Blind fit modeling of soft x-ray resonant reflectivity maps in nanoscale epitaxial iron oxide multilayers

Abstract

In the present paper, we apply a blind fitting algorithm to model two-dimensional energy-incidence angle maps of soft x-ray resonant reflectivity measured in nanoscale epitaxial multilayers of multiferroic ε-Fe2O3 grown by pulsed laser deposition. The possibility of fitting the spectral shape of the complex refraction index across the Fe L3 absorption edge without having an initial guess about the optical constants has been demonstrated. The spectral shape fitting of the real (f1) and imaginary (f2) parts of the atomic scattering factor has been carried out by using a specially designed software utilizing OpenCL fast calculations on graphical processing units. The Kramers-Kronig relations between f1 and f2 are automatically taken into account by the fitting algorithm. A reasonable agreement between blindly generated and reference scattering factor spectra derived independently from an x-ray absorption spectroscopy experiment has been demonstrated. The blind fitting has been compared with the alternative refinement routines, in which small free variations of the reference spectral shapes (or no variations at all) have been allowed. The presented approach to the resonant x-ray reflectometry modeling makes it unnecessary to acquire the optical constant spectral shapes in advance and, thus, is especially helpful when such spectra cannot be physically measured, e.g., for a buried layer of a multilayer system.