Chirality-induced `forbidden' reflections in X-ray resonant scattering

Abstract

It is shown that additional Bragg re¯ections can appear exclusively owing to the local chirality associated with the left±right asymmetric environment of scattering atoms in non-magnetic crystals. The structure amplitude of these re¯ections depends on the antisymmetric part of a third-rank tensor describing the spatial dispersion effects. It enhances for resonant near-edge scattering through a mixed multipole transition, which includes a dipole±quadrupole contribution. It is shown that this mechanism works even for centrosymmetric crystals, and some realistic examples are considered in detail ( -Fe 2 O 3 , LiNbO 3 etc.). For instance, the interference between the dipole±quadrupole and quadrupole±quadrupole terms may be responsible for the threefold symmetry of the azimuthal dependence of the hhh, h = 2n + 1, re¯ections observed recently in hematite.

Chiral and magnetic effects in forbidden x-ray scattering from antiferromagnetic hematiteα-Fe2O3and eskolaiteCrKokubun1, Watanabe2, Uehara3 et al. 2008Phys. Rev. B224340View full textAdd to dashboardCite

“…For the 4c site, there is only one symmetry operation, the threefold rotation. Therefore, the second-, third-, and fourth-rank tensors for the metal atom at ͑x , x , x͒, atom 1, can be written as 3,32,34 ͑1͒ a second rank tensor ͑two independent components͒,…”

“…28,29 These scattering are presumed to be due to quadrupolequadrupole or dipole-quadrupole transitions. 30,31 It was shown some time ago 32 that the local chirality of atoms in centrosymmetric crystals, related with the antisymmetric dipole-quadrupole contribution to the tensor atomic factors, could result in a special type of "forbidden" reflections. This antisymmetric contribution could explain the threefold azimuthal symmetry of the hhh "forbidden" reflections observed for hematite and eskolaite in the present paper ͑preliminary results were published in Refs.…”

Resonant diffraction inFeS2:Determination of the x-ray polarization anisotropy of iron atoms

“…25,26 In the latter case, as a rather delicate consequence of distorted wave functions the local chirality of atoms in nonchiral crystals can be probed. 27 However, similar to ''normal'' allowed reflections, the information retrievable from forbidden reflections is limited by the so-called phase problem: one can only measure the structure dependent intensity of a reflection whereas the phase information gets lost. But, since the phase is sensitive to distortions of the atomic wave functions, it would be very important to measure its value, particularly when the interpretation of the forbidden reflections is controversial, as applies to an orbital ordering problem.…”

Polarization anisotropy of X-ray atomic factors and `forbidden' resonant reflections

“…Since the Fe atoms are on the threefold axes, their f tensors are uniaxial (in the dd approximation) and oriented along the threefold axes so that they have the same form for all the atoms and hence yield zero structure factors for the glideplane reflections hhh, h ¼ 2n þ 1. In contrast, the dq and qq f tensors possess different signs of some tensor components of the glide-plane-related atoms, and just the components f dqa zxy and f qq xxxz give non-zero contributions to the structure factors of the 'forbidden' reflections (Dmitrienko & Ovchinnikova, 2001):…”