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.

Defect induced forbidden X-ray reflections in RbH₂PO₄.

Resonant X-ray diffraction was used to study the proton jumps in hydrogen-bonded rubidium dihydrogen phosphate (RDP) crystals. In the paraelectric RDP phase, hydrogen is delocalized between two crystallographically equivalent positions. At lower temperatures, this symmetry can be broken, which defines the processes that lead to the para- to ferroelectric phase transition. We have measured the energy spectra of the forbidden reflections 006 and 550 at incident radiation energies close to the Rb K-edge in a wide temperature range, down to the temperature of the ferroelectric phase transition. In the paraelectric phase we observed a growth of integrated intensity for both forbidden reflections with temperature. This behavior is opposite to conventional non-resonant Bragg reflections, where the intensity decreases in accordance with the Debye-Waller factor. The developed theoretical model explains this effect with the thermal motion induced (TMI) scattering mechanism and also confirms the adiabatic approximation stating that electrons instantly follow the nuclei movements. In the 550 energy spectra, we have observed an additional contribution to the resonant structure factor which could be associated with the presence of transient Slater-type proton configurations (PC) in the half-filled hydrogen position.