Analysis of Resonant Soft X-ray Reflectivity of Anisotropic Layered Materials

Abstract

We present here a method for the quantitative prediction of the spectroscopic specular reflectivity line-shape in anisotropic layered media. The method is based on a 4 × 4 matrix formalism and on the simulation from the first principles (through density functional theory—DFT) of the anisotropic absorption cross-section. The approach was used to simulate the reflectivity at the oxygen K-edge of a 3,4,9,10-perylene-tetracarboxylic dianhydride (PTCDA) thin film on Au(111). The effect of film thickness, orientation of the molecules, and grazing incidence angle were considered. The simulation results were compared to the experiment, permitting us to derive information on the film geometry, thickness, and morphology, as well as the electronic structure.

Disclosing the Nature of Asymmetric Interface Magnetism in Co/Pt Multilayers

“…48−51 The averaged and dichroic reflectivity spectra were fitted using the ReMagX code, 52 which calculates the reflectance spectra from a magnetic multilayer using the Zak tensor formalism for magnetooptics, 53 derived from the general 4 × 4-tensor formalism for the propagation of light in anisotropic materials. 54,55 In the advanced element-specific simulation mode, the dielectric tensor of every layer is calculated from the atomic charge and magnetic scattering factors…”

“…Analysis of XRMR measurements was carried out following a general procedure already described in the literature. − The averaged and dichroic reflectivity spectra were fitted using the ReMagX code, which calculates the reflectance spectra from a magnetic multilayer using the Zak tensor formalism for magneto-optics, derived from the general 4 × 4-tensor formalism for the propagation of light in anisotropic materials. , In the advanced element-specific simulation mode, the dielectric tensor of every layer is calculated from the atomic charge and magnetic scattering factors f ( E ) = f 1 ( E ) – if 2 ( E ) and f m ( E ) = f 1 m ( E ) – if 2 m ( E ), respectively, where E = h ν is the photon energy . The determination of the atomic scattering factors for the various elements is the first step in the analysis of the resonant reflectivity spectra .…”

Resonant Soft X-ray Reflectivity in the Study of Magnetic Properties of Low-Dimensional Systems

“…The real and imaginary parts of the refractive index can then be used to compute the dielectric tensor and to derive the specular reflectivity (and related dichroism) according to the procedure described by us in [25].…”

“…In this case, the Parrat formalism [15] is often used to simulate the reflectivity. Anisotropic materials can be treated and more refined results can be obtained applying the 4×4 matrix method [16][17][18][19][20][21][22][23][24][25][26], where each layer is considered anisotropic and described by a suitable dielectric tensor. Since the chemical (compositional) depth profile can be different from the magnetic profile, two independent structural models could be necessary in order to simulate the chemical contrast and magnetic responses.…”

A computational approach to predict and enhance the sensitivity of X-ray resonant magnetic reflectometry to the magnetic behavior of deeply buried interfaces

“…Because of the interest in such structures, non-destructive methods are required for depthresolved studies of structural, chemical and magnetic properties of heterostructures at the nanoscale. This paper is dedicated to the discussion of such a characterization technique based on the synchrotron method of X-ray resonant reflectometry and its magnetic version of X-ray resonant magnetic reflectometry (XRMR) (Fu ¨rsich et al, 2018;Krieft et al, 2020;Moskaltsova et al, 2020;Pasquali et al, 2021). The method is based on the measurement of the sample reflectance as a function of grazing angle, photon energy, photon helicity and applied magnetic field.…”