Exploiting the Acceleration Voltage Dependence of EMCD.

Energy-loss magnetic chiral dichroism (EMCD) is a versatile method for measuring magnetism down to the atomic scale in transmission electron microscopy (TEM). As the magnetic signal is encoded in the phase of the electron wave, any process distorting this characteristic phase is detrimental for EMCD. For example, elastic scattering gives rise to a complex thickness dependence of the signal. Since the details of elastic scattering depend on the electron's energy, EMCD strongly depends on the acceleration voltage. Here, we quantitatively investigate this dependence in detail, using a combination of theory, numerical simulations, and experimental data. Our formulas enable scientists to optimize the acceleration voltage when performing EMCD experiments.

Real-space mapping of electronic orbitals.

Electronic states are responsible for most material properties, including chemical bonds, electrical and thermal conductivity, as well as optical and magnetic properties. Experimentally, however, they remain mostly elusive. Here, we report the real-space mapping of selected transitions between p and d states on the Ångström scale in bulk rutile (TiO2) using electron energy-loss spectrometry (EELS), revealing information on individual bonds between atoms. On the one hand, this enables the experimental verification of theoretical predictions about electronic states. On the other hand, it paves the way for directly investigating electronic states under conditions that are at the limit of the current capabilities of numerical simulations such as, e.g., the electronic states at defects, interfaces, and quantum dots.

Measurement of atomic electric fields and charge densities from average momentum transfers using scanning transmission electron microscopy.

This study sheds light on the prerequisites, possibilities, limitations and interpretation of high-resolution differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM). We draw particular attention to the well-established DPC technique based on segmented annular detectors and its relation to recent developments based on pixelated detectors. These employ the expectation value of the momentum transfer as a reliable measure of the angular deflection of the STEM beam induced by an electric field in the specimen. The influence of scattering and propagation of electrons within the specimen is initially discussed separately and then treated in terms of a two-state channeling theory. A detailed simulation study of GaN is presented as a function of specimen thickness and bonding. It is found that bonding effects are rather detectable implicitly, e.g., by characteristics of the momentum flux in areas between the atoms than by directly mapping electric fields and charge densities. For strontium titanate, experimental charge densities are compared with simulations and discussed with respect to experimental artifacts such as scan noise. Finally, we consider practical issues such as figures of merit for spatial and momentum resolution, minimum electron dose, and the mapping of larger-scale, built-in electric fields by virtue of data averaged over a crystal unit cell. We find that the latter is possible for crystals with an inversion center. Concerning the optimal detector design, this study indicates that a sampling of 5mrad per pixel is sufficient in typical applications, corresponding to approximately 10×10 available pixels.

Magnetic properties of single nanomagnets: Electron energy-loss magnetic chiral dichroism on FePt nanoparticles.

Electron energy-loss magnetic chiral dichroism (EMCD) allows for the quantification of magnetic properties of materials at the nanometer scale. It is shown that with the support of simulations that help to identify the optimal conditions for a successful experiment and upon implementing measurement routines that effectively reduce the noise floor, EMCD measurements can be pushed towards quantitative magnetic measurements even on individual nanoparticles. With this approach, the ratio of orbital to spin magnetic moments for the Fe atoms in a single L10 ordered FePt nanoparticle is determined to be ml/ms=0.08±0.02. This finding is in good quantitative agreement with the results of XMCD ensemble measurements.

Mapping Atomic Orbitals with the Transmission Electron Microscope: Images of Defective Graphene Predicted from First-Principles Theory.

Transmission electron microscopy has been a promising candidate for mapping atomic orbitals for a long time. Here, we explore its capabilities by a first-principles approach. For the example of defected graphene, exhibiting either an isolated vacancy or a substitutional nitrogen atom, we show that three different kinds of images are to be expected, depending on the orbital character. To judge the feasibility of visualizing orbitals in a real microscope, the effect of the optics' aberrations is simulated. We demonstrate that, by making use of energy filtering, it should indeed be possible to map atomic orbitals in a state-of-the-art transmission electron microscope.

Real-space localization and quantification of hole distribution in chain-ladder Sr3Ca11Cu24O41 superconductor.

Understanding the physical properties of the chain-ladder Sr3Ca11Cu24O41 hole-doped superconductor has been precluded by the unknown hole distribution among chains and ladders. We use electron energy-loss spectrometry (EELS) in a scanning transmission electron microscope (STEM) at atomic resolution to directly separate the contributions of chains and ladders and to unravel the hole distribution from the atomic scale variations of the O-K near-edge structures. The experimental data unambiguously demonstrate that most of the holes lie within the chain layers. A quantitative interpretation supported by inelastic scattering calculations shows that about two holes are located in the ladders, and about four holes in the chains, shedding light on the electronic structure of Sr3Ca11Cu24O41. Combined atomic resolution STEM-EELS and inelastic scattering calculations is demonstrated as a powerful approach toward a quantitative understanding of the electronic structure of cuprate superconductors, offering new possibilities for elucidating their physical properties.

Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction.

By focusing electrons on probes with a diameter of 50 pm, aberration-corrected scanning transmission electron microscopy (STEM) is currently crossing the border to probing subatomic details. A major challenge is the measurement of atomic electric fields using differential phase contrast (DPC) microscopy, traditionally exploiting the concept of a field-induced shift of diffraction patterns. Here we present a simplified quantum theoretical interpretation of DPC. This enables us to calculate the momentum transferred to the STEM probe from diffracted intensities recorded on a pixel array instead of conventional segmented bright-field detectors. The methodical development yielding atomic electric field, charge and electron density is performed using simulations for binary GaN as an ideal model system. We then present a detailed experimental study of SrTiO3 yielding atomic electric fields, validated by comprehensive simulations. With this interpretation and upgraded instrumentation, STEM is capable of quantifying atomic electric fields and high-contrast imaging of light atoms.

Oriented attachment explains cobalt ferrite nanoparticle growth in bioinspired syntheses.

Oriented attachment has created a great debate about the description of crystal growth throughout the last decade. This aggregation-based model has successfully described biomineralization processes as well as forms of inorganic crystal growth, which could not be explained by classical crystal growth theory. Understanding the nanoparticle growth is essential since physical properties, such as the magnetic behavior, are highly dependent on the microstructure, morphology and composition of the inorganic crystals. In this work, the underlying nanoparticle growth of cobalt ferrite nanoparticles in a bioinspired synthesis was studied. Bioinspired syntheses have sparked great interest in recent years due to their ability to influence and alter inorganic crystal growth and therefore tailor properties of nanoparticles. In this synthesis, a short synthetic version of the protein MMS6, involved in nanoparticle formation within magnetotactic bacteria, was used to alter the growth of cobalt ferrite. We demonstrate that the bioinspired nanoparticle growth can be described by the oriented attachment model. The intermediate stages proposed in the theoretical model, including primary-building-block-like substructures as well as mesocrystal-like structures, were observed in HRTEM measurements. These structures display regions of substantial orientation and possess the same shape and size as the resulting discs. An increase in orientation with time was observed in electron diffraction measurements. The change of particle diameter with time agrees with the recently proposed kinetic model for oriented attachment.

Site-specific ionisation edge fine-structure of Rutile in the electron microscope.

Combined Bloch-wave and density functional theory simulations are performed to investigate the effects of different channelling conditions on the fine-structure of electron energy-loss spectra. The simulated spectra compare well with experiments. Furthermore, we demonstrate that using this technique, the site-specific investigation of atomic orbitals is possible. This opens new possibilities for chemical analyses.

The post-peak spectra in electron energy loss near edge structure.

The origin of post-peak spectra in electron energy loss near edge structure (ELNES) spectra of pure Ni and NiO is investigated through ab initio calculation. Contrary to the general view that post-peak spectra in ELNES are generated by transitions to continuum states, it is found that orbit hybridization is the main cause of post-peak spectra in the low energy range above the Fermi level based on the calculation of electronic structure and ELNES. Reasons for the intensity differences of the simulated and experimental spectra are discussed. This work contributes to the understanding of ELNES and to the quantification of ELNES spectra.

Observation of the Larmor and Gouy rotations with electron vortex beams.

Electron vortex beams carrying intrinsic orbital angular momentum (OAM) are produced in electron microscopes where they are controlled and focused by using magnetic lenses. We observe various rotational phenomena arising from the interaction between the OAM and magnetic lenses. First, the Zeeman coupling, proportional to the OAM and magnetic field strength, produces an OAM-independent Larmor rotation of a mode superposition inside the lens. Second, when passing through the focal plane, the electron beam acquires an additional Gouy phase dependent on the absolute value of the OAM. This brings about the Gouy rotation of the superposition image proportional to the sign of the OAM. A combination of the Larmor and Gouy effects can result in the addition (or subtraction) of rotations, depending on the OAM sign. This behavior is unique to electron vortex beams and has no optical counterpart, as Larmor rotation occurs only for charged particles. Our experimental results are in agreement with recent theoretical predictions.

Transition probability functions for applications of inelastic electron scattering.

In this work, the transition matrix elements for inelastic electron scattering are investigated which are the central quantity for interpreting experiments. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in the Slater-type and the hydrogen-like orbital models. These expressions are shown to be composed of a finite sum of polynomials and elementary trigonometric functions. Hence, they are easy to use, require little computation time, and are significantly more accurate than commonly used approximations.

Image simulation of high resolution energy filtered TEM images.

Inelastic image simulation software is presented, implementing the double channeling approximation which takes into account the combination of multiple elastic and single inelastic scattering in a crystal. The approach is described with a density matrix formalism. Two applications in high resolution energy filtered (EFTEM) transmission electron microscopy (TEM) images are presented: thickness-defocus maps for SrTiO(3) and exit plane intensities for an (LaAlO(3))(3)(SrTiO(3))(3) multilayer system. Both systems show a severe breakdown in direct interpretability which becomes worse for higher acceleration voltages, thicker samples and lower excitation edge energies. Since this effect already occurs in the exit plane intensity, it is a fundamental limit and image simulations in EFTEM are indispensable just as they are indispensable for elastic high resolution TEM images.

Fringe contrast in inelastic LACBED holography.

We discuss diffraction holography in a scattering geometry reported by Herring [Ultramicroscopy 104 (2005) 261, Ultramicroscopy 106 (2006) 960] and interpreted in terms of the density matrix of the fast electrons. Whereas the previous description used an approximation replacing the LACBED by a CBED geometry and consequently left some doubts about the conclusions (namely the non-detectability of the MDFF) we now fully include the Fresnel propagator and the biprism operator in order to calculate the density matrix of the inelastically scattered electrons in LACBED geometry. We show that a defocus on the biprism with respect to the sample does not cause a significant effect on the fringe patterns that are formed when the discs are exactly overlapping. An important difference to the CBED geometry is however that the fringe contrast decreases when the shear deviates from a reciprocal lattice vector. This should enable to measure the spatial coherence for smaller shears than is possible in image holography.

Magnetic circular dichroism in EELS: towards 10 nm resolution.

We describe a new experimental setup for the detection of magnetic circular dichroism with fast electrons (EMCD). As compared to earlier findings the signal is an order of magnitude higher, while the probed area could be significantly reduced, allowing a spatial resolution of better than 40 nm. A simplified analysis of the experimental results is based on the decomposition of the mixed dynamic form factor S(q-->,q-->('),E) into a real part related to the scalar product and an imaginary part related to the vector product of the scattering vectors q--> and q-->('). Following the recent detection of chiral electronic transitions in the electron microscope the present experiment is a crucial demonstration of the potential of EMCD for nanoscale investigations.

The Fresnel effect of a defocused biprism on the fringes in inelastic holography.

We present energy filtered holography experiments on a thin foil of Al. By propagating the reduced density matrix of the probe electron through the microscope, we quantitatively predict the fringe contrast as a function of energy loss. Fringe contrast simulations include the effect of Fresnel fringes created at the edges of the defocused biprism, the effect of partial coherence in combination with inelastic scattering, and the effect of a finite energy distribution of the incoming beam.

Local field effects in the electron energy loss spectra of rutile TiO2.

We present an ab initio calculation of the electron energy loss spectrum of rutile TiO2 in the energy range of 0 to 60 eV, focusing our interest on the excitation from the titanium 3p semicore levels. The results are compared to our measurements. Local field effects turn out to be crucial at those energies, and their inclusion in the calculation yields excellent agreement between theory and experiment. We show how in rutile these effects induce an anisotropy in the otherwise isotropic transitions from quasispherical 3p semicore states to 3d states of almost cubic symmetry.