Right handed or left handed? Forbidden x-ray diffraction reveals chirality

Negative Refraction of Weyl Phonons at Twin Quartz Interfaces

In Nature, α-quartz crystals frequently form contact twins, which are two adjacent crystals with the same chemical structure but different crystallographic orientation, sharing a common lattice plane. As α-quartz crystallizes in a chiral space group, such twinning can occur between enantiomorphs with the same handedness or with opposite handedness. Here, we use first-principles methods to investigate the effect of twinning and chirality on the bulk and surface phonon spectra, as well as on the topological properties of phonons in α-quartz. We demonstrate that, even though the dispersion appears identical for all twins along all high-symmetry lines and at all high-symmetry points in the Brillouin zone, the dispersions can be distinct at generic momenta for some twin structures. Furthermore, when the twinning occurs between different enantiomorphs, the charges of all Weyl nodal points flip, which leads to mirror symmetric isofrequency contours of the surface arcs on certain surfaces. We show that this allows negative refraction to occur at interfaces between certain twins of α-quartz.

Chirality-Induced Selectivity of Phonon Angular Momenta in Chiral Quartz Crystals

A generation, propagation, and transfer of phonon angular momenta are examined on thermal transport in chiral insulative and diamagnetic crystals of α-quartz. We found that thermally driven phonons carry chirality-dependent angular momenta in the quartz crystals and they could be extracted from the quartz as a spin signal. Namely, chirality-induced selectivity of phonon angular momenta is realized in the chiral quartz. We argue that chiral phonons available in chiral materials could be a key element in triggering or enhancing chirality-induced spin selectivity with robust spin polarization and long-range spin transport found in various chiral materials.

Chiral phonons in quartz probed by X-rays

The concept of chirality is of great relevance in nature, from chiral molecules such as sugar to parity transformations in particle physics. In condensed matter physics, recent studies have demonstrated chiral fermions and their relevance in emergent phenomena closely related to topology1-3. The experimental verification of chiral phonons (bosons) remains challenging, however, despite their expected strong impact on fundamental physical properties4-6. Here we show experimental proof of chiral phonons using resonant inelastic X-ray scattering with circularly polarized X-rays. Using the prototypical chiral material quartz, we demonstrate that circularly polarized X-rays, which are intrinsically chiral, couple to chiral phonons at specific positions in reciprocal space, allowing us to determine the chiral dispersion of the lattice modes. Our experimental proof of chiral phonons demonstrates a new degree of freedom in condensed matter that is both of fundamental importance and opens the door to exploration of new emergent phenomena based on chiral bosons.

Amplification of elliptically polarized sub-femtosecond pulses in neon-like X-ray laser modulated by an IR field

Amplification of attosecond pulses produced via high harmonic generation is a formidable problem since none of the amplifiers can support the corresponding PHz bandwidth. Producing the well defined polarization state common for a set of harmonics required for formation of the circularly/elliptically polarized attosecond pulses (which are on demand for dynamical imaging and coherent control of the spin flip processes) is another big challenge. In this work we show how both problems can be tackled simultaneously on the basis of the same platform, namely, the plasma-based X-ray amplifier whose resonant transition frequency is modulated by an infrared field.

Semiconductors with Chiral Crystal Structure in Group IVB Transition Metal Pernitrides

Group IVB transition metal (TM) nitrides rarely exhibit semiconductor phase, except for TM3N4 (TM = Ti, Zr, and Hf) compounds. In this study, using the ab-initio calculations based on density...

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.

Chirality of Liquid Crystals Formed from Achiral Molecules Revealed by Resonant X-Ray Scattering

Intensive research on chiral liquid crystals (LCs) has been fueled by their actively tunable physicochemical properties and structural complexity, comparable to those of sophisticated natural materials. Herein, recent progress in the discovery of new classes of chiral LCs, enabled by a combination of nano- and macroscale investigations is reviewed. First, an overview is provided of liquid crystalline phases, made of chiral and achiral low-weight molecules, that exhibit chiral structure and/or chiral morphology. Then, recent progress in the discovery of new classes of chiral LCs, particularly enabled by the application of resonant X-ray scattering is described. It is shown that the method is sensitive to modulations of molecular orientation and therefore provides information hardly accessible by means of other techniques, such as the sense of helical structures or chirality transfer across length scales. Finally, a perspective is presented on the future scope, opportunities, and challenges in the field of chiral LCs, in particular related to nanocomposites.

Detecting Crystallographic Lattice Chirality using Resonant Inelastic X-ray Scattering

The control and detection of crystallographic chirality is an important and challenging scientific problem. Chirality has wide ranging implications from medical physics to cosmology including an intimate but subtle connection in magnetic systems, for example Mn1-xFexSi. X-ray diffraction techniques with resonant or polarized variations of the experimental setup are currently utilized to characterize lattice chirality. We demonstrate using theoretical calculations the feasibility of indirect K -edge bimagnon resonant inelastic X-ray scattering (RIXS) spectrum as a viable experimental technique to distinguish crystallographic handedness. We apply spin wave theory to the recently discovered √5 × √5 vacancy ordered chalcogenide Rb0.89Fe1.58Se2 for realistic X-ray experimental set up parameters (incoming energy, polarization, Bragg angle, and experimental resolution) to show that the computed RIXS spectrum is sensitive to the underlying handedness (right or left) of the lattice. A Flack parameter definition that incorporates the right- and left- chiral lattice RIXS response is introduced. It is shown that the RIXS response of the multiband magnon system RbFeSe arises both from inter- and intra- band scattering processes. The extinction or survival of these RIXS peaks are sensitive to the underlying chiral lattice orientation. This in turn allows for the identification of the two chiral lattice orientations.

Emergent chirality in the electric polarization texture of titanate superlattices

Chirality is a geometrical property by which an object is not superimposable onto its mirror image, thereby imparting a handedness. Chirality determines many important properties in nature-from the strength of the weak interactions according to the electroweak theory in particle physics to the binding of enzymes with naturally occurring amino acids or sugars, reactions that are fundamental for life. In condensed matter physics, the prediction of topologically protected magnetic skyrmions and related spin textures in chiral magnets has stimulated significant research. If the magnetic dipoles were replaced by their electrical counterparts, then electrically controllable chiral devices could be designed. Complex oxide BaTiO₃/SrTiO₃ nanocomposites and PbTiO₃/SrTiO₃ superlattices are perfect candidates, since "polar vortices," in which a continuous rotation of ferroelectric polarization spontaneously forms, have been recently discovered. Using resonant soft X-ray diffraction, we report the observation of a strong circular dichroism from the interaction between circularly polarized light and the chiral electric polarization texture that emerges in PbTiO₃/SrTiO₃ superlattices. This hallmark of chirality is explained by a helical rotation of electric polarization that second-principles simulations predict to reside within complex 3D polarization textures comprising ordered topological line defects. The handedness of the texture can be topologically characterized by the sign of the helicity number of the chiral line defects. This coupling between the optical and novel polar properties could be exploited to encode chiral signatures into photon or electron beams for information processing.

Observation of quadrupole helix chirality and its domain structure in DyFe3(BO3)4

Resonant X-ray diffraction (RXD) uses X-rays in the vicinity of a specific atomic absorption edge and is a powerful technique for studying symmetry breaking by motifs of various multipole moments, such as electric monopoles (charge), magnetic dipoles (spin) and electric quadrupoles (orbital). Using circularly polarized X-rays, this technique has been developed to verify symmetry breaking effects arising from chirality, the asymmetry of an object upon its mirroring. Chirality plays a crucial role in the emergence of functionalities such as optical rotatory power and multiferroicity. Here we apply spatially resolved RXD to reveal the helix chirality of Dy 4f electric quadrupole orientations and its domain structure in DyFe3(BO3)4, which shows a reversible phase transition into an enantiomorphic space-group pair. The present study provides evidence for a helix chiral motif of quadrupole moments developed in crystallographic helix chirality.

Effects of dispersion and absorption in resonant Bragg diffraction of x-rays

Resonant diffraction of x-rays by crystals with anisotropic optical properties is investigated theoretically, to assess how the intensity of a Bragg spot is influenced by effects related to dispersion (birefringence) and absorption (dichroism). Starting from an exact but opaque expression, simple analytic results are found to expose how intensity depends on dispersion and absorption in the primary and secondary beams and, also, the azimuthal angle (rotation of the crystal about the Bragg wavevector). If not the full story for a given application, our results are more than adequate to explore consequences of dispersion and absorption in the intensity of a Bragg spot. Results are evaluated for antiferromagnetic copper oxide, and low quartz. For CuO, one of our results reproduces all salient features of a previously published simulation of the azimuthal-angle dependence of a magnetic Bragg peak. It is transparent in our analytic result that dispersion and absorption effects alone cannot reproduce published experimental data. Available data for the azimuthal-angle dependence of space-group forbidden reflections (0,0, l), with l ≠ 3n, of low quartz depart from symmetry imposed by the triad axis of rotation symmetry. The observed asymmetry can be induced by dispersion and absorption even though absorption coefficients are constant, independent of the azimuthal angle, in this class of reflections.

Acentric magnetic and optical properties of chalcopyrite (CuFeS2)

The absence of spatial inversion symmetry at both local (point group 4) and global (crystal class (4)2m) levels greatly influences the electronic properties of chalcopyrite (CuFeS(2)). The predicted dichroic signals (natural circular, non-reciprocal and magneto-chiral) and resonant, parity-odd Bragg diffraction patterns at space-group forbidden reflections portray the uncommon, acentric symmetry. Despite extensive experimental investigations over several decades, by mineralogists, chemists and physicists, there is no consensus view about the electrical and magnetic properties of chalcopyrite. New spectroscopic and diffraction data, gathered at various temperatures in the vicinity of the copper and iron L(2,3) edges, provide necessary confidence in the magnetic motif used in our analytic simulations of x-ray scattering. With the sample held at 10 and 65 K, our data establish beyond reasonable doubt that there is no valence transition, and ordering of the copper moments as the origin of the low-temperature phase (T(c) ≈ 53 K) is ruled out.

Determination of the absolute chirality of tellurium using resonant diffraction with circularly polarized x-rays

Many proteins, sugars and pharmaceuticals crystallize into two forms that are mirror images of each other (enantiomers) like our right and left hands. Tellurium is one enantiomer having a space group pair, P3(1)21 (right-handed screw) and P3(2)21 (left-handed screw). X-ray diffraction with dispersion correction terms has been playing an important role in determining the handedness of enantiomers for a long time. However, this approach is not applicable for an elemental crystal such as tellurium or selenium. We have demonstrated that positive and negative circularly polarized x-rays at the resonant energy of tellurium can be used to absolutely distinguish right from left tellurium. This method is applicable to chiral motifs that occur in biomolecules, liquid crystals, ferroelectrics and antiferroelectrics, multiferroics, etc.

Chirality, magnetic charge and other strange entities in resonant x-ray Bragg diffraction

Subtleties in the electronic structure of complex materials can be directly observed, in great detail, by means of the Bragg diffraction of x-rays whose energy matches an atomic resonance. Strange atomic multipoles can be encountered in the interpretation of measured Bragg intensities, e.g., chirality and magnetic charge. Additionally, the x-ray technique allows the direct observation of the enantiomorphic screw-axis in chiral crystals, such as tellurium, low quartz and berlinite.

An ultrahigh-vacuum apparatus for resonant diffraction experiments using soft x rays (hnu=300-2000 eV)

We have developed an ultrahigh-vacuum instrument for resonant diffraction experiments using polarized soft x rays in the energy range of hnu=300-2000 eV at beamline BL17SU of SPring-8. The diffractometer consists of modified differentially pumped rotary feedthroughs for theta-2theta stages, a sample manipulator with motor-controlled x-y-z-, tilt (chi)-, and azimuth (phi)-axes, and a liquid helium flow-type cryostat for temperature dependent measurements between 30 and 300 K. Test results indicate that the diffractometer exhibits high reproducibility (better than 0.001 degrees ) for a Bragg reflection of alpha-quartz 100 at a photon energy of hnu=1950 eV. Typical off- and on-resonance Bragg reflections in the energy range of 530-1950 eV could be measured using the apparatus. The results show that x-ray diffraction experiments with energy-, azimuth-, and incident photon polarization-dependence can be reliably measured using soft x rays in the energy range of approximately 300-2000 eV. The facility can be used for resonant diffraction experiments across the L-edge of transition metals, M-edge of lanthanides, and up to the Si K-edge of materials.

Crystal handedness and spin helix chirality in Fe1-xCoxSi

We show, with the help of polarized neutrons, that the cubic magnets Fe1-xCoxSi with Dzyaloshinskii-Moriya interaction can be switched between left (for x=0.1, 0.15) and right (for x=0.2, 0.25, 0.3, 0.5) chiral states of the spin helix. The absolute structure was evaluated using x-ray diffraction. The crystals are shown to be enantiopure and the structural chirality changes from right handed for x<0.2 to left handed for x>0.2. These compounds are compared with the etalon sample of MnSi which is identified as having the left-handed chirality both in the magnetic and crystallographic sense.

Resonant diffraction of circularly polarized x-rays by a chiral crystal (low quartz)

A correlation in x-ray resonant scattering between crystal chirality and circular polarization (helicity) is explored in the context of an analysis of Bragg diffraction from low quartz (α-SiO(2)). There is a one-to-one correlation between chirality and helicity when one resonant event is present in diffraction and thus, in this simple case, resonant Bragg diffraction of circularly polarized x-rays is a direct probe of crystal chirality. The presence of more than one resonant event is shown to add phase relations to the scattering amplitude and then coupling of helicity and chirality is no longer transparent.