Electron Ptychography for Investigating Magnetic Textures in Micro- and Nano- Scale Magnets via Lorentz Transmission Electron Microscopy

Engineering novel magnetic materials that exhibit topologically non-trivial spin states requires, in part, the observation and quantification of magnetic domain behaviour at high resolution that spans across atomic, nano-, and meso- length scales to better understand the fundamental physics and its dynamics. To that end, we aim to explore ferromagnetic materials down to the monolayer limit and, if possible, non-collinear antiferromagnets that may have a non-zero magnetic moment. Aberration-corrected Lorentz transmission electron microscopy (ALTEM) is perfectly suited for directly observing crystallographic features such as morphology and structural defects, in addition to magnetic domains in a field-free region with spatial resolution down to 2 nm [1]. Understanding the magnetic information relies on the accurate quantification of the phase shift imparted to the electron wave as it traverses the sample. Current methods of obtaining this information via the transport of intensity equation (TIE) [2] and reverse-mode automatic differentiation (AD) algorithms [3] are limited in spatial resolution by the aberrations of the image-forming lenses in electron microscopy. In this work, we explore a coherent diffractive imaging technique, namely electron ptychography, using ALTEM, that can extend beyond the lens limits into the atomic length scale. Reconstruction of the complex object wave function through a numerical ptychographic iterative algorithm is carried out from a series of diffraction patterns acquired in the back focal plane while scanning the electron beam across the sample with sufficient overlap in real-space [4]. Micro- and nano-scale Permalloy magnets were lithographically fabricated, to within ± 2.0% of specified size range for length and width, to assess the feasibility and validity of electron ptychography compared with other phase-reconstruction approaches for quantifying the magnetic information obtained using ALTEM as shown in Fig. 1 (a). Here, we present the application of open-access models for TIE and AD phase reconstruction on nanoscale magnets using code that we have written and published open source, namely PyLorentz [2] and ADLTEM [3], respectively. The total phase was reconstructed from a single through-focal series (TFS) ALTEM dataset and processed using the maximum defocus condition (magnitude 2.806 mm). This ptychographic-centric investigation will be analysed against two robust techniques (TIE and AD) highlighting variations in the total phase as shown in Fig. 1 (b) as well as in the magnetic induction as shown in Figs. 2 (a-b). Furthermore, magnetic simulations will be performed using Mumax3 followed by electron microscopy simulations to reconstruct the associated phase shift to further assess the electron ptychography approach as a function of noise tolerance and resolution of retrieved phase [5]. (a) Normalized ALTEM in-focus image of permalloy nanoscale magnets; (b) total phase reconstruction maps using TIE and AD, respectively. (a) Magnetic induction maps retrieved from gradient of the total phase using TIE and AD models, respectively; (d) gradient of the phase comparison of line profile 1 (change in phase with respect to x-direction) and line profile 2 (change in phase with respect to y-direction) on the smallest lithographically fabricated nanoscale magnets, approximately 283.1 nm by 52.4 nm with spacing of 50.6 nm.