X-ray resonant magnetic scattering from structurally and magnetically rough interfaces in multilayered systems I. Specular reflectivity

TL;DR

This paper develops a theoretical framework for x-ray resonant magnetic scattering from rough multilayer interfaces, deriving formulas for specular reflectivity that account for structural and magnetic roughness, and validates with numerical and experimental data.

Contribution

It introduces a generalized theoretical model for resonant magnetic scattering from rough multilayer interfaces, extending existing formulas to complex multilayer systems.

Findings

Derived a general expression for specular reflectivity with magnetic roughness.

Generalized Nevot-Croce formula for magnetic interfaces.

Validated theory with numerical examples and experimental data from Gd/Fe multilayers.

Abstract

The theoretical formulation of x-ray resonant magnetic scattering from rough surfaces and interfaces is given for specular reflectivity. A general expression is derived for both structurally and magnetically rough interfaces in the distorted-wave Born approximation (DWBA) as the framework of the theory. For this purpose, we have defined a ``structural'' and a ``magnetic'' interface to represent the actual interfaces. A generalization of the well-known Nevot-Croce formula for specular reflectivity is obtained for the case of a single rough magnetic interface using the self-consistent method. Finally, the results are generalized to the case of multiple interfaces, as in the case of thin films or multilayers. Theoretical calculations for each of the cases are illustrated with numerical examples and compared with experimental results of magnetic reflectivity from a Gd/Fe multilayer.