Tensor description of X-ray magnetic dichroism at the Fe L2,3-edges of Fe3O4.

Hebatalla Elnaggar,Frank M. F. de Groot,Maurits W. Haverkort,Mai Hussein Hamed,Sarnjeet S. Dhesi

doi:10.1107/s1600577520015027

Hebatalla Elnaggar, Frank M. F. de Groot

Open Access

https://doi.org/10.1107/s1600577520015027

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Abstract

A procedure to build the optical conductivity tensor that describes the full magneto-optical response of the system from experimental measurements ispresented. Applied to the Fe L2,3-edge of a 38.85 nm Fe3O4/SrTiO3 (001) thin-film, it is shown that the computed polarization dependence using the conductivity tensor is in excellent agreement with that experimentally measured. Furthermore, the magnetic field angular dependence is discussed using a set of fundamental spectra expanded on spherical harmonics. It is shown that the convergence of this expansion depends on the details of the ground state of the system in question and in particular on the valence-state spin-orbit coupling. While a cubic expansion up to the third order explains the angular-dependent X-ray magnetic linear dichroism of Fe3+ well, higher-order terms are required for Fe2+ when the orbital moment is not quenched.

Highlights

The determination of the electronic and magnetic structure of engineered magnetic nanostructures is essential to tailor their properties for technological applications such as information storage, spin transport and sensing technology
The angular dependence of the magnetic field is discussed using a set of fundamental spectra expanded using spherical harmonics which can describe the full magnetooptical response of the system (Haverkort et al, 2010)
Such expansions have been used previously to explain the angular dependence of X-ray magnetic linear dichroism (XMLD) (Arenholz et al, 2006, 2007; van der Laan et al, 2008, 2011), yet the new aspect we provide in this work is a thorough inspection of the convergence of the expansion using a comprehensive set of XMLD data measured on Fe3O4 in combination with theoretical calculations

Summary

Introduction

The determination of the electronic and magnetic structure of engineered magnetic nanostructures is essential to tailor their properties for technological applications such as information storage, spin transport and sensing technology. The angular dependence of the magnetic field is discussed using a set of fundamental spectra expanded using spherical harmonics which can describe the full magnetooptical response of the system (Haverkort et al, 2010) Such expansions have been used previously to explain the angular dependence of XMLD (Arenholz et al, 2006, 2007; van der Laan et al, 2008, 2011), yet the new aspect we provide in this work is a thorough inspection of the convergence of the expansion using a comprehensive set of XMLD data measured on Fe3O4 in combination with theoretical calculations. This provides us with an opportunity to study the effect of the electronic structure on the quality of the expansion between the orbital singlet Fe3+ and the orbital triplet Fe2+ ions

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