Streamlined approach to mapping the magnetic induction of skyrmionic materials

Highlights: • A method to reconstruction the phase of electrons after pasting though a sample that requires a single defocused image is presented. • Restrictions as to when it is appropriate to apply this method are described. • The relative error associated with this method is compared to conventional transport of intensity equation analysis. - Abstract: Recently, Lorentz transmission electron microscopy (LTEM) has helped researchers advance the emerging field of magnetic skyrmions. These magnetic quasi-particles, composed of topologically non-trivial magnetization textures, have a large potential for application as information carriers in low-power memory and logic devices. LTEM is one of a very few techniques for direct, real-space imaging of magnetic features at the nanoscale. For Fresnel-contrast LTEM, the transport of intensity equation (TIE) is the tool of choice for quantitative reconstruction of the local magnetic induction through the sample thickness. Typically, this analysis requires collection of at least three images. Here, we show that for uniform, thin, magnetic films, which includes many skyrmionic samples, the magnetic induction can be quantitatively determined from a single defocused image using a simplified TIE approach.