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This deliverable is meant to summarise the final results regarding the plasmon analysis based on OAM sorter. The aim is to prove that we can achieve a substantial scientific advancement using the OAM-sorter that was not possible without it. We document here both the actual scientific results and the partial attempts that could not be brought to conclusions. The deliverable is separated into 2 main chapters. Chapter 1 reports the efforts to produce the Q-SORT setup for different kinds of plasmon observation and explains why the setup has to be different for every specific experiment. Chapter 2 reports the actual scientific results, of high fundamental relevance, that we obtained for volume plasmons. The experimental results are qualitatively and quantitatively compared with simulation. Conclusions are drawn at the end. It is worth highlighting here that the OAM sorter allowed us to better understand the characteristics of plasmon loss excitation and to find a new phenomenon consisting of the ‘spontaneous Emission’ of quanta of OAM in the interaction with plasmon. Surprising theoretical results were also obtained thanks to the definition of coherence through innovative density matrix formalism: we showed that the coherence of the initial OAM state superposition of the electron is partially preserved after the electron-plasmon scattering, which is reflected mathematically by the possibility of expressing the post-scattering electron density matrix as the sum of one fully coherent term containing the initial OAM values and another term which is characterised by full OAM decoherence. The theory was confirmed by experiment in this case as well.

This deliverable reports the comprehensive results and activities aimed to demonstrate Electron Magnetic Circular Dichroism (EMCD). It is difficult to keep the delicate OAM sorter alignment at the large energy-loss of the iron L-edge (about 700 eV). Considering also the slowdowns due to COVID-19 pandemic we opted for an equally and similar problem by looking at the difference in the σ* and π* transition in 2D material in the energy range of 200eV energy loss. The kind of information and the OAM–EELS theory is fundamentally the same as real EMCD but the difficulty in the alignment is reduced. The experiment therefore succeeds in demonstrating the importance of the combination of OAM-EELS experiment also to study atomic transitions. Considering the similarities of the two experiments this work demonstrate that EMCD is feasible and that automatic alignment procedure should soon allow to explore the energy loss range of EMCD. For these reasons, most of this work will be of quite general interest and only a small part will regard the case of h-BN. Given the rising importance of 2D material that are now receiving even more attention than magnetic structure the result has also a large importance in its own right and fully demonstrates the potentialities of a OAM sorter in material science. Chapter 1 will explain all the improvements we carried out in the direction of EMCD and in OAM–EELS experiments. A large space has been dedicated to the automatic control of the microscope by means of a neural network. Given the difficulties to control the many parameters, this will probably be the best way to carry out the most difficult future experiments. Chapter 2 will explain all problems of localization and decoherence. Once again this theoretical framework is valid for all OAM–EELS experiments and is of general interest to understand our data and to design future experiments. Chapter 3 is dedicated to effective manuscript draft with experiments and data analysis. As for the setup also the deconvolution method used in this section can be easily transported to the case of EMCD.

In quantum mechanics, each conserved quantity (e.g., energy, position, linear momentum and angular momentum) is associated with a Hermitian operator. Its expected value can then be determined by performing a measurement on the wavefunction. In modern electron microscopy, one can select the initial and final states of the electron and the measurement basis by performing measurements of scattering processes. For example, the orbital angular momentum (OAM) of an electron can be used to reveal the n-fold symmetry of a wavefunction scattered by a sample. Here, we introduce a new composite planar chirality operator that can be used to measure a spiral-like feature in a sample. This concept develops the concept of chirality to highlight a specific roto-scale symmetry. We show that planar chirality can be characterized using an electron OAM sorter to uncover the atomic structures of biomolecules in cryo electron microscopy, either in a stand-alone analysis for fast identification of protein structures or in the context of conventional cryo electron microscopy to produce faster and more detailed 3D reconstructions by solving upside-down orientation ambiguities., available also at arXiv:2110.03391 This project has received fundings also from the Deutsche Forschungsgemeinschaft (Project-ID 405553726 – TRR 270), from the DARPA TEE program (Grant MIPR# HR0011831554) and from an Ontario Early Researcher Award (ERA) and a Canada Research Chair (CRC).

Nanomaterials : open access journal 11(2), 466 (2021). doi:10.3390/nano11020466 special issue: "Special Issue "Characterization of Quantum Effects in Nanomaterials, Nano-Devices, and Nanophotonics" / Special Issue Editor: Prof. Dr. Jeong Ryeol Cho, Guest Editor", Published by MDPI, Basel

Advanced functional materials 2008306 (2021). doi:10.1002/adfm.202008306, Published by Wiley-VCH, Weinheim

This deliverable reports on the progress that has been achieved in the direction of the dose-effective imaging of organic molecules. We report several essential experimental advancements, including a successful experimental scheme of ghost imaging that could be realised in Modena without the need of travelling. Overall this deliverable includes material for at least 3 papers and a patent. The restriction on travels due to Covid-19 imposed hard constraints on the performance of the intended experiment. The complete experiment on proteins would, in fact, have required the simultaneous presence of three groups at the microscope in Jülich: FZJ personnel for main operation on the microscope, people from MU for the cryomicroscopy part, and people from CNR for the lateral control of software and for the coordination of the experiment. Moreover, the preparation of the experiment required the intervention of FEI personnel. Unfortunately, in spite of the partial release of the restrictions during the extra 6 months allotted to Q-SORT, for the reasons given above these conditions were impossible to meet. This was unforeseeable at the moment the project extension was asked. Given these hard constraints, we chose the combination of experimental activities that allowed us to achieve the greatest possible amount of project goals. In fact, Q-SORT scientists achieved more than what was foreseen; novel results include: 1) the first patentable phase plates of different design ( designed in WP3 D3.4 for protein recognition) able to control up to 24 electrodes by multiplexing the initial 8 inputs. 2) the first computational ghost imaging experiment in microscopy and its optimization for low dose regime 3) a state of the art neural network control for an efficient prediction of the generated caustic pattern. Two approaches to the protein recognition were chosen at the end of WP3: a) the extension of the OAM sorter with an additional programmable phase plate. Such approach is referred to as GOAMS (generalised OAM sorter) in D3.2 as b) the computational ghost imaging with increasingly complex masks. Under the given constraints, it was found that the computational ghost imaging approach (D3.2, task 3.1 & 3.2) was the most appropriate and effective to pursue - enabling the greatest advancement. This development is also consistent with contingency plan #6 “Test random or Hadamard sparse sampling”. The results have been also written as a manuscript that is going to be submitted soon. The hardware for the 3-element GOAMS (i.e. the second approach that was found to be most promising in WP3) was also developed, with the design of an additional element that allowed the recognition of the radial degree of freedom. Such extended “protein specific” phase modulator (D3.4) was also finished and tested as one of the design of the programmable phase plates. [...]

Magnetoelectric (ME) coupling in La0.7Sr0.3MnO3/Pb(Mg1/3Nb2/3)0.7Ti0.3O3 (LSMO/PMN–PT (001)) has been probed in the past years to identify the underlying mechanism behind it. PMN–PT, which is well known for its excellent piezoelectric properties, also exhibits ferroelectricity. This motivates our interest to differentiate which effect is dominant for this 'voltage control of magnetism'. Here, we present results for the ME coupling at different temperatures: 300 K and 80 K. In this article we discuss and explain, how the nature of ME coupling is influenced by different parameters such as magnetic field, electric field, directional dependence (hard axis, easy axis) and temperature. Owing to large lattice mismatch between LSMO and PMN–PT, the strain-mediated coupling is strongly prevalent, however the change in strain behaviour from butterfly loop to linear loop is observed as a function of temperature. ME measurements are performed along hard axis [100] and easy axis [110] of LSMO in the presence of remanent magnetic field which showcases the pure influence of electric field on the system, resulting in a combination of strain- and charge-mediated coupling. The magnetic depth profile is probed by polarized neutron reflectometry as a function of electric field which demonstrates the existence of an interlayer with reduced nuclear scattering length density and reduced magnetic scattering length density at the interface. From transmission electron microscopy, stoichiometric variations are observed due to the presence of Mn3O4 particles at the interface.

Advanced functional materials 2008609 (2021). doi:10.1002/adfm.202008609, Published by Wiley-VCH, Weinheim

The growth of cobalt nanopatterns (NPs) using focused electron‐beam induced deposition (FEBID) for localised magnetic studies is presented. The initial FEBID products are shown to be polycrystalline and form hetero‐structured core‐shell NPs through surface oxidation. Off‐axis electron holography is performed to reconstruct their morphology, thickness profile and image their individual magnetic vortex domain states. In situ annealing to 400°C promoted migration of the Co‐overspray to grow the Co NPs and improved their crystallinity through coarsening, as well as induced diffusion of embedded carbon out of their surface. It is found that the change in their morphology and chemical instability under heating restricts their suitability for examining thermally induced magnetic variations.

Arrays of interacting 2D nanomagnets display unprecedented electromagnetic properties via collective effects, demonstrated in artificial spin ices and magnonic crystals. Progress toward 3D magnetic metamaterials is hampered by two challenges: fabricating 3D structures near intrinsic magnetic length scales (sub-100 nm) and visualizing their magnetic configurations. Here, we fabricate and measure nanoscale magnetic gyroids, periodic chiral networks comprising nanowire-like struts forming three-connected vertices. Via block copolymer templating, we produce Ni75Fe25 single-gyroid and double-gyroid (an inversion pair of single-gyroids) nanostructures with a 42 nm unit cell and 11 nm diameter struts, comparable to the exchange length in Ni-Fe. We visualize their magnetization distributions via off-axis electron holography with nanometer spatial resolution and interpret the patterns using finite-element micromagnetic simulations. Our results suggest an intricate, frustrated remanent state which is ferromagnetic but without a unique equilibrium configuration, opening new possibilities for collective phenomena in magnetism, including 3D magnonic crystals and unconventional computing.