Parallel Mode Differential Phase Contrast in Transmission Electron Microscopy, II: K₂CuF₄ Phase Transition

Abstract

Abstract

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

“…Such experiments often produce suitable reference images, allowing the technique presented to be applied to the same dataset as would be collected for TIE analysis, with little or no requirement for additional measurements. We demonstrate this and other aspects of the technique using experimental data in Part II of this work, which also includes details of the magnetic phase transition in K 2 CuF 4 (Paterson et al, 2021).…”

“…When a suitable regularization parameter is not known, it is best to start with a large value and then gradually reduce it in order to improve the spatial resolution while monitoring the convergence and the noise level in the vector field plot. Further discussion of these points accompanied by data from experiment is provided in Part II of this work (Paterson et al, 2021).…”

“…The exact profiles used are not critical to the arguments made so, for simplicity, we use an analytical form of a cross-tie domain wall (Metlov, 2001):where is a constant proportional to the exchange length that controls the scaling. This model has smoother features than is typical of cross-tie DWs and was chosen as it resembles aspects of the experimental data reported in Part II (Paterson et al, 2021), which has a combination of uniform, circulatory, and divergent magnetization; the scaling here was also chosen to be somewhat similar to the experimental data. Figure 5 summarizes the simulation results.…”

“…Importantly, there may also be changes in magnification, in illumination brightness, centering or uniformity, and in optical distortions, particularly at larger defocus values, potentially giving rise to systematic errors. These will all adversely affect the TIE method, but since the TEM-DPC method uses positional rather than intensity changes, and in the version of the method employed here, uses as a reference an image obtained at the same defocus, it is largely unaffected by these factors [the experimental data of Part II (Paterson et al, 2021) provides an example of this]. Of course, a method to alter the polarization of the sample is required for this version of the TEM-DPC method, but this is often already an integral part of many in situ experiments.…”

“…In Part II of this work (Paterson et al, 2021), we apply the TEM-DPC technique to experimental cryo-TEM Fresnel images of the magnetic phase transition of a thin lamella of KCuF, a material of interest for its quasi 2D ferromagnetism at low temperatures (Hirakawa, 1982; Togawa et al, 2021).…”