Exploiting the Acceleration Voltage Dependence of EMCD.

Stefan Löffler,Walid Hetaba,Michael Stöger-Pollach,Peter Schattschneider,Andreas Steiger-Thirsfeld

doi:10.3390/ma14051314

Abstract

Energy-loss magnetic chiral dichroism (EMCD) is a versatile method for measuring magnetism down to the atomic scale in transmission electron microscopy (TEM). As the magnetic signal is encoded in the phase of the electron wave, any process distorting this characteristic phase is detrimental for EMCD. For example, elastic scattering gives rise to a complex thickness dependence of the signal. Since the details of elastic scattering depend on the electron’s energy, EMCD strongly depends on the acceleration voltage. Here, we quantitatively investigate this dependence in detail, using a combination of theory, numerical simulations, and experimental data. Our formulas enable scientists to optimize the acceleration voltage when performing EMCD experiments.

Highlights

Acceleration Voltage Dependence of Circular dichroism in X-ray Absorption Spectroscopy (XAS) probes the chirality of the scatterer, related either to a helical arrangement of atoms or to spin polarized transitions as studied in X-ray Magnetic Circular Dichroism (XMCD)
We limit the derivation to an incident three-beam and outgoing two-beam case in the zero-order Laue zone of a sample that is single-crystalline in the probed region with a centro-symmetric crystal structure; We assume that the sample is a slab of thickness t with an entrance and an exit plane essentially perpendicular to the beam propagation axis; We assume that the inelastic scattering process is at least four-fold rotationally symmetric around the optical axis and that the characteristic momentum transfer qe is Materials 2021, 14, 1314
Much smaller than the chosen reciprocal lattice distance | G |. This implies that the inelastic scattering in the chosen geometry is only dependent on the scattering atom’s spin-state, but not influenced significantly by any anisotropic crystal field; We assume that the atoms of the investigated species are homogeneously distributed along the beam propagation axis and that G · x = 2mπ, m ∈ Z for all atom positions x and the chosen lattice vector G

Summary

Introduction

Acceleration Voltage Dependence of Circular dichroism in X-ray Absorption Spectroscopy (XAS) probes the chirality of the scatterer, related either to a helical arrangement of atoms or to spin polarized transitions as studied in X-ray Magnetic Circular Dichroism (XMCD). The formal equivalence between the polarization vector in XAS and the scattering vector in EELS tells us that any effect observable in XAS should have its counterpart in EELS. Anisotropy in XAS corresponds to anisotropy of the double differential scattering cross section (DDSCS) in EELS. In XMCD, the polarization vector is helical—a superposition of two linear polarization vectors e x ± iey orthogonal to each other—resembling a left- and right-handed helical photon, respectively. What is the counterpart of photon helicity in EELS?

Methods

Results

Discussion

Conclusion