Holographic generation of highly twisted electron beams

Free electrons can possess an intrinsic orbital angular momentum, similar to those in an electron cloud, upon free-space propagation. The wavefront corresponding to the electron's wavefunction forms a helical structure with a number of twists given by the \emph{angular speed}. Beams with a high number of twists are of particular interest because they carry a high magnetic moment about the propagation axis. Among several different techniques, electron holography seems to be a promising approach to shape a \emph{conventional} electron beam into a helical form with large values of angular momentum. Here, we propose and manufacture a nano-fabricated phase hologram for generating a beam of this kind with an orbital angular momentum up to 200$\hbar$. Based on a novel technique the value of orbital angular momentum of the generated beam are measured, then compared with simulations. Our work, apart from the technological achievements, may lead to a way of generating electron beams with a high quanta of magnetic moment along the propagation direction, and thus may be used in the study of the magnetic properties of materials and for manipulating nano-particles.Comment: 4 pages, 4 figures - Supplementary Material (3 pages and 2 figures) accompanies this manuscrip

Multiple slit interference and diffraction

The recent advances in nanotechnology and electron microscopy are making today possible the realization of experiments of diffraction and interference at multiple slits which formerly were carried out with extremely skilled specimen preparation techniques and dedicated electron optical apparatus [1]. Recently we have used the focused ion beam (FIB) to fabricate two slits on a commercial silicon nitride membrane suspended on a 100x100μm2 window realized on a 200μm thick silicon substrate, and observe the Fraunhofer image in a conventional TEM-JEOL 2010 [2]. Here we adopt a less expensive support for nano slits fabrication, consisting of a commercial continuous carbon film on a standard copper grid, which was subsequently evaporated with a gold layer about 120 nm in thickness. The slits (nominally 80nm wide, 420 nm spaced) were fabricated with a 9 pa, 30keV, Ga+ beam of a FEI Strata235M dual beam. The quality of the slits is really excellent, as shown in Fig. 1, which displays two (a), and three (b) slits. An additional advantage of these samples with respect to the previous 200μm thick ones, is that they can be inserted in almost all TEM-FEG specimen holder. The diffraction and interference experiments were carried out with the FEG-TEM JEM-2200FS. Owing to the larger coherence of the FEG with respect to the thermionic source, it has been possible to record interference and diffraction images with exposure times of few seconds. The three-slit case is illustrated in Fig. 2: (a) shows the image in focus, (b-d) the images taken at a nominal defocus of -10 mm, -20 mm and -40 mm respectively. They show the transition from the nearly separated Fresnel diffraction images of the single slits (b), to their subsequent overlapping as the defocus increases (c), displaying interference phenomena, till (d) the transition to a nearly Fraunhofer image. Fig. 3 displays the true Fraunhofer image, taken at a nominal defocus of -53 mm, which clearly shows the secondary minima between the more intense maxima. In the same in the perpendicular direction the single slit Fraunhofer images corresponding to the longer side of the slits can also be observed

Nondestructive Measurement of Orbital Angular Momentum for an Electron Beam

Free electrons with a helical phase front, referred to as "twisted" electrons, possess an orbital angular momentum (OAM) and, hence, a quantized magnetic dipole moment along their propagation direction. This intrinsic magnetic moment can be used to probe material properties. Twisted electrons thus have numerous potential applications in materials science. Measuring this quantity often relies on a series of projective measurements that subsequently change the OAM carried by the electrons. In this Letter, we propose a nondestructive way of measuring an electron beam's OAM through the interaction of this associated magnetic dipole with a conductive loop. Such an interaction results in the generation of induced currents within the loop, which are found to be directly proportional to the electron's OAM value. Moreover, the electron experiences no OAM variations and only minimal energy losses upon the measurement, and, hence, the nondestructive nature of the proposed technique.Comment: 5 pages, 3 figures, and supplemental material that is comprised of text and 4 figure

Generation of Nondiffracting Electron Bessel Beams

Almost 30 years ago, Durnin discovered that an optical beam with a transverse intensity profile in the form of a Bessel function of the first order is immune to the effects of diffraction. Unlike most laser beams, which spread upon propagation, the transverse distribution of these Bessel beams remains constant. Electrons also obey a wave equation (the Schrödinger equation), and therefore Bessel beams also exist for electron waves. We generate an electron Bessel beam by diffracting electrons from a nanoscale phase hologram. The hologram imposes a conical phase structure on the electron wave-packet spectrum, thus transforming it into a conical superposition of infinite plane waves, that is, a Bessel beam. We verify experimentally that these beams can propagate for 0.6 m without measurable spreading and can also reconstruct their intensity distributions after being partially obstructed by an obstacle. Finally, we show by numerical calculations that the performance of an electron microscope can be increased dramatically through use of these beams

Generation of Nondiffracting Electron Bessel Beams

Almost 30 years ago, Durnin discovered that an optical beam with a transverse intensity profile in the form of a Bessel function of the first order is immune to the effects of diffraction. Unlike most laser beams, which spread upon propagation, the transverse distribution of these Bessel beams remains constant. Electrons also obey a wave equation (the Schrodinger equation), and therefore Bessel beams also exist for electron waves. We generate an electron Bessel beam by diffracting electrons from a nanoscale phase hologram. The hologram imposes a conical phase structure on the electron wave-packet spectrum, thus transforming it into a conical superposition of infinite plane waves, that is, a Bessel beam. We verify experimentally that these beams can propagate for 0.6 m without measurable spreading and can also reconstruct their intensity distributions after being partially obstructed by an obstacle. Finally, we show by numerical calculations that the performance of an electron microscope can be increased dramatically through use of these beams

Magnetic characterization of cobalt nanowires and square nanorings fabricated by focused electron beam induced deposition

The magnetic properties of nanowires (NWs) and square nanorings, which were deposited by focused electron beam induced deposition (FEBID) of a Co carbonyl precursor, are studied using off-axis electron holography (EH), Lorentz transmission electron microscopy (L-TEM) and magnetic force microscopy (MFM). EH shows that NWs deposited using beam energies of 5 and 15 keV have the characteristics of magnetic dipoles, with larger magnetic moments observed for NWs deposited at lower energy. L-TEM is used to image magnetic domain walls in NWs and nanorings and their motion as a function of applied magnetic field. The NWs are found to have almost square hysteresis loops, with coercivities of ca. 10 mT. The nanorings show two different magnetization states: for low values of the applied in-plane field (0.02 T) a horseshoe state is observed using L-TEM, while for higher values of the applied in-plane field (0.3 T) an onion state is observed at remanence using L-TEM and MFM. Our results confirm the suitability of FEBID for nanofabrication of magnetic structures and demonstrate the versatility of TEM techniques for the study and manipulation of magnetic domain walls in nanostructures

Influence of the First Preparation Steps on the Properties of GaN Layers Grown on 6H-SIC by Mbe

AbstractThe Gan heteroepitaxy on 6H-SiC is affected by the bad morphology of the substrate surface. We performed a hydrogen etching at 1550°C on the 6H-SiC(0001) substrates to obtain atomically flat terraces. An improvement of the structural properties of GaN grown by MBE on such substrates after deposition of a LT-AIN buffer layer is observed. A value of less than 220 arcsec of the FWHM of the XRD rocking curve, showing a reduced screw dislocations density, is comparable with the best results reported until now for thick GaN samples. Photoluminescence showed a structured near band edge emission spectrum with evidence of the A, B and C free exciton recombinations

Experimental realization of the Ehrenberg-Siday thought experiment

In 1949, at the end of a paper dedicated to the concept of the refractive index in electron optics, Ehrenberg and Siday noted that wave-optical effects will arise from an isolated magnetic field even when the rays themselves travel in magnetic-field-free space. They proposed a two-slit experiment, in which a magnetic flux is enclosed between interfering electron beams. Now, through access to modern nanotechnology tools, we used a focused ion beam to open two nanosized slits in a gold-coated silicon nitride membrane and focused electron beam induced deposition to fabricate a thin magnetic bar between the two slits. We then performed Fraunhofer experiments in a transmission electron microscope equipped with a field emission gun and a Lorentz lens. By tilting the specimen in the objective lens field of the electron microscope, the magnetization of the bar could be reversed and the corresponding change in the phase of the electron wave observed directly in the form of a shift in the interference fringe pattern

Measuring the orbital angular momentum spectrum of an electron beam

Electron waves that carry orbital angular momentum (OAM) are characterized by a quantized and unbounded magnetic dipole moment parallel to their propagation direction. When interacting with magnetic materials, the wavefunctions of such electrons are inherently modified. Such variations therefore motivate the need to analyse electron wavefunctions, especially their wavefronts, to obtain information regarding the material’s structure. Here, we propose, design and demonstrate the performance of a device based on nanoscale holograms for measuring an electron’s OAM components by spatially separating them. We sort pure and superposed OAM states of electrons with OAM values of between −10 and 10. We employ the device to analyse the OAM spectrum of electrons that have been affected by a micron-scale magnetic dipole, thus establishing that our sorter can be an instrument for nanoscale magnetic spectroscopy