# Numerical and experimental investigations of Boersch Phase Plate equipped Condenser Apertures for use in Electron Magnetic Circular Dichroism experiments in a Transmission Electron Microscope

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## Abstract

In this work we have proposed a new setup for measuring EMCD experiments, which does — in theory — not rely on a crystalline sample for providing the required phase shifted beams. FEM calculations of the electrostatic potentials caused by phase plates justify the commonly assumed constant phase shift approximation inside a ring electrode for small radii, which are an order of magnitude larger than their thickness; if the radius is increased by another order of magnitude the phase shift has to be described by a hyperbolic cosine. On the other hand we have shown that the phase shift outside of the ring electrode in general cannot be neglected. Based on these insights we have investigated the intensity distribution and phase difference in the sample plane caused by a twin aperture. Thereby we have demonstrated the effects of different phase shifting models and aberrations. From these we have concluded that aberrations can be neglected for the particular microscope and that the effects of most investigated non-constant phase shift models are still in reasonable agreement with the analytical model as the strongest effects due do non-constant phase shifts appear to be a shift of the non-phase-shifted beam in the sample plane and a “blurring” of the phase shifted beam. Calculations of the expected magnetic signal by Jan Rusz suggest a strong dichroic signal due to interference of the two incident waves assuming plane waves instead of convergent ones. In experiments we have seen that for the construction of phase plates in the condenser system thick layers of Pt are needed and that a common cross over of two incident waves originating from the twin aperture is possible. An interference pattern in this cross over was not observable — mainly due to technical issues. The proposed setup uses convergent waves with a phase difference that is not determined by the crystal structure as in the intrinsic EMCD method, but by the microscope and twin aperture geometry. Thus the phase plate geometry (aperture radius and displacement) would need to be optimized for a specific microscope and the lattice constant of the primary investigated material.

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