Magnetism-the spontaneous alignment of atomic moments in a material-is driven by quantum mechanical exchange interactions that operate over interatomic distances. Some magnetic interactions cause 1,2 , or are caused by 3,4 , a twisting of arrangements of atoms. This can lead to the magnetoelectric e ect, predicted to play a prominent role in future technology, and to the phenomenon of weak ferromagnetism, governed by the so-called Dzyaloshinskii-Moriya interaction 5-8 . Here we determine the sign of the latter interaction in iron borate (FeBO 3 ) by using synchrotron radiation. We present a novel experimental technique based on the interference between two X-ray scattering processes, where one acts as a reference wave. Our experimental results are validated by state-ofthe-art ab initio calculations. Together, our experimental and theoretical approaches are expected to open up new possibilities for exploring, modelling and exploiting novel magnetic and magnetoelectric materials.There is considerable mystery behind the origins of complicated structures. Although the dominant short-range interactions that allow the building blocks to grow are well understood, the much more subtle forces that lead to a particular twisting at larger lengthscales, such as chiral biological molecules and liquid crystals 9 , and canted magnetic systems 3 , remain subjects of topical debate. In this Letter we seek to address this question for the case of magnetism. Our main findings are twofold: first, we demonstrate a novel and elegant experimental method for exploring magnetic materials with weak relativistic spin-orbit interactions, and second, we present a state-of-the-art quantum-mechanical many-body approach to the detailed description of such interactions in crystals. As a touchstone example we selected crystalline iron borate (FeBO 3 ), which is a strongly correlated electron system with a relatively simple crystal structure, nonetheless allowing a nontrivial canted and locally twisted magnetic ordering pattern. Taken together, these two strands demonstrate that modern condensed matter theory is capable of determining the elusive sign of the Dzyaloshinskii-Moriya interaction, and is thus able to elucidate the mechanism for coupling electric and magnetic degrees of freedom in magnetoelectric multiferroics, and to begin to predict the properties of this important class of materials.The interactions between atomic magnetic moments (or spins) are not direct, but mediated by the intervening matter. Coupling can be diminished through screening 10 , or enhanced, for example, by superexchange via oxygen atoms 11 . Moreover, the coupling is a property of the material and, according to Neumann's principle, must therefore possess all of its symmetries. The most general form of the bilinear coupling energy between two spins contains a scalar (isotropic) exchange term, exchange anisotropy (which we will neglect for the present discussion) and an antisymmetric term that reverses with permutation of the spin indices. The latter is the Dzyaloshi...

Interfaces between polarity domains in nitride semiconductors, the so-called Inversion Domain Boundaries (IDB), have been widely described, both theoretically and experimentally, as perfect interfaces (without dislocations and vacancies). Although ideal planar IDBs are well documented, the understanding of their configurations and interactions inside crystals relies on perfect-interface assumptions. Here, we report on the microscopic configuration of IDBs inside n-doped gallium nitride wires revealed by coherent X-ray Bragg imaging. Complex IDB configurations are evidenced with 6 nm resolution and the absolute polarity of each domain is unambiguously identified. Picoscale displacements along and across the wire are directly extracted from several Bragg reflections using phase retrieval algorithms, revealing rigid relative displacements of the domains and the absence of microscopic strain away from the IDBs. More generally, this method offers an accurate inner view of the displacements and strain of interacting defects inside small crystals that may alter optoelectronic properties of semiconductor devices.

Crystal defects induce strong distortions in diffraction patterns. A single defect alone can yield strong and fine features that are observed in high-resolution diffraction experiments such as coherent X-ray diffraction. The case of facecentred cubic nanocrystals is studied numerically and the signatures of typical defects close to Bragg positions are identified. Crystals of a few tens of nanometres are modelled with realistic atomic potentials and 'relaxed' after introduction of well defined defects such as pure screw or edge dislocations, or Frank or prismatic loops. Diffraction patterns calculated in the kinematic approximation reveal various signatures of the defects depending on the Miller indices. They are strongly modified by the dissociation of the dislocations. Selection rules on the Miller indices are provided, to observe the maximum effect of given crystal defects in the initial and relaxed configurations. The effect of several physical and geometrical parameters such as stacking fault energy, crystal shape and defect position are discussed. The method is illustrated on a complex structure resulting from the simulated nanoindentation of a gold nanocrystal.

Structural quality and stability of nanocrystals are fundamental problems that bear important consequences for the performances of small-scale devices. Indeed, at the nanoscale, their functional properties are largely influenced by elastic strain and depend critically on the presence of crystal defects. It is thus of prime importance to be able to monitor, by noninvasive means, the stability of the microstructure of nano-objects against external stimuli such as mechanical load. Here we demonstrate the potential of Bragg coherent diffraction imaging for such measurements, by imaging in 3D the evolution of the microstructure of a nanocrystal exposed to in situ mechanical loading. Not only could we observe the evolution of the internal strain field after successive loadings, but we also evidenced a transient microstructure hosting a stable dislocation loop. The latter is fully characterized from its characteristic displacement field. The mechanical behavior of this small crystal is clearly at odds with what happens in bulk materials where many dislocations interact. Moreover, this original in situ experiment opens interesting possibilities for the investigation of plastic deformation at the nanoscale.

The structure of the quasicrystalline approximant Al 13 Co 4 (100) has been determined by surface x-ray diffraction (SXRD) and complementary density-functional-theory (DFT) calculations. Thanks to the use of a two-dimensional pixel detector, which speeds up the data acquisition enormously, an exceptionally large set of experimental data, consisting of 124 crystal truncation rods, has been collected and used to refine this complex structure of large unit cell and low symmetry. Various models were considered for the SXRD analysis. The best fit is consistent with a surface termination at the puckered type of planes but with a depletion of the protruding Co atoms. The surface energy of the determined surface model was calculated using DFT, and it takes a rather low value of 1.09 J/m 2. The results for the atomic relaxation of surface planes found by SXRD or DFT were in excellent agreement. This work opens up additional perspectives for the comprehension of related quasicrystalline surfaces.

A compact scanning force microscope has been developed for in situ combination with nanofocused X-ray diffraction techniques at third-generation synchrotron beamlines. Its capabilities are demonstrated on Au nano-islands grown on a sapphire substrate. The new in situ device allows for in situ imaging the sample topography and the crystallinity by recording simultaneously an atomic force microscope (AFM) image and a scanning X-ray diffraction map of the same area. Moreover, a selected Au island can be mechanically deformed using the AFM tip while monitoring the deformation of the atomic lattice by nanofocused X-ray diffraction. This in situ approach gives access to the mechanical behavior of nanomaterials.

Abstract:We demonstrate magnetic lensless imaging by Fourier transform holography using extended references. A narrow slit milled through an opaque gold mask is used as a holographic reference and magnetic contrast is obtained by x-ray magnetic circular dichroism. We present images of magnetic domains in a Co/Pt multilayer thin film with perpendicular magnetic anisotropy. This technique holds advantages over standard Fourier transform holography, where small holes are used to define the reference beam. An increased intensity through the extended reference reduces the counting time to record the farfield diffraction pattern. Additionally it was found that manufacturing narrow slits is less technologically demanding than the same procedure for holes. We achieve a spatial resolution of ∼30 nm, which was found to be limited by the sample period of the chosen experimental setup.

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.