Theory of x-ray absorption spectroscopy for ferrites

The theoretical calculation of the interaction of electromagnetic radiation with matter remains a challenging problem for contemporary electronic structure methods, in particular, for x-ray spectroscopies. This is not only due to the strong interaction between the core hole and the photoexcited electron, but also due to the elusive multiplet effects that arise from the Coulomb interaction among the valence electrons. In this work we report a method based on density functional theory in conjunction with multiplet ligand-field theory to investigate various core-level spectroscopies, in particular, x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD). The developed computational scheme is applied to the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>L</a:mi><a:mrow><a:mn>2</a:mn><a:mo>,</a:mo><a:mn>3</a:mn></a:mrow></a:msub></a:math> XAS and XMCD edges of magnetite <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mo>(</b:mo><b:mrow><b:msub><b:mi>Fe</b:mi><b:mn>3</b:mn></b:msub><b:msub><b:mi mathvariant="normal">O</b:mi><b:mn>4</b:mn></b:msub></b:mrow><b:mo>)</b:mo></b:math> as well as cobalt ferrite <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mo>(</d:mo><d:mrow><d:msub><d:mi>CoFe</d:mi><d:mn>2</d:mn></d:msub><d:msub><d:mi mathvariant="normal">O</d:mi><d:mn>4</d:mn></d:msub></d:mrow><d:mo>)</d:mo></d:math> and nickel ferrite <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mo>(</f:mo><f:mrow><f:msub><f:mi>NiFe</f:mi><f:mn>2</f:mn></f:msub><f:msub><f:mi mathvariant="normal">O</f:mi><f:mn>4</f:mn></f:msub></f:mrow><f:mo>)</f:mo></f:math>. The results are in overall good agreement with experimental observations, both regarding the XAS <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:msub><h:mi>L</h:mi><h:mn>2</h:mn></h:msub><h:mo>/</h:mo><h:msub><h:mi>L</h:mi><h:mn>3</h:mn></h:msub></h:mrow></h:math> branching ratio, the peak positions, as well as the relative intensities. The agreement between theory and experiment is equally good for XAS and the XMCD spectra, for all studied systems. The results are analyzed in terms of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msub><i:mi>e</i:mi><i:mi>g</i:mi></i:msub></i:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:msub><j:mi>t</j:mi><j:mrow><j:mn>2</j:mn><j:mi>g</j:mi></j:mrow></j:msub></j:math> orbital contribution, and the robustness of the spectra with regard to the uncertainties of the Slater parameters is investigated. The analysis also highlights the strong effect of the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mn>2</k:mn><k:mi>p</k:mi><k:mtext>−</k:mtext><k:mn>3</k:mn><k:mi>d</k:mi></k:mrow></k:math> interaction in x-ray spectroscopy. Published by the American Physical Society 2024