Perturbative Theory of Grazing-Incidence Diffuse Nuclear Resonant Scattering of Synchrotron Radiation

TL;DR

This paper develops a perturbative theoretical framework for off-specular grazing-incidence nuclear resonant scattering of synchrotron radiation, enabling detailed analysis of thin film structures with hyperfine interactions and lateral inhomogeneities.

Contribution

It introduces a Distorted Incident-Wave Approximation (DIWA) for analytical formulas of diffuse SMR, compares it with DWBA, and applies the theory to experimental and simulated multilayer data.

Findings

DIWA provides accurate analytical formulas for diffuse SMR.

Comparison shows DIWA's advantages and limitations relative to DWBA.

Experimental SMR maps agree with the theoretical simulations.

Abstract

Theoretical description of off-specular grazing-incidence nuclear resonant scattering of synchrotron radiation (Synchrotron M\"{o}ssbauer Reflectometry, SMR) is presented. The recently developed SMR, similarly to polarized neutron reflectometry (PNR), is an analytical tool for the determination of isotopic and magnetic structure of thin films and multilayers. It combines the sensitivity of M\"{o}ssbauer spectroscopy to hyperfine interactions and the depth selectivity of x-ray reflectometry. Specular reflection provides information on the depth profile, while off-specular scattering on the lateral structure of scattering layers. Off-specular SMR and PNR intensity formulae of a rather general multilayer with different domains, based on a Distorted Incident-Wave Approximation (DIWA) are presented. The Distorted-Wave Born Approximation (DWBA) results are given in an Appendix. Physical and numerical implications, why using DIWA, are explained. The temporal character of SMR imposes specific differences between SMR and PNR. In order to reveal the limits of DIWA and to compare the two analytical methods, two-dimensional diffuse SMR and PNR maps of an antiferromagnetic multilayer are calculated and critically compared. Experimental '$\omega-2\theta$' SMR map of a periodic $[ \mathrm{Fe}/\mathrm{Cr}]_{20}$ multilayer is presented and compared with simulations by the present theory.