Standing wave approach in the theory of x-ray magnetic reflectivity

TL;DR

This paper extends x-ray resonant magnetic reflectivity theory by incorporating standing wave effects, enabling more sensitive analysis of magnetic multilayer depth profiles and faster calculations of magnetic reflectivity asymmetries.

Contribution

The authors developed an extended theory that accounts for standing wave effects in x-ray magnetic reflectivity, improving interpretability and computational efficiency.

Findings

Standing waves determine magnetic reflectivity contributions.

The approach simplifies calculations of asymmetry ratios.

Enhanced sensitivity to magnetic depth profiles.

Abstract

We have developed the extension of the exact x-ray resonant magnetic reflectivity theory taking into account the small value of the magnetic terms in the x-ray susceptibility tensor. We have shown that squared standing waves (forth powder of the total electric field module) determine the output of the magnetic addition to the total reflectivity from a magnetic multilayer. The approach gives the easily understandable results especially for the reflectivity part with the rotated polarization and the obtained relationship can essentially speed up the calculation of the asymmetry ratio of the magnetic reflectivity relative the sign of the circular polarization in the incident radiation. The connection of the magnetic contribution with the standing wave structure in the magnetic multilayer means that the magnetic reflectivity with rotated polarization possesses higher sensitivity to the depth profiles of magnetization and magnetic elements depth distribution than the secondary radiation registration at the specular reflection condition.