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- ItemBridging nano-optics and condensed matter formalisms in a unified description of inelastic scattering of relativistic electron beams(Amsterdam : SciPost Foundation, 2021) Lourenço-Martins, Hugo; Lubk, Axel; Kociak, MathieuIn the last decades, the blossoming of experimental breakthroughs in the domain of electron energy loss spectroscopy (EELS) has triggered a variety of theoretical developments. Those have to deal with completely different situations, from atomically resolved phonon mapping to electron circular dichroism passing by surface plasmon mapping. All of them rely on very different physical approximations and have not yet been reconciled, despite early attempts to do so. As an effort in that direction, we report on the development of a scalar relativistic quantum electrodynamic (QED) approach of the inelastic scattering of fast electrons. This theory can be adapted to describe all modern EELS experiments, and under the relevant approximations, can be reduced to any of the last EELS theories. In that aim, we present in this paper the state of the art and the basics of scalar relativistic QED relevant to the electron inelastic scattering. We then give a clear relation between the two once antagonist descriptions of the EELS, the retarded green Dyadic, usually applied to describe photonic excitations and the quasi-static mixed dynamic form factor (MDFF), more adapted to describe core electronic excitations of material. We then use this theory to establish two important EELS-related equations. The first one relates the spatially resolved EELS to the imaginary part of the photon propagator and the incoming and outgoing electron beam wavefunction, synthesizing the most common theories developed for analyzing spatially resolved EELS experiments. The second one shows that the evolution of the electron beam density matrix is proportional to the mutual coherence tensor, proving that quite universally, the electromagnetic correlations in the target are imprinted in the coherence properties of the probing electron beam.
- ItemMagnetic Nanoparticle Chains in Gelatin Ferrogels: Bioinspiration from Magnetotactic Bacteria(Weinheim : Wiley-VCH, 2019) Sturm, Sebastian; Siglreitmeier, Maria; Wolf, Daniel; Vogel, Karin; Gratz, Micha; Faivre, Damien; Lubk, Axel; Büchner, Bernd; Sturm, Elena V.; Cölfen, HelmutInspired by chains of ferrimagnetic nanocrystals (NCs) in magnetotactic bacteria (MTB), the synthesis and detailed characterization of ferrimagnetic magnetite NC chain-like assemblies is reported. An easy green synthesis route in a thermoreversible gelatin hydrogel matrix is used. The structure of these magnetite chains prepared with and without gelatin is characterized by means of transmission electron microscopy, including electron tomography (ET). These structures indeed bear resemblance to the magnetite assemblies found in MTB, known for their mechanical flexibility and outstanding magnetic properties and known to crystallographically align their magnetite NCs along the strongest <111> magnetization easy axis. Using electron holography (EH) and angular dependent magnetic measurements, the magnetic interaction between the NCs and the generation of a magnetically anisotropic material can be shown. The electro- and magnetostatic modeling demonstrates that in order to precisely determine the magnetization (by means of EH) inside chain-like NCs assemblies, their exact shape, arrangement and stray-fields have to be considered (ideally obtained using ET). © 2019 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
- ItemExploiting Combinatorics to Investigate Plasmonic Properties in Heterogeneous Ag-Au Nanosphere Chain Assemblies(Weinheim : Wiley-VCH, 2021) Schletz, Daniel; Schultz, Johannes; Potapov, Pavel L.; Steiner, Anja Maria; Krehl, Jonas; König, Tobias A.F.; Mayer, Martin; Lubk, Axel; Fery, AndreasChains of coupled metallic nanoparticles are of special interest for plasmonic applications because they can sustain highly dispersive plasmon bands, allowing strong ballistic plasmon wave transport. Whereas early studies focused on homogeneous particle chains exhibiting only one dominant band, heterogeneous assemblies consisting of different nanoparticle species came into the spotlight recently. Their increased configuration space principally allows engineering multiple bands, bandgaps, or topological states. Simultaneously, the challenge of the precise arrangement of nanoparticles, including their distances and geometric patterns, as well as the precise characterization of the plasmonics in these systems, persists. Here, the surface plasmon resonances in heterogeneous Ag-Au nanoparticle chains are reported. Wrinkled templates are used for directed self-assembly of monodisperse gold and silver nanospheres as chains, which allows assembling statistical combinations of more than 109 particles. To reveal the spatial and spectral distribution of the plasmonic response, state-of-the-art scanning transmission electron microscopy coupled with electron energy loss spectroscopy accompanied by boundary element simulations is used. A variety of modes in the heterogeneous chains are found, ranging from localized surface plasmon modes occurring in single gold or silver spheres, respectively, to modes that result from the hybridization of the single particles. This approach opens a novel avenue toward combinatorial studies of plasmonic properties in heterosystems. © 2021 The Authors. Advanced Optical Materials published by Wiley-VCH GmbH
- ItemTailoring Plasmonics of Au@Ag Nanoparticles by Silica Encapsulation(Weinheim : Wiley-VCH, 2021) Schultz, Johannes; Kirner, Felizitas; Potapov, Pavel; Büchner, Bernd; Lubk, Axel; Sturm, Elena V.Hybrid metallic nanoparticles (NPs) encapsulated in oxide shells are currently intensely studied for plasmonic applications in sensing, medicine, catalysis, and photovoltaics. Here, a method for the synthesis of Au@Ag@SiO2 cubes with a uniform silica shell of variable and adjustable thickness in the nanometer range is introduced and their excellent, highly reproducible, and tunable optical response is demonstrated. Varying the silica shell thickness, the excitation energies of the single NP plasmon modes can be tuned in a broad spectral range between 2.55 and 3.25 eV. Most importantly, a strong coherent coupling of the surface plasmons is revealed at the silver–silica interface with Mie resonances at the silica–vacuum interface leading to a significant field enhancement at the encapsulated NP surface in the range of 100% at shell thicknesses t ≃ 20 nm. Consequently, the synthesis method and the field enhancement open pathways to a widespread use of silver NPs in plasmonic applications including photonic crystals and may be transferred to other non-precious metals. © 2021 The Authors. Advanced Optical Materials published by Wiley-VCH GmbH
- ItemAxion Mie theory of electron energy loss spectroscopy in topological insulators(Amsterdam : SciPost Foundation, 2021) Schultz, Johannes; Nogueira, Flavio S.; Büchner, Bernd; van den Brink, Jeroen; Lubk, AxelElectronic topological states of matter exhibit novel types of responses to electromagnetic fields. The response of strong topological insulators, for instance, is characterized by a so-called axion term in the electromagnetic Lagrangian which is ultimately due to the presence of topological surface states. Here we develop the axion Mie theory for the electromagnetic response of spherical particles including arbitrary sources of fields, i.e., charge and current distributions. We derive an axion induced mixing of transverse magnetic and transverse electric modes which are experimentally detectable through small induced rotations of the field vectors. Our results extend upon previous analyses of the problem. Our main focus is on the experimentally relevant problem of electron energy loss spectroscopy in topological insulators, a technique that has so far not yet been used to detect the axion electromagnetic response in these materials.
- ItemDirect Observation of Plasmon Band Formation and Delocalization in Quasi-Infinite Nanoparticle Chains(Washington, DC : ACS Publ., 2019) Mayer, Martin; Potapov, Pavel L.; Pohl, Darius; Steiner, Anja Maria; Schultz, Johannes; Rellinghaus, Bernd; Lubk, Axel; König, Tobias A.F.; Fery, AndreasChains of metallic nanoparticles sustain strongly confined surface plasmons with relatively low dielectric losses. To exploit these properties in applications, such as waveguides, the fabrication of long chains of low disorder and a thorough understanding of the plasmon-mode properties, such as dispersion relations, are indispensable. Here, we use a wrinkled template for directed self-assembly to assemble chains of gold nanoparticles. With this up-scalable method, chain lengths from two particles (140 nm) to 20 particles (1500 nm) and beyond can be fabricated. Electron energy-loss spectroscopy supported by boundary element simulations, finite-difference time-domain, and a simplified dipole coupling model reveal the evolution of a band of plasmonic waveguide modes from degenerated single-particle modes in detail. In striking difference from plasmonic rod-like structures, the plasmon band is confined in excitation energy, which allows light manipulations below the diffraction limit. The non-degenerated surface plasmon modes show suppressed radiative losses for efficient energy propagation over a distance of 1500 nm. © 2019 American Chemical Society.
- ItemThree-Dimensional Composition and Electric Potential Mapping of III–V Core–Multishell Nanowires by Correlative STEM and Holographic Tomography(Washington, DC : ACS Publ., 2018-7-13) Wolf, Daniel; Hübner, René; Niermann, Tore; Sturm, Sebastian; Prete, Paola; Lovergine, Nico; Büchner, Bernd; Lubk, AxelThe nondestructive characterization of nanoscale devices, such as those based on semiconductor nanowires, in terms of functional potentials is crucial for correlating device properties with their morphological/materials features, as well as for precisely tuning and optimizing their growth process. Electron holographic tomography (EHT) has been used in the past to reconstruct the total potential distribution in three-dimension but hitherto lacked a quantitative approach to separate potential variations due to chemical composition changes (mean inner potential, MIP) and space charges. In this Letter, we combine and correlate EHT and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) tomography on an individual ⟨111⟩ oriented GaAs–AlGaAs core–multishell nanowire (NW). We obtain excellent agreement between both methods in terms of the determined Al concentration within the AlGaAs shell, as well as thickness variations of the few nanometer thin GaAs shell acting as quantum well tube. Subtracting the MIP determined from the STEM tomogram, enables us to observe functional potentials at the NW surfaces and at the Au–NW interface, both ascribed to surface/interface pinning of the semiconductor Fermi level.
- ItemAutocorrected off-axis holography of two-dimensional materials(College Park, ML : American Physical Society, 2020) Kern, Felix; Linck, Martin; Wolf, Daniel; Alem, Nasim; Arora, Himani; Gemming, Sibylle; Erbe, Artur; Zettl, Alex; Büchner, Bernd; Lubk, AxelThe reduced dimensionality in two-dimensional materials leads to a wealth of unusual properties, which are currently explored for both fundamental and applied sciences. In order to study the crystal structure, edge states, the formation of defects and grain boundaries, or the impact of adsorbates, high-resolution microscopy techniques are indispensable. Here we report on the development of an electron holography (EH) transmission electron microscopy (TEM) technique, which facilitates high spatial resolution by an automatic correction of geometric aberrations. Distinguished features of EH beyond conventional TEM imaging are gap-free spatial information signal transfer and higher dose efficiency for certain spatial frequency bands as well as direct access to the projected electrostatic potential of the two-dimensional material. We demonstrate these features with the example of h-BN, for which we measure the electrostatic potential as a function of layer number down to the monolayer limit and obtain evidence for a systematic increase of the potential at the zig-zag edges.
- ItemFlexomagnetism and vertically graded Néel temperature of antiferromagnetic Cr2O3 thin films([London] : Nature Publishing Group UK, 2022) Makushko, Pavlo; Kosub, Tobias; Pylypovskyi, Oleksandr V.; Hedrich, Natascha; Li, Jiang; Pashkin, Alexej; Avdoshenko, Stanislav; Hübner, René; Ganss, Fabian; Wolf, Daniel; Lubk, Axel; Liedke, Maciej Oskar; Butterling, Maik; Wagner, Andreas; Wagner, Kai; Shields, Brendan J.; Lehmann, Paul; Veremchuk, Igor; Fassbender, Jürgen; Maletinsky, Patrick; Makarov, DenysAntiferromagnetic insulators are a prospective materials platform for magnonics, spin superfluidity, THz spintronics, and non-volatile data storage. A magnetomechanical coupling in antiferromagnets offers vast advantages in the control and manipulation of the primary order parameter yet remains largely unexplored. Here, we discover a new member in the family of flexoeffects in thin films of Cr2O3. We demonstrate that a gradient of mechanical strain can impact the magnetic phase transition resulting in the distribution of the Néel temperature along the thickness of a 50-nm-thick film. The inhomogeneous reduction of the antiferromagnetic order parameter induces a flexomagnetic coefficient of about 15 μB nm−2. The antiferromagnetic ordering in the inhomogeneously strained films can persist up to 100 °C, rendering Cr2O3 relevant for industrial electronics applications. Strain gradient in Cr2O3 thin films enables fundamental research on magnetomechanics and thermodynamics of antiferromagnetic solitons, spin waves and artificial spin ice systems in magnetic materials with continuously graded parameters.
- ItemObservation of fractional spin textures in a Heusler material([London] : Nature Publishing Group UK, 2022) Jena, Jagannath; Göbel, Börge; Hirosawa, Tomoki; Díaz, Sebastián A.; Wolf, Daniel; Hinokihara, Taichi; Kumar, Vivek; Mertig, Ingrid; Felser, Claudia; Lubk, Axel; Loss, Daniel; Parkin, Stuart S.P.Recently a zoology of non-collinear chiral spin textures has been discovered, most of which, such as skyrmions and antiskyrmions, have integer topological charges. Here we report the experimental real-space observation of the formation and stability of fractional antiskyrmions and fractional elliptical skyrmions in a Heusler material. These fractional objects appear, over a wide range of temperature and magnetic field, at the edges of a sample, whose interior is occupied by an array of nano-objects with integer topological charges, in agreement with our simulations. We explore the evolution of these objects in the presence of magnetic fields and show their interconversion to objects with integer topological charges. This means the topological charge can be varied continuously. These fractional spin textures are not just another type of skyrmion, but are essentially a new state of matter that emerges and lives only at the boundary of a magnetic system. The coexistence of both integer and fractionally charged spin textures in the same material makes the Heusler family of compounds unique for the manipulation of the real-space topology of spin textures and thus an exciting platform for spintronic and magnonic applications.