Resonant X-Ray Scattering and Absorption

Abstract

This chapter outlines some of the basic ideas behind nonresonant and resonant X-ray scattering, using classical or semiclassical pictures wherever possible; specifically, we highlight symmetry arguments governing the observation of X-ray optical effects, such as X-ray magnetic circular dichroism and resonant "forbidden" diffraction. Without dwelling on the microscopic physics that underlies resonant scattering, we outline some key steps required for calculating its rotation and polarization dependence, based on Cartesian and spherical tensor frameworks. Several examples of resonant scattering, involving electronic anisotropy and magnetism, are given as illustrations. Our goal is not to develop or defend theoretical concepts in X-ray scattering, but to bring together existing ideas in a pragmatic and utilitarian manner. Absorption and Scattering: The Optical TheoremAbsorption is a special case of scattering. The mathematical relationship between the two, known as the optical theorem, is very general and fundamental. It can be written aswhere is the linear absorption coefficient and n 0 is the atomic density, q, q 0 , ", " 0 are the incident and scattered wavevectors and polarization, and E is the photon energy. We see that absorption scales with the imaginary part of the forward scattering amplitude for a scattered beam that is in the same state (energy, wavevector, polarization) as the incident wave. This can be understood very easily if we accept that the only way to diminish an electromagnetic wave is to add to it a wave that is the same but of opposite phase. Such a wave can be caused by scattering, and

Anisotropy in Borrmann spectroscopy

“…polarization vector, ε, and wavevector, q). We do not concern ourselves with the details of how the tensors couple to give the (scalar) absorption coefficient, as this is dealt with elsewhere [9][10][11][12]14] but simply represent some generic tensor coupling with the symbol, •. The X tensors in turn can be written as a generic coupling of the X-ray beam vectors,…”

“…allowing us again to take advantage of the extensive existing treatments of quadrupole absorption by a single wave field [9][10][11][12]14]. Drawing parallels with the superposition of polarization vectors, this suggests the intriguing possibility (not realized in the Borrmann case) of permitting the effective wave vector to become complex, possibly coupling to chiral sample properties.…”

“…The shape of the anisotropy (although not its magnitude or sign) can be determined from a symmetry analysis of the resonant absorption tensor [9,14] as shown in Fig. 4, bottom left.…”