X-ray natural circular dichroism in a uniaxial gyrotropic single crystal of LiIO3

Giant X-Ray Circular Dichroism in a Time-Reversal Invariant Antiferromagnet

X-ray circular dichroism, arising from the contrast in X-ray absorption between opposite photon helicities, serves as a spectroscopic tool to measure the magnetization of ferromagnetic materials and identify the handedness of chiral crystals. Antiferromagnets with crystallographic chirality typically lack X-ray magnetic circular dichroism because of time-reversal symmetry, yet exhibit weak X-ray natural circular dichroism. Here, the observation of giant natural circular dichroism in the Ni L3-edge X-ray absorption of Ni3TeO6 is reported, a polar and chiral antiferromagnet with effective time-reversal symmetry. To unravel this intriguing phenomenon, a phenomenological model is proposed that classifies the movement of photons in a chiral crystal within the same symmetry class as that of a magnetic field. The coupling of X-ray polarization with the induced magnetization yields giant X-ray natural circular dichroism, revealing typical ferromagnetic behaviors allowed by the symmetry in an antiferromagnet, i.e., the altermagnetism of Ni3TeO6. The findings provide evidence for the interplay between magnetism and crystal chirality in natural optical activity. Additionally, the first example of a new class of magnetic materials exhibiting circular dichroism is established with time-reversal symmetry.

Chirality in the Solid State: Chiral Crystal Structures in Chiral and Achiral Space Groups

Chirality depends on particular symmetries. For crystal structures it describes the absence of mirror planes and inversion centers, and in addition to translations, only rotations are allowed as symmetry elements. However, chiral space groups have additional restrictions on the allowed screw rotations as a symmetry element, because they always appear in enantiomorphous pairs. This study classifies and distinguishes the chiral structures and space groups. Chirality is quantified using Hausdorff distances and continuous chirality measures and selected crystal structures are reported. Chirality is discussed for bulk solids and their surfaces. Moreover, the band structure, and thus, the density of states, is found to be affected by the same crystal parameters as chirality. However, it is independent of handedness. The Berry curvature, as a topological measure of the electronic structure, depends on the handedness but is not proof of chirality because it responds to the inversion of a structure. For molecules, optical circular dichroism is one of the most important measures for chirality. Thus, it is proposed in this study that the circular dichroism in the angular distribution of photoelectrons in high symmetry configurations can be used to distinguish the handedness of chiral solids and their surfaces.

Probing Molecular Chirality of Ground and Electronically Excited States in the UV-vis and X-ray Regimes: An EOM-CCSD Study

We present several strategies for computing electronic circular dichroism (CD) spectra across different frequency ranges at the equation-of-motion coupled-cluster singles and doubles level of theory. CD spectra of both ground and electronically excited states are discussed. For selected cases, the approach is compared with coupled-cluster linear response results as well as time-dependent density functional theory. The extension of the theory to include the effect of spin-orbit coupling is presented and illustrated by calculations of X-ray CD spectra at the L-edge.

Chirality determination in crystals

This tutorial review article discusses chirality determination in the solid state, both in single crystals and in crystal assemblies, with an emphasis on X-ray diffraction. The main principles of using X-ray diffraction to reliably determine absolute structure are summarized, and the complexity which can be encountered in chiral structures-kryptoracemates, scalemates, and inversion twinning-is illustrated with examples from our laboratories and the literature. We then address the problem of the bulk crystallization and discuss different techniques to determine chirality in a large assembly of crystal structures, with a special prominence given to an X-ray natural circular dichroism mapping technique that we recently reported.

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.

X-ray Natural Circular Dichroism Imaging of Multiferroic Crystals

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 SmFe3(BO3)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.

Hard X-ray magnetochiral dichroism in a paramagnetic molecular 4f complex

Magnetochiral dichroism (MΧD) originates in the coupling of local electric fields and magnetic moments in systems where a simultaneous break of space parity and time-reversal symmetries occurs. This magnetoelectric coupling, displayed by chiral magnetic materials, can be exploited to manipulate the magnetic moment of molecular materials at the single molecule level. We demonstrate herein the first experimental observation of X-ray magnetochiral dichroism in enantiopure chiral trigonal single crystals of a chiral mononuclear paramagnetic lanthanide coordination complex, namely, holmium oxydiacetate, at the Ho L₃-edge. The observed magnetochiral effect is opposite for the two enantiomers and is rationalised on the basis of a multipolar expansion of the matter–radiation interaction. These results demonstrate that 4f–5d hybridization in chiral lanthanoid coordination complexes is at the origin of magnetochiral dichroism, an effect that could be exploited for addressing of their magnetic moment at the single molecule level.

Magnetochiral Dichroism of chiral mononuclear lanthanoid complexes is for the first time detected by X-ray absorption measurements on single crystals of Holmium oxydiacetate, at the Ho L₃-edge. The effect is of opposite sign for the two enantiomers.

Enantiomeric resolution and X-ray optical activity of a tricobalt extended metal atom chain

A simple procedure based on anion exchange was employed for the enantiomeric resolution of the extended metal atom chain (EMAC) [Co3(dpa)4(MeCN)2]2+. Use of the chiral salt (NBu4)2[As2(tartrate)2], (Λ-1 or Δ-1), resulted in the selective crystallization of the EMAC enantiomers as [Δ-Co3(dpa)4(MeCN)2](NBu4)2[Λ-As2(tartarte)2]2, (Δ-2) and [Λ-Co3(dpa)4(MeCN)2](NBu4)2[Δ-As2(tartrate)2]2 (Λ-2), respectively, in the P4212 space group, whereas a racemic mixture of 1 yielded [Co3(dpa)4(MeCN)2][As2(tartrate)2]·2MeCN (rac-3), which crystallized in the C2/c space group. The local electronic and magnetic structure of the EMAC enantiomers was studied, exploiting a variety of dichroisms in single crystals. A strong linear dichroism at the Co K-edge was observed in the orthoaxial configuration, whereas it vanished in the axial orientation, thus spectroscopically confirming the D4 crystal symmetry. Compounds Δ-2 and Λ-2 are shown to be enantiopure materials as evidenced by mirror-image natural circular dichroism spectra in the UV/vis in solution and in the X-ray range at the Co K-edge in single crystals. The surprising absence of detectable X-ray magnetic circular dichroism or X-ray magnetochiral dichroism signals at the Co K-edge, even at low temperature (3 K) and a high magnetic field (17 T), is ascribed to a strongly delocalized spin density on the tricobalt core.

X-ray natural circular dichroism in langasite crystal

Optical activity in the X-ray range stems from the electric-dipole-electric-quadrupole interference terms mixing multipoles of opposite parity, and can be observed exclusively in systems with broken inversion symmetry. The gyration tensor formalism is used to describe the X-ray optical activity in langasite La₃Ga₅SiO₁₄ crystal with the P321 space group. An experimental study of the X-ray natural circular dichroism (XNCD) near the Ga K-edge in La₃Ga₅SiO₁₄ single crystal was performed at ESRF beamline ID12, both along and perpendicular to the crystal optical axis. The combination of the quantum mechanical calculations and high-quality experimental results has allowed us to separate the contributions into X-ray absorption and XNCD spectra of Ga atoms occupying three distinct Wyckoff positions.

X-ray circular dichroism signals: a unique probe of local molecular chirality

Core-resonant circular dichroism (CD) signals are induced by molecular chirality and vanish for achiral molecules and racemic mixtures. The highly localized nature of core excitations makes them ideal probes of local chirality within molecules. Simulations of the circular dichroism spectra of several molecular families illustrate how these signals vary with the electronic coupling to substitution groups, the distance between the X-ray chromophore and the chiral center, geometry, and chemical structure. Clear insight into the molecular structure is obtained through analysis of the X-ray CD spectra.

Extended X-ray absorption fine structure of bimetallic nanoparticles

Electronic and magnetic properties strongly depend on the structure of the material, especially on the crystal symmetry and chemical environment. In nanoparticles, the break of symmetry at the surface may yield different physical properties with respect to the corresponding bulk material. A useful tool to investigate the electronic structure, magnetic behaviour and local crystallographic structure is X-ray absorption spectroscopy. In this review, recent developments in the field of extended X-ray absorption fine structure measurements and in the analysis methods for structural investigations of bimetallic nanoparticles are highlighted. The standard analysis based on Fourier transforms is compared to the relatively new field of wavelet transforms that have the potential to outperform traditional analysis, especially in bimetallic alloys. As an example, the lattice expansion and inhomogeneous alloying found in FePt nanoparticles is presented, and this is discussed below in terms of the influence of employed density functional theory calculations on the magnetic properties.

Magnetic circular dichroism in electron energy loss spectrometry

The measurement of circular dichroism in the electron microscope is a new, emerging method and, as such, it is subject to constant refinement and improvement. Different ways can be envisaged to record the signal. We present an overview of the key steps in the energy-loss magnetic chiral dichroism (EMCD) experiment as well as a detailed review of the methods used in the intrinsic way where the specimen is used as a beam splitter. Lateral resolution up to 20-30 nm can be achieved, and the use of convergent beam techniques leads to an improved S/N ratio. Dichroic effects are shown for Ni and Co single crystal; as a counterexample, measurements were carried also for a non-magnetic (Ti) sample, where no dichroic effect was found.

Calculation of K-edge circular dichroism of amino acids: comparison of random phase approximation with other methods

Soft x-ray natural circular dichroism of amino acids is studied by means of ab initio methods. Several approaches to evaluate the oscillator and rotary strengths of core-to-valence excitations are compared from the viewpoint of basis set dependence: ground-state Hartree-Fock (HF) orbital set employed in (i) random phase approximation (RPA), (ii) static exchange approach (STEX) (unrelaxed), (iii) core-ionized state HF orbital set applied in STEX (relaxed), and (iv) HF excited state orbital set for each core-to-valence excited state. Furthermore in (i) the PRA in the framework of the density functional method (DFT) is compared with the RPA where the ab initio HF orbital set is used. In (iv), the oscillator and rotary strengths evaluated by different orbital sets for the initial and final states, namely, nonorthogonal ground-state and core-excited HF orbitals, are compared with those evaluated by using the core-excited HF orbital set to describe the initial (ground) state. It was shown that, among considered methods, the RPA provides most consistent and less time-consuming results for circular dichroism core excitation spectra. Discussion of the low energy part of K edge circular dichroism spectra of five common amino acids obtained with the help of RPA is presented.

Core Electron Transitions as a Probe for Molecular Chirality: Natural Circular Dichroism at the Carbon K-edge of Methyloxirane

We have measured for the first time the X-ray natural circular dichroism (XNCD) of a chiral molecule in an isotropic medium. In this condition the only surviving term contributing to CD is the cross product between the electric dipole and the magnetic dipole transition moments. The non-zero value of the magnetic dipole transition moment in a 1s-to-valence electron transition is attributed to contribution of valence states to core molecular orbitals. These results open the way to a "local" chiral molecular analysis and to the study of stereochemically selected photochemical processes.

Local chiral-symmetry breaking in globally centrosymmetric crystals

A thorough tensor analysis of the Bragg-forbidden reflection (00.3)(h) in corundum systems having a global center of inversion, such as V2O3 and alpha-Fe2O3, shows that anomalous x-ray resonant diffraction can access chiral properties related to the dipole-quadrupole (E1-E2) channel via an interference with the pure quadrupole-quadrupole (E2-E2) process. This is also confirmed by independent ab initio numerical simulations. In such a way, it becomes possible to detect chiral quantities in systems where dichroic absorption techniques are ineffective.

A proposal for dichroic experiments in the electron microscope

Building upon the similarities between inelastic electron scattering and X-ray absorption we show that dichroism can be observed in electron energy loss spectrometry (EELS) in the transmission electron microscope (TEM). Natural or magnetic linear dichroism can be studied in electron scattering experiment with definite wave vector transfer in the interaction.The detection of circular dichroism in the TEM relies on interferometric EELS in a particular scattering geometry that allows extraction of the mixed dynamic form factor from energy loss spectra. Similarities between dichroic signals in energy loss near edge structures and X-ray absorption near edge structures are discussed, and a new experimental setup for dichroic measurements in the TEM is proposed.

X-ray magnetochiral dichroism: a new spectroscopic probe of parity nonconserving magnetic solids

We report the first experimental detection of x-ray magnetochiral dichroism in magnetoelectric Cr2O3. This dichroism, which does not require any polarized x-ray beam, is related to the time-reversal odd part of the optical activity tensor dominated by electric dipole-electric quadrupole E1E2 interference terms. The experiments were carried out using either a single crystal or a powdered pellet required to grow a single antiferromagnetic domain by magnetoelectric annealing. This new element (edge) specific spectroscopy offers unique access to the atomic orbital anapole moment Omega-z.

First observation of nonreciprocal X-Ray gyrotropy

We report the first observation of a nonreciprocal x-ray linear dichroism caused by the time-reversal odd, real part zeta of the complex gyrotropy tensor zeta(*) which is dominated by electric dipole-electric quadrupole E1E2 interference terms. A nonreciprocal transverse anisotropy was observed in the low temperature insulating phase of a Cr doped V2O3 Mott crystal when a single antiferromagnetic domain was grown by magnetoelectric annealing along the hexagonal c axis. This new element (edge) specific spectroscopy could nicely complement x-ray magnetic circular dichroism which is silent for antiferromagnetic materials.