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Advanced Holographic Tomographies for Nanoscale Materials: Revealing Electromagnetic and Deformation Fields, Chemical Composition and Quantum States at Atomic Resolution.

Periodic Reporting for period 3 - ATOM (Advanced Holographic Tomographies for Nanoscale Materials: Revealing Electromagnetic and Deformation Fields, Chemical Composition and Quantum States at Atomic Resolution.)

Reporting period: 2020-01-01 to 2021-06-30

The ongoing miniaturization in nanotechnology and functional materials puts an ever increasing
focus on the development of three-dimensional (3D) nanostructures, such as structured nanowires, nanoantennas or nanomagnetic textures such as skyrmions, which permit
a better performance of optical or electronic devices in terms of speed and energy efficiency. To
develop and advance such technologies and to improve the understanding of the underlying
fundamental physical effects, the nondestructive and quantitative 3D characterization of
physical, e.g. electric or magnetic, fields down to atomic resolution is indispensable. AToM will provide a ground-breaking
tomographic methodology for current nanotechnology by mapping electric and magnetic
fields as well as crucial properties of the underlying atomic structure in solids, such as the
chemical composition, mechanical strain or spin configuration in 3D down to atomic
The project is divided into two main areas: Holographic tomography of physical fields in materials and Quantum state reconstruction of inelastically scattered electrons for comprehensive analysis of dielectric response.

In order achieve atomic-resolution in the 3D reconstruction of electrostatic fields we combined two ideas. First, we use to maximal information extractable from a tomographic elastic scattering experiment, i.e. the (holographically reconstructed) electron wave function. Second, we identified a suitable (nonlinear) mapping of that holographic tilt series into a projection series linearly depending on the 3D electrostatic potential (based on Rytov approximation and diffraction tomography). This scheme has been successfully applied to simulated tilt series of wave functions, which had been scattered on nanoobjects, such as WS2 nanotubes.
Several major breakthroughs have been accomplished in the development of magnetic vector field tomography for nanoscale magnetic textures (Fig. 1). We developed and applied dedicated multiple tilt holographic series acquisition routines, holographic and tomographic reconstruction algorithms for the magnetization texture in non-trivial 3D nanomagnets (such as skyrmions, Bloch points, etc.). Moreover, we extended the method to cryogenic conditions and developed a insitu magnetic field holder, which allowed us to reconstruct for the first time the 3D magnetic texture pertaining to Bloch skyrmion tubes in a helimagnet.
The problem of 3D strain field reconstruction as been tackled by our ERC project partner from the TU Berlin, Dr. T. Niermann and Dr. L. Meißner, who developed and tested several tomographic schemes for the 3D reconstruction of strain fields including the beam tilt method proposed in AToM. We developed a novel method, which allows to distinguish between mesoscale potentials due to space charge regions (purely electronic potentials) and atomic potentials reflecting the chemical composition (i.e. mean inner potentials), by combining electron holographic tomography and high-angle annular dark field tomography. This method has been applied to multi-quantum-well semiconductor nanowires, where the 3D morphology of the wells and the nanowire determine its optical properties. We developed a novel automatic residual aberration correction scheme dedicated to 2D materials, which allows study the charge distribution down to atomic resolution in a dose optimized way.
We completed the development of the JEOL 2010F JEM Dresden-special insitu TEM. We installed the continuous-flow liquid He cryostat and performed the first cryogenic experiments on topical materials (e.g. transition metal dichalgogenites containing charge density waves at low temperatures). Subsequently the insitu TEM has been mainly employed in cryogenic studies on low temperature magnetic skyrmion formation (mostly in lacunar spinels).

One original goal in this area is the measurement of all Cartesian components of the probability current of the inelastically scattered electron beam as a means to measure transient electric and magnetic fields pertaining charge excitations (mainly surface plasmon polaritions). To that end we developed the inelastic momentum transfer method, where we scan a focused electron probe over the sample and measure both the deflection of the scattered probe in an energy resolved way. We have employed the technique to study various aluminum based plasmonic nanostructures, plasmonic wave guides based on nanoparticle chains as well as thin gold networks.
The quantum state of inelastically scattered electrons provides access to the fully non-local dielectric response. We showed, how the fully non-local response can be completely reconstructed by employing inelastic electron ptychography, which is difficult and currently not possible to obtain from other spectroscopic techniques. Moreover, we developed dedicated measurement ptychographic measurement schemes, including an automated recording of the ptychographic dataset on the TEM and independent measurements of the probe phase space distribution.
In order to develop a fully relativistic inelastic electron scattering code, facilitating the computation of both core and low-loss spectra as well as energy filtered imaging and diffraction, we elaborated on the theoretical foundations of inelastic electron scattering. We particularly studied the ramifications of 3D effects (typically neglected in current inelastic scattering implementations) and the various approximation levels to relativistic effects (e.g. fully relativistic vs. scalar relativistic vs. quasi static). We could, amongst others, provide a unified framework for core-loss and low-loss scattering incorporating current-current coupling as the leading order relativistic effects in both core-loss and low-loss scattering.
Progress beyond the state of the art has been mainly achieved in two areas so far: (1) Development of vector field tomography as a unique and flexible tool for studying 3D magnetization textures such as vortices or Skyrmions at several nanometer resolution. We successfully reconstructed complex 3D magnetization texture in a magnetic Co-Cu stacked nanowire and highly anisotropic CoNi nanowires. By extending the technique to cryogenic conditions and a rotatable external magnetic field, we resolved the 3D magnetization texture of Skyrmion tubes and plan to extend it to other non-trival textures such as Bloch point domain walls until the end of the project. These studies reveal the crucial impact of spatial confinement, surface and bulk anisotropies and various other parameters on the formation of 3D magnetization textures and their functionalization in devices. (2) Development of a novel nanoscale probing technique for transient electric and magnetic fields of (collective) charge excitations (i.e. surface plasmons). Here, we adapted the conventional differential phase contrast technique such to allow for spectrally resolving time-dependent fields. The technique has been successfully applied to characterize the plasmonic response of several plasmonic nanostructures. We currently work on aberration corrected setups facilitating a higher sensitivity of the technique, e.g. for characterizing magnetic surface plasmon modes or peculiar magnetoelectric coupling effects in topological insulators (axion plasmonics). Major breakthroughs are expected until the end of the project resulting from the further development and application of the developed methodology.