RESUMEN
In light optics, beams with orbital angular momentum (OAM) can be produced by employing a properly-tuned two-cylinder-lens arrangement, also called π/2 mode converter. It is not possible to convey this concept directly to the beam in an electron microscope due to the non-existence of cylinder lenses in commercial transmission electron microscopes (TEMs). A viable work-around are readily-available electron optical elements in the form of quadrupole lenses. In a proof-of-principle experiment in 2012, it has been shown that a single quadrupole in combination with a Hilbert phase-plate produces a spatially-confined, transient vortex mode. Here, an analogue to an optical π/2 mode converter is realized by repurposing a CEOS DCOR probe corrector in an aberration corrected TEM in a way that it resembles a dual cylinder lens using two quadrupoles. In order to verify the presence of OAM in the output beam, a fork dislocation grating is used as an OAM analyser. The possibility to use magnetic quadrupole fields instead of, e.g., prefabricated fork dislocation gratings to produce electron beams carrying OAM enhances the beam brightness by almost an order of magnitude and delivers switchable high-mode purity vortex beams without unwanted side-bands.
RESUMEN
In optics, mode conversion is an elegant way to switch between Hermite Gaussian and Laguerre Gaussian beam profiles and thereby impart orbital angular momentum onto the beam and to create vortices. In optics such vortex beams can be produced in a setup consisting of two identical cylinder lenses. In electron optics, quadrupole lenses can be used for the same purpose. Here we investigate generalized asymmetric designs of a quadrupole mode converter that may be realized within the constraints of existing electron microscopes and can steer the development of dedicated vortex generators for high brilliance electron vortex probes of atomic scale.
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Interaction of the probe with the specimen in an electron microscope inevitably leads to entanglement between the probe and the scatterer. In spite of the importance of entanglement in many areas of modern physics, this subject has not been touched in the literature. Here, we develop some ideas about entanglement in electron microscopy for a number of scattering mechanisms. The relationship between entropy, density matrices, and coherence is discussed. In addition, we explore the questions "Why is Bragg scattering coherent and energy loss incoherent?" and "When does decoherence play a role?" It seems to be possible to measure decoherence on extremely short timescales of â¼10-8s. This is especially important in view of recent developments in ultrafast electron microscopy.
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We discuss the feasibility of detecting spin polarized electronic transitions with a vortex filter. This approach does not rely on the principal condition of the standard electron energy-loss magnetic chiral dichroism (EMCD) technique, the precise alignment of the crystal in order to use it as a beam splitter, and thus would pave the way for the application of EMCD to new classes of materials and problems, like amorphous magnetic alloys and interface magnetism. The dichroic signal strength at the L2, 3-edge of ferromagnetic Cobalt (Co) is estimated on theoretical grounds using a single atom scattering approach. To justify this approach, multi-slice simulations were carried out in order to confirm that orbital angular momentum (OAM) is conserved in amorphous materials over an extended range of sample thickness and also in very thin crystalline specimen, which is necessary for the detection of EMCD. Also artefact sources like spot size, mask tilt and astigmatism are discussed. In addition, the achievable SNR under typical experimental conditions is assessed.
RESUMEN
The theoretical possibility to use an electron microscope as a spin polarizer is studied. It turns out that a Bessel beam passing a standard magnetic objective lens is intrinsically spin polarized when post-selected on-axis. In the limit of infinitely small detectors, the spin polarisation tends to 100%. Increasing the detector size, the polarisation decreases rapidly, dropping below 10-4 for standard settings of medium voltage microscopes. For extremely low voltages, the Figure of Merit increases by two orders of magnitude, approaching that of existing Mott detectors. Our findings may lead to new desings of spin filters, an attractive option in view of its inherent combination with the electron microscope, especially at low voltage.
RESUMEN
The theoretical possibility to use an electron microscope as a spin polarizer is studied. It turns out that a Bessel beam passing a standard magnetic objective lens is intrinsically spin polarized when post-selected on-axis. In the limit of infinitely small detectors, the spin polarisation tends to 100%. Increasing the detector size, the polarisation decreases rapidly, dropping below 10-4 for standard settings of medium voltage microscopes. For extremely low voltages, the Figure of Merit increases by two orders of magnitude, approaching that of existing Mott detectors. Our findings may lead to new desings of spin filters, an attractive option in view of its inherent combination with the electron microscope, especially at low voltage.
RESUMEN
Standard electron optics predicts Larmor image rotation in the magnetic lens field of a TEM. Introducing the possibility to produce electron vortex beams with quantized orbital angular momentum brought up the question of their rotational dynamics in the presence of a magnetic field. Recently, it has been shown that electron vortex beams can be prepared as free electron Landau states showing peculiar rotational dynamics, including no and cyclotron (double-Larmor) rotation. Additionally very fast Gouy rotation of electron vortex beams has been observed. In this work a model is developed which reveals that the rotational dynamics of electron vortices are a combination of slow Larmor and fast Gouy rotations and that the Landau states naturally occur in the transition region in between the two regimes. This more general picture is confirmed by experimental data showing an extended set of peculiar rotations, including no, cyclotron, Larmor and rapid Gouy rotations all present in one single convergent electron vortex beam.
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Landau levels and states of electrons in a magnetic field are fundamental quantum entities underlying the quantum Hall and related effects in condensed matter physics. However, the real-space properties and observation of Landau wave functions remain elusive. Here we report the real-space observation of Landau states and the internal rotational dynamics of free electrons. States with different quantum numbers are produced using nanometre-sized electron vortex beams, with a radius chosen to match the waist of the Landau states, in a quasi-uniform magnetic field. Scanning the beams along the propagation direction, we reconstruct the rotational dynamics of the Landau wave functions with angular frequency ~100 GHz. We observe that Landau modes with different azimuthal quantum numbers belong to three classes, which are characterized by rotations with zero, Larmor and cyclotron frequencies, respectively. This is in sharp contrast to the uniform cyclotron rotation of classical electrons, and in perfect agreement with recent theoretical predictions.
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We discuss the feasibility of detecting magnetic transitions with focused electron vortex probes, suggested by selection rules for the magnetic quantum number. We theoretically estimate the dichroic signal strength in the L2,3 edge of ferromagnetic d metals. It is shown that under realistic conditions, the dichroic signal is undetectable for nanoparticles larger than â¼1 nm. This is confirmed by a key experiment with nanometer-sized vortices.
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We demonstrate how the mixed dynamic form factor (MDFF) can be interpreted as a quadratic form. This makes it possible to use matrix diagonalization methods to reduce the number of terms that need to be taken into account when calculating the inelastic scattering of electrons in a crystal. It also leads in a natural way to a new basis that helps elucidate the underlying physics. The new method is applied to several cases to show its versatility. In particular, predictions are made for directly imaging atomic orbitals in crystals.
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A mode converter for electron vortex beams is described. Numerical simulations, confirmed by experiment, show that the converter transforms a vortex beam with a topological charge m=±1 into beams closely resembling Hermite-Gaussian HG(10) and HG(01) modes. The converter can be used as a mode discriminator or filter for electron vortex beams. Combining the converter with a phase plate turns a plane wave into modes with topological charge m=±1. This combination serves as a generator of electron vortex beams of high brilliance.
RESUMEN
The holographic mask technique is used to create freely moving electrons with quantized angular momentum. With electron optical elements they can be focused to vortices with diameters below the nanometer range. The understanding of these vortex beams is important for many applications. Here, we produce electron vortex beams and compare them to a theory of electrons with topological charge. The experimental results show excellent agreement with simulations. As an immediate application, fundamental experimental parameters like spherical aberration and partial coherence are determined.
RESUMEN
The recent creation of electron vortex beams and their first practical application motivates a better understanding of their properties. Here, we develop the theory of free electron vortices with quantized angular momentum, based on solutions of the Schrödinger equation for cylindrical boundary conditions. The principle of transformation of a plane wave into vortices with quantized angular momentum, their paraxial propagation through round magnetic lenses, and the effect of partial coherence are discussed.
Asunto(s)
Simulación por Computador , Electrones , Lentes , Luz , Modelos TeóricosRESUMEN
The validity of the dipole approximations commonly used in the inelastic scattering theory for transmission electron microscopy is reviewed. Both experimental and numerical arguments are presented, emphasizing that the dipole approximations cause significant errors of the order of up to 25% even at small momentum transfer. This behavior is attributed mainly to non-linear contributions to the dynamic form factor due to the overlap of wave functions.
RESUMEN
Vortex beams (also known as beams with a phase singularity) consist of spiralling wavefronts that give rise to angular momentum around the propagation direction. Vortex photon beams are widely used in applications such as optical tweezers to manipulate micrometre-sized particles and in micro-motors to provide angular momentum, improving channel capacity in optical and radio-wave information transfer, astrophysics and so on. Very recently, an experimental realization of vortex beams formed of electrons was demonstrated. Here we describe the creation of vortex electron beams, making use of a versatile holographic reconstruction technique in a transmission electron microscope. This technique is a reproducible method of creating vortex electron beams in a conventional electron microscope. We demonstrate how they may be used in electron energy-loss spectroscopy to detect the magnetic state of materials and describe their properties. Our results show that electron vortex beams hold promise for new applications, in particular for analysing and manipulating nanomaterials, and can be easily produced.
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In this work, the theoretical framework for energy-loss magnetic chiral dichroism (EMCD) is reviewed and a new, fast, and easy-to-use software package is presented. This software is used to simulate the dependence of the EMCD signal on various parameters such as sample thickness and sample tilt. The results are found to be in excellent agreement with other theoretical predictions and experimental data. Furthermore, it is shown that the simulations are fast enough for the planning of experiments "on-the-fly" and for live didactic demonstrations.
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Measuring magnetic properties at a nanometre scale could be achieved in a transmission electron microscope by using dedicated techniques. Among these, the energy-loss magnetic chiral dichroism has already proven its efficiency and needs improvements to be widely used. The energy spectrum imaging technique can be used to measure dichroism but some image treatments are necessary due to distortions. This paper deals with the corrections that need to be applied on the data to remove all distortions, especially drift and non-isochromaticity, and extract reliable information. The measure and correction procedures are developed on an artificial data cube containing the dichroic signal and some noise to prove the efficiency of the routines.
RESUMEN
Considering the rapid technical development of transmission electron microscopes, we investigate the possibility to map electronic transitions in real space on the atomic scale. To this purpose, we analyse the information carried by the scatterer's initial and final state wave functions and the role of the different atomic transition channels for the inelastic scattering cross section. It is shown that the change in the magnetic quantum number in the transition can be mapped. Two experimental set-ups are proposed, one blocking half the diffraction plane, the other one using a cylinder lens for imaging. Both methods break the conventional circular symmetry in the electron microscope making it possible to detect the handedness of electronic transitions as an asymmetry in the image intensity. This finding is of important for atomic resolution energy-loss magnetic chiral dichroism (EMCD), allowing to obtain the magnetic moments of single atoms.
