title: Quadrupole transitions revealed by Borrmann spectroscopy.
abstract: The Borrmann effect-a dramatic increase in transparency to X-ray beams-is observed when X-rays satisfying Bragg's law diffract through a perfect crystal. The minimization of absorption seen in the Borrmann effect has been explained by noting that the electric field of the X-ray beam approaches zero amplitude at the crystal planes, thus avoiding the atoms. Here we show experimentally that under conditions of absorption suppression, the weaker electric quadrupole absorption transitions are effectively enhanced to such a degree that they can dominate the absorption spectrum. This effect can be exploited as an atomic spectroscopy technique; we show that quadrupole transitions give rise to additional structure at the L(1), L(2) and L(3) absorption edges of gadolinium in gadolinium gallium garnet, which mark the onset of excitations from 2s, 2p(1/2) and 2p(3/2) atomic core levels, respectively. Although the Borrmann effect served to underpin the development of the theory of X-ray diffraction, this is potentially the most important experimental application of the phenomenon since its first observation seven decades ago. Identifying quadrupole features in X-ray absorption spectroscopy is central to the interpretation of 'pre-edge' spectra, which are often taken to be indicators of local symmetry, valence and atomic environment. Quadrupolar absorption isolates states of different symmetries to that of the dominant dipole spectrum, and typically reveals orbitals that dominate the electronic ground-state properties of lanthanides and 3d transition metals, including magnetism. Results from our Borrmann spectroscopy technique feed into contemporary discussions regarding resonant X-ray diffraction and the nature of pre-edge lines identified by inelastic X-ray scattering. Furthermore, because the Borrmann effect has been observed in photonic materials, it seems likely that the quadrupole enhancement reported here will play an important role in modern optics.
authors.affiliation: Department of Physics, University of Warwick, Coventry CV4 7AL, UK.
authors.forename: Robert F
authors.initials: RF
authors.lastname: Pettifer
authors.forename: Stephen P
authors.initials: SP
authors.lastname: Collins
authors.forename: David
authors.initials: D
authors.lastname: Laundy