Quantitative phase retrieval and characterization of magnetic nanostructures via Lorentz (scanning) transmission electron microscopy

Magnetic materials phase reconstruction using Lorentz transmission electron microscopy (LTEM) measurements have traditionally been achieved using longstanding methods such as off-axis holography (OAH) fast-Fourier transform technique and the transport-of-intensity equation (TIE). The increase in access to processing power alongside the development of advanced algorithms have allowed for phase retrieval of nanoscale magnetic materials with greater efficacy and resolution. Specifically, reverse-mode automatic differentiation (RMAD) and the extended electron ptychography iterative engine (ePIE) are two recent developments of phase retrieval that can be applied to analyzing micro-to-nano- scale magnetic materials. This work evaluates phase retrieval using TIE, RMAD, and ePIE in simulations of Permalloy (Ni₈₀Fe₂₀) nanoscale islands, or nanomagnets. Extending beyond simulations, we demonstrate total phase retrieval and image reconstructions of a NiFe nanowire using OAH and RMAD in LTEM and ePIE in Lorentz-mode-4D scanning transmission electron microscopy experiments and determine the saturation magnetization through corroborations with micromagnetic modeling. Finally, we demonstrate the efficacy of these methods in retrieving the total phase and highlight its use in characterizing and analyzing the proximity effect of the magnetic nanostructures.. Authors: Mendoza, Kayna L. [Northwestern University, Evanston, IL (United States); Argonne National Laboratory (ANL), Argonne, IL (United States)] (ORCID:0000000193069987); Ni, Haoyang [University of Illinois at Urbana-Champaign, IL (United States)] (ORCID:0000000344933032); Varnavides, Georgios [University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)] (ORCID:0000000183383323); Chi, Miaofang [Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Sciences (CNMS)] (ORCID:0000000307641567); Ophus, Colin [Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)] (ORCID:0000000323488558). DOE Contract: AC02-05CH11231. Subjects: Lorentz transmission electron microscopy; magnetic nanostructures; phase retrieval