depend on energy, or absorbing atom atomic number. This is thus feasible at other edges or with other compounds, such as GeO2, having the same symmetry. This opens the possibility of characterizing the light polarization on a wide energy range. This study is supported by ab initio simulations on REXS and linear dichroism to validate our demonstration and to eliminate the other possibilities such as higher contribution in term of transition channels (E1E2 or E2E2) or birefringence effects.

Measuring the sense of the Dzyaloshinskii-Moriya interaction

The spin-orbit Dzyaloshinskii-Moriya (DM) interaction EDM=D·[s1×s2] can induce small canting of neighboring magnetic moments s1 and s2. It is also very important for multiferroics and helimagnetic MnSi-type crystals with the spiral or Skyrmionic structures. The sense of the DM vector D has been experimentally determined for the first time in canted antiferromagnetic FeBO3 crystal [1]. The technique of interference between magnetic and resonant channels in synchrotron x-ray scattering was exploited. The phase of antiferromagnetic ordering (and scattering) was fixed by external magnetic field and the phase of resonant scattering was calculated with FDMNES program. Similar experiments have been also performed for MnCO3 and CoCO3 crystals. For Fe2O3 hematite crystal, the technique of interference between magnetic and multiple diffraction channels has been used. The experimental measurements are supported by ab initio calculations of the DM interaction. The first-principles calculations have been performed with Local Density Approximation incorporating the on-site Coulomb interaction U and the Spin-Orbit coupling (LDA+U+SO) [2,3]. It was found how DM interaction depends on displacements of oxygen atoms. These experimental and theoretical approaches open up new possibilities for exploring, modeling and exploiting novel magnetic and multiferroic materials. VED and ENO are grateful to the RFBR research project No. 13-02-00760 and to the project of Presidium of Russian Academy of Sciences No. 24. The work of VVM is supported by the grant program of President of Russian Federation MK-5565.2013.2, the contracts of the Ministry of education and science of Russia N 14.A18.21.0076 and 14.A18.21.0889. MIK acknowledges a financial support by FOM (The Netherlands).

Mapping domains in the weak ferromagnet CoCO₃

The Dzyaloshinskii-Moriya (DM) interaction [1,2] produces a perpendicular component in the coupling of neighbouring spins when the symmetry between the spins is low, or can drive a distortion of intervening atoms to create a spontaneous electric polarization in some magnetoelectrics. In weak ferromagnets, the canting of the atomic moments due to the DM interaction leads to a small parasitic ferromagnetic polarization in an otherwise antiferromagnetic structure. Recently, we determined the sign of the Dzyaloshinskii-Moriya interaction in the weak ferromagnet FeBO3 by measuring the interference between resonant x-ray scattering and non-resonant magnetic scattering at a forbidden reflection [3]. Using the same method, we determine its sign in the carbonates MnCO3 and CoCO3. These isostructural materials turn out to show opposite interference effect: further analysis is underway to confirm or not that they actually have Dzyaloshinskii-Moriya interactions of opposite signs. We go one step further and apply the same principle to map the absolute orientation (direction and sense) of the magnetisation in a crystal of CoCO3: by mapping the 009 forbidden reflection at 3 azimuthal angles, we obtain 3 projections of the local magnetisation allowing its unambiguous determination. The reconstructed magnetisation map, whose spacial resolution is about 20 µm x 20 µm (the size of the focused x-ray beam), was measured after zero-field cooling to 9 K, well below the Neel temperature. It confirms the strong in-plane anisotropy of the material, with magnetisation domains essentially along 6 orientations separated by 60⁰. Two of them, with orientation at 60⁰ to each other (green and orange in the figure), are largely dominant on the part of the sample that was imaged. To our knowledge it is the first experimental determination of the absolute orientation of the magnetic moments in a weak ferromagnet. The figure shows the reconstructed map of magnetisation, with the direction of the local in-plane magnetisation encoded (in radians) on a periodic colour map.