Abstract text (incl. figure legends and references)

Nanometer and sub-nanometer resolution is crucial for the correlation of magnetic properties and devices to their intrinsic and nanoscale atomic structure for applications.The applications are in the range from nanostructured permanent magnets, high density magnetic memory storage, magnetic glasses and magnetic shape memory alloys. These can be used for crucial developments in the areas of energy efficient generators and motors, magnetic cooling systems and new IT infrastructure solutions. STEM is one of the few techniques, which is able to image the atomic structure of the material and the magnetic induction field at the nanoscale. The aim of this work is to break the current resolution limit and therefore enhance the developments in magnetic materials.

STEM nowadays can easily reach sub-nm resolution in the range of 30 to 60 pm. For magnetic imaging especially DPC imaging the resolution is between 5-10 nm. The reason for the decrease in resolution is, that the objective lenses of the microscope needs to be turned off as the magnetic field produced by the objective lenses is up to 2 T and these strong magnetic fields interfere with the magnetic structure of the samples. Therefore, the condenser lens which is far away from the sample is used for focusing the probe. Another issue is the influence of Bragg diffraction and dynamic scattering in crystalline materials. This leads to artifacts at grain boundaries and due to bend contours limiting the research in magnetic nanostructures.

In order to overcome the resolution limit and to create a robust interpretable contrast, the phase reconstruction method ptychography is used. The magnetic information is stored in the phase gradient of the sample. Electron ptychography leads to higher spatial resolution and quantifiable information than the optical limit of the instrument. For the phase reconstruction a two-stage process is used. In the first stage the Wigner Distribution Deconvolution (WDD) reconstruction algorithm is used. This algorithm uses the global approach which is more resistant against noise, but this algorithm does not lead to super resolution. In the second stage the newly developed Alternating Amplitude Flow algorithm is used. This algorithm is an iterative algorithm comparable to ePIE. In comparison to ePIE, it is more robust, always converges and is faster in tests with simulated data. Finally, the first derivative of the reconstructed phase is used to calculate the magnetic structure.

Additionally, a new pre-information analysis is used for getting a better approximation of the object. The object assumption is normally set to be pure vacuum in X-ray ptychography. Instead of this with the new approach a first approximation of the phase and amplitude of the object is generated by iDPC and brightfield data before the data is transferred into the algorithms. Furthermore, in the preprocessing stage the data is improved by the removal of noise and correction of the diffraction pattern positioning.

A preliminary result can be seen in Figures 1&2, there an iDPC image (left) of an FeRh thin film with precipitates and the reconstruction from the ptychography algorithm (right) can be seen. The reconstruction is optimized for running stable in this point of time. An enhancement to superresolution is the next step.