Fully relativistic theory for the magnetic extended x-ray absorption fine structure

Abstract

A fully relativistic theoretical description of the magnetic extended x-ray absorption fine structure (MEXAFS) is presented that has been set up within the framework of relativistic multiple scattering theory on the basis of the Dirac equation for spin-polarized, magnetic solids. The multiple scattering processes in the final state are treated using the scattering path expansion technique for finite atomic clusters. Results of the approach for the Fe K and the Gd L edges are presented and are compared with experiment. An analysis of the theoretical spectra clearly shows that the MEXAFS spectra can be interpreted on the basis of the so-called sum rules in a way completely analogous to the case of near-edge x-ray magnetic circular dichroism. This means that the K- and L1-edge spectra directly reflect the orbital polarization of the final states with p character. The L2,3-edge spectra, on the other hand, give, after suitable superposition, access to the spin and orbital polarization of the d states.

Functionalization of Zeolitic Cavities: Grafting NH2 Groups in Framework T Sites of B-SSZ-13 A Way to Obtain Basic Solids Catalysts?

“…This approximation is serious, especially when the photoelectron kinetic energy is close to the value of the approximation done on the potential, and moreover, it makes the results depend on the size of the interstitial region between the muffin-tin spheres. To avoid the restriction imposed by this approximation several computing methods have been developed and successfully applied. − Between them the finite difference method currently included in the FDMNES code emerges as providing more reliable results and greater algorithmic stability . This method has been used in this work to simulate the NEXAFS of B atoms in B-SSZ-13.…”

“…To avoid the restriction imposed by this approximation several computing methods have been developed and successfully applied. [67][68][69][70] Between them the finite difference method currently included in the FDMNES code emerges as providing more reliable results and greater algorithmic stability. 70 This method has been used in this work to simulate the NEXAFS of B atoms in B-SSZ-13.…”

Reactivity of Surface Species in Heterogeneous Catalysts Probed by In Situ X-ray Absorption Techniques

“…Moreover, it makes the results dependent on the size of the interstitial region between the muffin tin spheres. To avoid the restriction imposed by this approximation, several computing methods have been developed and successfully applied. , Among them, the finite difference method currently included in the FDMNES code is emerging for the reliable results and the stability of the algorithm. , Other alternative methods are possible: a plane wave’s base is useful for periodic structures because it allows to employ periodic limit conditions but is not appropriate to describe the region in the neighborhood of the atomic nuclei. This problem was partially overcome by Wien2k, , using linear augmented plane, or by Paratec, introducing pseudopotentials in combination with plane waves.…”

Calculating X-ray absorption near-edge structure at very low energy

“…In particular, the discrete variational method (Ellis & Painter, 1970) uses a discretization of the potential to calculate matrix elements but keeps the usual expansion in plane waves in its Koringa±Kohn± Rostoker version. Ebert and co-workers (Huhne et al, 1998), also using the Korringa±Kohn±Rostoker formalism in a full potential approach, have successfully applied the formalism to XANES (Ahlers, Attenkofer & Schu È tz, 1998;Ahlers, Schu È tz et al, 1998;Huhne & Ebert, 1999). The full-linear augmented plane wave (FLAPW) approach (Blaha et al, 1990) is also extensively used to calculate band structure without the muf®n-tin approximation, but all of these methods are restricted to periodic potential.…”