Parallel Mode Differential Phase Contrast in Transmission Electron Microscopy, I: Theory and Analysis

Abstract

In Part I of this diptych, we outline the parallel mode of differential phase contrast (TEM-DPC), which uses real-space distortion of Fresnel images arising from electrostatic or magnetostatic fields to quantify the phase gradient of samples with some degree of structural contrast. We present an analysis methodology and the associated software tools for the TEM-DPC method and, using them together with numerical simulations, compare the technique to the widely used method of phase recovery based on the transport-of-intensity equation (TIE), thereby highlighting the relative advantages and limitations of each. The TEM-DPC technique is particularly suitable for in situ studies of samples with significant structural contrast and, as such, complements the TIE method since structural contrast usually hinders the latter, but is an essential feature that enables the former. In Part II of this work, we apply the theory and methodology presented to the analysis of experimental data to gain insight into two-dimensional magnetic phase transitions.

Simulated Guidance in Interpreting Nano-Patterned Co70Fe30 Film Imaging with Differential Phase Contrast

“…To support the experiment, micromagnetic simulations provide an important context that helps to identify artifacts in the measurement and predict potentially interesting sample structures. Recent advances in DPC microscopy have made it possible to study the electronic structure of a material with atomic resolution [ 10 , 11 ]. However, due to the limitations in producing a suitable sample for this technique, it is difficult to produce a sufficiently large sample for the study of magnetic domains.…”