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

Reporting period: 2021-07-01 to 2022-12-31

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 resolution.
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 holographically reconstruct the maximal information extractable from a tomographic elastic scattering experiment, i.e. the 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. This scheme has been successfully applied to simulated tilt series of wave functions, which had been scattered on nanoobjects. Several major breakthroughs have been accomplished in the development of magnetic vector field tomography for nanoscale magnetic textures (Fig. 1). We developed dedicated multiple tilt axis holographic series acquisition and reconstruction routines for the magnetization texture in 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, 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 determine its optical properties. We developed a novel automatic residual aberration correction scheme dedicated to 2D materials, which allows study the charge distribution 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. charge density waves at low temperatures, magnetic cycloic and helical modulation formation in lacunar spinels and LaTiO3 thin films as well as the formation of mesoscale polar domain patterns). The experiences gathered from this experimental setup are now exploited for a the development and set-up of a novel high-resolution transmission electron microscope dedicated to electron energy loss spectroscopy (HR3-EELS), which will be equipped with a largely improved liquid Helium cooling stage.

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. To that end we developed the inelastic momentum transfer method, where we scan a focused electron probe over the sample and measure its deflection 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. Recently, the technique has been significantly improved by recording the deflection data in the omega-q resolved way, facilitating better control / correction of the energy drift as well as mitigation of the elastic vignetting problem hampering the interpretation of the deflection data in terms of transient electric and magnetic fields. Moreover, we showed, how the fully non-local response can be completely reconstructed by employing inelastic electron ptychography, which is currently not possible to obtain from other spectroscopic techniques. In order to develop a fully relativistic inelastic electron scattering code, 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 provided 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. Recently, we incorporated the implications of axion electrodynamics occurring at the surface of topological insulators in this scheme.
Progress beyond the state of the art has been mainly achieved in three areas: (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 including staggered vortex states and chiral domain walls in a magnetic Co-Cu stacked nanowire, a highly anisotropic CoNi nanowires, and curved soft magnetic thin films. By extending the technique to cryogenic conditions and a rotatable external magnetic field, we resolved the 3D magnetization texture of skyrmion tubes. These studies reveal the crucial impact of spatial confinement, surface and bulk anisotropies, symmetric and antisymmetric exchange, 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. 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 ordered and disordered plasmonic nanostructures, e.g. identifying the role of disorder driven Anderson localization in the optical properties of 2D random gold networks. (3) We applied and improved in-situ electron microscopy and holography by developing new continuous-flow liquid Helium cooling stages as well as miniaturized magnetic charge particle optics.The former allows to study low-temperature physics, whereas the latter facilitates ultrafast imaging, e.g. of magnetization dynamics.
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