1
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Stöger-Pollach M, Ederer M. Experimental evidence of magnetism in a 2D electron gas at the CoO/Co 3O 4 interface by employing EMCD. Micron 2024; 185:103687. [PMID: 39053049 DOI: 10.1016/j.micron.2024.103687] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Revised: 06/25/2024] [Accepted: 06/26/2024] [Indexed: 07/27/2024]
Abstract
In the present study we investigate the CoO/Co3O4 interface in order to determine its intriguing magnetic behavior, which can be utilized for tailoring magnetic properties, enabling spin transport, enhancing magnetic coupling, tuning device functionalities, and realizing miniaturized magnetic devices for various technological applications. We decipher the magnetic properties of the CoO/Co3O4 interface from first principles calculations using Wien2k and probe them experimentally by employing electron energy-loss magnetic chiral dichroism (EMCD), which is an electron-energy loss spectrometry (EELS) based technique in the transmission electron microscope (TEM). Both, theory and experiment, are in perfect agreement and result in a ferromagnetic 2D-electron gas of 5Å thickness directly at the interface.
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Affiliation(s)
- Michael Stöger-Pollach
- University Service Center for Transmission Electron Microscopy (USTEM), Technische Universität Wien, Wiedner Hauptstraße 8-10, Wien 1040, Austria; Institute of Solid State Physics, Technische Universität Wien, Wiedner Hauptstraße 8-10, Wien 1040, Austria.
| | - Manuel Ederer
- University Service Center for Transmission Electron Microscopy (USTEM), Technische Universität Wien, Wiedner Hauptstraße 8-10, Wien 1040, Austria; Institute of Solid State Physics, Technische Universität Wien, Wiedner Hauptstraße 8-10, Wien 1040, Austria
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2
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Yu R, Huo P, Liu M, Zhu W, Agrawal A, Lu YQ, Xu T. Generation of Perfect Electron Vortex Beam with a Customized Beam Size Independent of Orbital Angular Momentum. NANO LETTERS 2023; 23:2436-2441. [PMID: 36723626 DOI: 10.1021/acs.nanolett.2c03822] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
The electron vortex beam (EVB)-carrying quantized orbital angular momentum (OAM) plays an essential role in a series of fundamental research. However, the radius of the transverse intensity profile of a doughnut-shaped EVB strongly depends on the topological charge of the OAM, impeding its wide applications in electron microscopy. Inspired by the perfect vortex in optics, herein, we demonstrate a perfect electron vortex beam (PEVB), which completely unlocks the constraint between the beam size and the beam's OAM. We design nanoscale holograms to generate PEVBs carrying different quanta of OAM but exhibiting almost the same beam size. Furthermore, we show that the beam size of the PEVB can be readily controlled by only modifying the design parameters of the hologram. The generation of PEVB with a customized beam size independent of the OAM can promote various in situ applications of free electrons carrying OAM in electron microscopy.
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Affiliation(s)
- Ruixuan Yu
- National Laboratory of Solid-State Microstructures and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing210093, China
- College of Engineering and Applied Sciences and Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing210093, China
| | - Pengcheng Huo
- National Laboratory of Solid-State Microstructures and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing210093, China
- College of Engineering and Applied Sciences and Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing210093, China
| | - Mingze Liu
- National Laboratory of Solid-State Microstructures and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing210093, China
- College of Engineering and Applied Sciences and Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing210093, China
| | - Wenqi Zhu
- Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland20899, United States
- Maryland NanoCenter, University of Maryland, College Park, Maryland20742, United States
| | - Amit Agrawal
- Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland20899, United States
- Maryland NanoCenter, University of Maryland, College Park, Maryland20742, United States
| | - Yan-Qing Lu
- National Laboratory of Solid-State Microstructures and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing210093, China
- College of Engineering and Applied Sciences and Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing210093, China
| | - Ting Xu
- National Laboratory of Solid-State Microstructures and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing210093, China
- College of Engineering and Applied Sciences and Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing210093, China
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3
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Planas XB, Ordóñez A, Lewenstein M, Maxwell AS. Ultrafast Imaging of Molecular Chirality with Photoelectron Vortices. PHYSICAL REVIEW LETTERS 2022; 129:233201. [PMID: 36563195 DOI: 10.1103/physrevlett.129.233201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Revised: 07/30/2022] [Accepted: 10/25/2022] [Indexed: 06/17/2023]
Abstract
Ultrafast imaging of molecular chirality is a key step toward the dream of imaging and interpreting electronic dynamics in complex and biologically relevant molecules. Here, we propose a new ultrafast chiral phenomenon exploiting recent advances in electron optics allowing access to the orbital angular momentum of free electrons. We show that strong-field ionization of a chiral target with a few-cycle linearly polarized 800 nm laser pulse yields photoelectron vortices, whose chirality reveals that of the target, and we discuss the mechanism underlying this phenomenon. Our Letter opens new perspectives in recollision-based chiral imaging.
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Affiliation(s)
- Xavier Barcons Planas
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Andrés Ordóñez
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Maciej Lewenstein
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA, Passeig de Lluís Companys 23, 08010 Barcelona, Spain
| | - Andrew S Maxwell
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark
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4
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Rosi P, Clausen A, Weber D, Tavabi AH, Frabboni S, Tiemeijer P, Dunin-Borkowski RE, Rotunno E, Grillo V. Automatic Alignment of an Orbital Angular Momentum Sorter in a Transmission Electron Microscope Using a Convolutional Neural Network. MICROSCOPY AND MICROANALYSIS : THE OFFICIAL JOURNAL OF MICROSCOPY SOCIETY OF AMERICA, MICROBEAM ANALYSIS SOCIETY, MICROSCOPICAL SOCIETY OF CANADA 2022; 29:1-9. [PMID: 36082682 DOI: 10.1017/s143192762201248x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We report on the automatic alignment of a transmission electron microscope equipped with an orbital angular momentum sorter using a convolutional neural network. The neural network is able to control all relevant parameters of both the electron-optical setup of the microscope and the external voltage source of the sorter without input from the user. It can compensate for mechanical and optical misalignments of the sorter, in order to optimize its spectral resolution. The alignment is completed over a few frames and can be kept stable by making use of the fast fitting time of the neural network.
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Affiliation(s)
- Paolo Rosi
- Istituto Nanoscienze - CNR, via G. Campi 213/A, Modena 41125, Italy
- FIM Department, University of Modena and Reggio Emilia, via G. Campi 213/A, Modena 41125, Italy
| | - Alexander Clausen
- Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, Jülich 52425, Germany
| | - Dieter Weber
- Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, Jülich 52425, Germany
| | - Amir H Tavabi
- Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, Jülich 52425, Germany
| | - Stefano Frabboni
- Istituto Nanoscienze - CNR, via G. Campi 213/A, Modena 41125, Italy
- FIM Department, University of Modena and Reggio Emilia, via G. Campi 213/A, Modena 41125, Italy
| | - Peter Tiemeijer
- Thermo Fisher Scientific, PO Box 80066, 5600 KA Eindhoven, The Netherlands
| | - Rafal E Dunin-Borkowski
- Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, Jülich 52425, Germany
| | - Enzo Rotunno
- Istituto Nanoscienze - CNR, via G. Campi 213/A, Modena 41125, Italy
| | - Vincenzo Grillo
- Istituto Nanoscienze - CNR, via G. Campi 213/A, Modena 41125, Italy
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5
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Löffler S. Unitary two-state quantum operators realized by quadrupole fields in the electron microscope. Ultramicroscopy 2022; 234:113456. [PMID: 35032788 DOI: 10.1016/j.ultramic.2021.113456] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2021] [Revised: 11/26/2021] [Accepted: 12/05/2021] [Indexed: 10/19/2022]
Abstract
In this work, a novel method for using a set of electromagnetic quadrupole fields is presented to implement arbitrary unitary operators on a two-state quantum system of electrons. In addition to analytical derivations of the required quadrupole and beam settings which allow an easy direct implementation, numerical simulations of realistic scenarios show the feasibility of the proposed setup. This is expected to pave the way not only for new measurement schemes in electron microscopy and related fields but even one day for the implementation of quantum computing in the electron microscope.
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Affiliation(s)
- Stefan Löffler
- University Service Centre for Transmission Electron Microscopy, TU Wien, Wiedner Hauptstraße 8-10/E057-02, 1040, Wien, Austria.
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6
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Roitman D, Shiloh R, Lu PH, Dunin-Borkowski RE, Arie A. Shaping of Electron Beams Using Sculpted Thin Films. ACS PHOTONICS 2021; 8:3394-3405. [PMID: 34938823 PMCID: PMC8679091 DOI: 10.1021/acsphotonics.1c00951] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Revised: 10/31/2021] [Accepted: 11/04/2021] [Indexed: 05/04/2023]
Abstract
Electron beam shaping by sculpted thin films relies on electron-matter interactions and the wave nature of electrons. It can be used to study physical phenomena of special electron beams and to develop technological applications in electron microscopy that offer new and improved measurement techniques and increased resolution in different imaging modes. In this Perspective, we review recent applications of sculpted thin films for electron orbital angular momentum sorting, improvements in phase contrast transmission electron microscopy, and aberration correction. For the latter, we also present new results of our work toward correction of the spherical aberration of Lorentz scanning transmission electron microscopes and suggest a method to correct chromatic aberration using thin films. This review provides practical insight for researchers in the field and motivates future progress in electron microscopy.
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Affiliation(s)
- Dolev Roitman
- School
of Electrical Engineering, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
| | - Roy Shiloh
- Physics
Department, Friedrich-Alexander-Universität
Erlangen-Nürnberg, Erlangen 91058, Germany
| | - Peng-Han Lu
- Ernst
Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter
Grünberg Institute, Forschungszentrum
Jülich, Jülich 52428, Germany
- RWTH
Aachen University, Aachen 52062, Germany
| | - Rafal E. Dunin-Borkowski
- Ernst
Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter
Grünberg Institute, Forschungszentrum
Jülich, Jülich 52428, Germany
| | - Ady Arie
- School
of Electrical Engineering, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
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7
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Schachinger T, Hartel P, Lu PH, Löffler S, Obermair M, Dries M, Gerthsen D, Dunin-Borkowski RE, Schattschneider P. Experimental realization of a π/2 vortex mode converter for electrons using a spherical aberration corrector. Ultramicroscopy 2021; 229:113340. [PMID: 34311124 DOI: 10.1016/j.ultramic.2021.113340] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Revised: 05/18/2021] [Accepted: 06/10/2021] [Indexed: 10/21/2022]
Abstract
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.
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Affiliation(s)
- T Schachinger
- Institute of Solid State Physics, TU Wien, Wiedner Hauptstraße 8-10, 1040 Wien, Austria; University Service Centre for Transmission Electron Microscopy (USTEM), TU Wien, Wiedner Hauptstraße 8-10, 1040 Wien, Austria.
| | - P Hartel
- CEOS Corrected Electron Optical Systems GmbH, Englerstraße 28, 69126 Heidelberg, Germany
| | - P-H Lu
- Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons (ER-C) and Peter Grünberg Institute, Forschungszentrum Jülich, 52425 Jülich, Germany; RWTH Aachen University, Ahornstraße 55, 52074 Aachen, Germany
| | - S Löffler
- University Service Centre for Transmission Electron Microscopy (USTEM), TU Wien, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
| | - M Obermair
- Laboratorium für Elektronenmikroskopie (LEM), Karlsruher Institut für Technologie (KIT), Engesserstraße 7, 76131 Karlsruhe, Germany
| | - M Dries
- Laboratorium für Elektronenmikroskopie (LEM), Karlsruher Institut für Technologie (KIT), Engesserstraße 7, 76131 Karlsruhe, Germany
| | - D Gerthsen
- Laboratorium für Elektronenmikroskopie (LEM), Karlsruher Institut für Technologie (KIT), Engesserstraße 7, 76131 Karlsruhe, Germany
| | - R E Dunin-Borkowski
- Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons (ER-C) and Peter Grünberg Institute, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - P Schattschneider
- Institute of Solid State Physics, TU Wien, Wiedner Hauptstraße 8-10, 1040 Wien, Austria; University Service Centre for Transmission Electron Microscopy (USTEM), TU Wien, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
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8
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Pozzi G, Rosi P, Tavabi AH, Karimi E, Dunin-Borkowski RE, Grillo V. A sorter for electrons based on magnetic elements. Ultramicroscopy 2021; 231:113287. [PMID: 33926773 DOI: 10.1016/j.ultramic.2021.113287] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2020] [Revised: 04/01/2021] [Accepted: 04/10/2021] [Indexed: 10/21/2022]
Abstract
The orbital angular momentum (OAM) sorter is an electron optical device for the measurement of an electron's OAM. It is based on two phase elements, which are referred to as an "unwrapper" and a "corrector" and are located in Fourier conjugate planes. The simplest implementation of the sorter is based on electrostatic phase elements, such as a charged needle for the unwrapper and electrodes with alternating charges or potentials for the corrector. Here, we use a formal analogy between phase shifts introduced by charges and vertical currents to propose alternative designs for the sorter elements, which are based on phase shifts introduced by magnetic fields. We use this concept to provide a general guide for phase element design, which promises to provide improved reliability of phase control in electron optics.
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Affiliation(s)
- Giulio Pozzi
- Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, 52425 Jülich, Germany; Department of Physics and Astronomy, University of Bologna, viale B. Pichat 6/2, 40127 Bologna, Italy
| | - Paolo Rosi
- Department FIM, University of Modena and Reggio Emilia, via G. Campi 213/a, 41125 Modena, Italy
| | - Amir H Tavabi
- Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, 52425 Jülich, Germany.
| | - Ebrahim Karimi
- Department of Physics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - Rafal E Dunin-Borkowski
- Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Vincenzo Grillo
- Department FIM, University of Modena and Reggio Emilia, via G. Campi 213/a, 41125 Modena, Italy; CNR-Institute of Nanoscience-S3, via G. Campi 213/a, 41125 Modena, Italy.
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9
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Konečná A, de Abajo FJG. Electron Beam Aberration Correction Using Optical Near Fields. PHYSICAL REVIEW LETTERS 2020; 125:030801. [PMID: 32745398 DOI: 10.1103/physrevlett.125.030801] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2020] [Accepted: 07/01/2020] [Indexed: 05/21/2023]
Abstract
The interaction between free electrons and optical near fields is attracting increasing attention as a way to manipulate the electron wave function in space, time, and energy. Relying on currently attainable experimental capabilities, we design optical near-field plates to imprint a lateral phase on the electron wave function that can largely correct spherical aberration without the involvement of electric or magnetic lenses in the electron optics, and further generate on-demand lateral focal spot profiles. Our work introduces a disruptive and powerful approach toward aberration correction based on light-electron interactions that could lead to compact and versatile time-resolved free-electron microscopy and spectroscopy.
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Affiliation(s)
- Andrea Konečná
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - F Javier García de Abajo
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys 23, 08010 Barcelona, Spain
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10
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Kramberger C, Löffler S, Schachinger T, Hartel P, Zach J, Schattschneider P. π/2 mode converters and vortex generators for electrons. Ultramicroscopy 2019; 204:27-33. [PMID: 31125763 DOI: 10.1016/j.ultramic.2019.05.003] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2018] [Revised: 05/07/2019] [Accepted: 05/12/2019] [Indexed: 10/26/2022]
Abstract
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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Affiliation(s)
- C Kramberger
- Institute of Solid State Physics, TU Wien, Wiedner Hauptstraße 8-10/E138, Wien 1040, Austria.
| | - S Löffler
- Institute of Solid State Physics, TU Wien, Wiedner Hauptstraße 8-10/E138, Wien 1040, Austria; University Service Center for Transmission Electron Microscopy, TU Wien, Wiedner Hauptstraße 8-10/E057-02, Wien 1040, Austria
| | - T Schachinger
- University Service Center for Transmission Electron Microscopy, TU Wien, Wiedner Hauptstraße 8-10/E057-02, Wien 1040, Austria
| | - P Hartel
- CEOS Corrected Electron Optical Systems GmbH, Englerstraße 28, Heidelberg 69126, Germany
| | - J Zach
- CEOS Corrected Electron Optical Systems GmbH, Englerstraße 28, Heidelberg 69126, Germany
| | - P Schattschneider
- Institute of Solid State Physics, TU Wien, Wiedner Hauptstraße 8-10/E138, Wien 1040, Austria; University Service Center for Transmission Electron Microscopy, TU Wien, Wiedner Hauptstraße 8-10/E057-02, Wien 1040, Austria.
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11
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Uesugi Y, Fukushima R, Saitoh K, Sato S. Creating electron phase holograms using femtosecond laser interference processing. OPTICS EXPRESS 2019; 27:20958-20964. [PMID: 31510182 DOI: 10.1364/oe.27.020958] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2019] [Accepted: 06/16/2019] [Indexed: 06/10/2023]
Abstract
Recently, electron beams with structured phase fronts, such as electron vortex beams, have attracted considerable interest. Herein, we present a novel method of fabricating electron phase holograms using a femtosecond laser interference processing. A 35-nm-thick silicon membrane, corresponding to a phase shift of π for 200-keV electrons, was processed using single-shot laser irradiation, whereas processing such thin membranes with a focused ion beam milling technique would be very difficult. This rapid and efficient technique is expected to produce phase diffraction elements for practical applications in a wide range of electron optics fields.
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12
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Grillo V, Tavabi AH, Venturi F, Larocque H, Balboni R, Gazzadi GC, Frabboni S, Lu PH, Mafakheri E, Bouchard F, Dunin-Borkowski RE, Boyd RW, Lavery MPJ, Padgett MJ, Karimi E. Measuring the orbital angular momentum spectrum of an electron beam. Nat Commun 2017; 8:15536. [PMID: 28537248 PMCID: PMC5458084 DOI: 10.1038/ncomms15536] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2016] [Accepted: 04/06/2017] [Indexed: 11/25/2022] Open
Abstract
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. Existing methods of characterizing electron beams carrying orbital angular momentum are inefficient as they allow measuring one OAM state at a time. Here the authors demonstrate an OAM spectrometer capable of analysing multiple OAM states and a potential tool for probing magnetic materials.
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Affiliation(s)
- Vincenzo Grillo
- CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena, Italy.,CNR-IMEM Parco Area delle Scienze 37/A, I-43124 Parma, Italy
| | - Amir H Tavabi
- Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Federico Venturi
- CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena, Italy.,Dipartimento FIM Universitá di Modenae Reggio Emilia, Via G Campi 213/a, I-41125 Modena, Italy
| | - Hugo Larocque
- Department of Physics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario, Canada K1N 6N5
| | | | - Gian Carlo Gazzadi
- CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena, Italy
| | - Stefano Frabboni
- CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena, Italy.,Dipartimento FIM Universitá di Modenae Reggio Emilia, Via G Campi 213/a, I-41125 Modena, Italy
| | - Peng-Han Lu
- Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Erfan Mafakheri
- Dipartimento FIM Universitá di Modenae Reggio Emilia, Via G Campi 213/a, I-41125 Modena, Italy
| | - Frédéric Bouchard
- Department of Physics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario, Canada K1N 6N5
| | - Rafal E Dunin-Borkowski
- Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Robert W Boyd
- Department of Physics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario, Canada K1N 6N5.,Institute of Optics, University of Rochester, Rochester, New York 14627, USA
| | - Martin P J Lavery
- School of Physics and Astronomy, Glasgow University, Glasgow, G12 8QQ Scotland, UK
| | - Miles J Padgett
- School of Physics and Astronomy, Glasgow University, Glasgow, G12 8QQ Scotland, UK
| | - Ebrahim Karimi
- Department of Physics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario, Canada K1N 6N5.,Department of Physics, Institute for Advanced Studies in Basic Sciences, 45137-66731 Zanjan, Iran
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13
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Guzzinati G, Béché A, Lourenço-Martins H, Martin J, Kociak M, Verbeeck J. Probing the symmetry of the potential of localized surface plasmon resonances with phase-shaped electron beams. Nat Commun 2017; 8:14999. [PMID: 28401942 PMCID: PMC5394338 DOI: 10.1038/ncomms14999] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2016] [Accepted: 02/16/2017] [Indexed: 11/17/2022] Open
Abstract
Plasmonics, the science and technology of the interaction of light with metallic objects, is fundamentally changing the way we can detect, generate and manipulate light. Although the field is progressing swiftly, thanks to the availability of nanoscale manufacturing and analysis methods, fundamental properties such as the plasmonic excitations' symmetries cannot be accessed directly, leading to a partial, sometimes incorrect, understanding of their properties. Here we overcome this limitation by deliberately shaping the wave function of an electron beam to match a plasmonic excitations' symmetry in a modified transmission electron microscope. We show experimentally and theoretically that this offers selective detection of specific plasmon modes within metallic nanoparticles, while excluding modes with other symmetries. This method resembles the widespread use of polarized light for the selective excitation of plasmon modes with the advantage of locally probing the response of individual plasmonic objects and a far wider range of symmetry selection criteria.
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Affiliation(s)
- Giulio Guzzinati
- EMAT, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium
| | - Armand Béché
- EMAT, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium
| | - Hugo Lourenço-Martins
- Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS UMR 8502, F-91405 Orsay, France
| | - Jérôme Martin
- Institut Charles Delaunay—Laboratoire de nanotechnologies et d'instrumentation optique, UMR CNRS 6281, Université de Technologie de Troyes, 10010 Troyes, France
| | - Mathieu Kociak
- Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS UMR 8502, F-91405 Orsay, France
| | - Jo Verbeeck
- EMAT, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium
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14
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Barnett SM. Relativistic Electron Vortices. PHYSICAL REVIEW LETTERS 2017; 118:114802. [PMID: 28368643 DOI: 10.1103/physrevlett.118.114802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2016] [Indexed: 06/07/2023]
Abstract
The desire to push recent experiments on electron vortices to higher energies leads to some theoretical difficulties. In particular the simple and very successful picture of phase vortices of vortex charge ℓ associated with ℓℏ units of orbital angular momentum per electron is challenged by the facts that (i) the spin and orbital angular momentum are not separately conserved for a Dirac electron, which suggests that the existence of a spin-orbit coupling will complicate matters, and (ii) that the velocity of a Dirac electron is not simply the gradient of a phase as it is in the Schrödinger theory suggesting that, perhaps, electron vortices might not exist at a fundamental level. We resolve these difficulties by showing that electron vortices do indeed exist in the relativistic theory and show that the charge of such a vortex is simply related to a conserved orbital part of the total angular momentum, closely related to the familiar situation for the orbital angular momentum of a photon.
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Affiliation(s)
- Stephen M Barnett
- School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
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15
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McMorran BJ, Agrawal A, Ercius PA, Grillo V, Herzing AA, Harvey TR, Linck M, Pierce JS. Origins and demonstrations of electrons with orbital angular momentum. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:rsta.2015.0434. [PMID: 28069765 PMCID: PMC5247478 DOI: 10.1098/rsta.2015.0434] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 10/28/2016] [Indexed: 05/14/2023]
Abstract
The surprising message of Allen et al. (Allen et al. 1992 Phys. Rev. A 45, 8185 (doi:10.1103/PhysRevA.45.8185)) was that photons could possess orbital angular momentum in free space, which subsequently launched advancements in optical manipulation, microscopy, quantum optics, communications, many more fields. It has recently been shown that this result also applies to quantum mechanical wave functions describing massive particles (matter waves). This article discusses how electron wave functions can be imprinted with quantized phase vortices in analogous ways to twisted light, demonstrating that charged particles with non-zero rest mass can possess orbital angular momentum in free space. With Allen et al. as a bridge, connections are made between this recent work in electron vortex wave functions and much earlier works, extending a 175 year old tradition in matter wave vortices.This article is part of the themed issue 'Optical orbital angular momentum'.
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Affiliation(s)
| | - Amit Agrawal
- Center for Nanoscale Science and Technology, National Institute of Standards Technology, Gaithersburg, MD 20899, USA
- Maryland NanoCenter, University of Maryland, College Park, MD 20742, USA
| | - Peter A Ercius
- National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA
| | - Vincenzo Grillo
- Department of Physics, University of Oregon, Eugene, OR, USA
- CNR-Istituto Nanoscienze, Centro S3, Via G. Campi 213/a, 41125 Modena, Italy
| | - Andrew A Herzing
- Materials Measurement Laboratory, National Institute of Standards Technology, Gaithersburg, MD 20899, USA
| | - Tyler R Harvey
- Department of Physics, University of Oregon, Eugene, OR, USA
| | - Martin Linck
- Corrected Electron Optical Systems GmbH, Englerstraße 28, 69126 Heidelberg, Germany
| | - Jordan S Pierce
- Department of Physics, University of Oregon, Eugene, OR, USA
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16
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Grillo V, Harris J, Gazzadi GC, Balboni R, Mafakheri E, Dennis MR, Frabboni S, Boyd RW, Karimi E. Generation and application of bessel beams in electron microscopy. Ultramicroscopy 2016; 166:48-60. [PMID: 27203186 DOI: 10.1016/j.ultramic.2016.03.009] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2015] [Revised: 03/15/2016] [Accepted: 03/23/2016] [Indexed: 10/22/2022]
Abstract
We report a systematic treatment of the holographic generation of electron Bessel beams, with a view to applications in electron microscopy. We describe in detail the theory underlying hologram patterning, as well as the actual electron-optical configuration used experimentally. We show that by optimizing our nanofabrication recipe, electron Bessel beams can be generated with relative efficiencies reaching 37±3%. We also demonstrate by tuning various hologram parameters that electron Bessel beams can be produced with many visible rings, making them ideal for interferometric applications, or in more highly localized forms with fewer rings, more suitable for imaging. We describe the settings required to tune beam localization in this way, and explore beam and hologram configurations that allow the convergences and topological charges of electron Bessel beams to be controlled. We also characterize the phase structure of the Bessel beams generated with our technique, using a simulation procedure that accounts for imperfections in the hologram manufacturing process.
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Affiliation(s)
- Vincenzo Grillo
- CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena, Italy; CNR-IMEM, Parco Area delle Scienze 37/A, I-43124 Parma, Italy.
| | - Jérémie Harris
- Department of Physics, University of Ottawa, 25 Templeton St., Ottawa, Ontario, Canada K1N 6N5
| | - Gian Carlo Gazzadi
- CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena, Italy
| | | | - Erfan Mafakheri
- Dipartimento di Fisica Informatica e Matematica, Università di Modena e Reggio Emilia, via G Campi 213/a, I-41125 Modena, Italy
| | - Mark R Dennis
- H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - Stefano Frabboni
- CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena, Italy; Dipartimento di Fisica Informatica e Matematica, Università di Modena e Reggio Emilia, via G Campi 213/a, I-41125 Modena, Italy
| | - Robert W Boyd
- Department of Physics, University of Ottawa, 25 Templeton St., Ottawa, Ontario, Canada K1N 6N5
| | - Ebrahim Karimi
- Department of Physics, University of Ottawa, 25 Templeton St., Ottawa, Ontario, Canada K1N 6N5
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17
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Béché A, Winkler R, Plank H, Hofer F, Verbeeck J. Focused electron beam induced deposition as a tool to create electron vortices. Micron 2015; 80:34-8. [PMID: 26432987 DOI: 10.1016/j.micron.2015.07.011] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2015] [Revised: 07/24/2015] [Accepted: 07/25/2015] [Indexed: 11/18/2022]
Abstract
Focused electron beam induced deposition (FEBID) is a microscopic technique that allows geometrically controlled material deposition with very high spatial resolution. This technique was used to create a spiral aperture capable of generating electron vortex beams in a transmission electron microscope (TEM). The vortex was then fully characterized using different TEM techniques, estimating the average orbital angular momentum to be ∼0.8ℏ per electron with almost 60% of the beam ending up in the ℓ=1 state.
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Affiliation(s)
- A Béché
- EMAT, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium.
| | - R Winkler
- Graz Centre for Electron Microscopy, Steyrergasse 17, 8010 Graz, Austria
| | - H Plank
- Graz Centre for Electron Microscopy, Steyrergasse 17, 8010 Graz, Austria; Institute for Electron Microscopy and Nanoanalysis, Graz University of Technology, Steyrergasse 17, A-8010 Graz, Austria
| | - F Hofer
- Institute for Electron Microscopy and Nanoanalysis, Graz University of Technology, Steyrergasse 17, A-8010 Graz, Austria
| | - J Verbeeck
- EMAT, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium
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18
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Schachinger T, Löffler S, Stöger-Pollach M, Schattschneider P. Peculiar rotation of electron vortex beams. Ultramicroscopy 2015; 158:17-25. [PMID: 26103046 DOI: 10.1016/j.ultramic.2015.06.004] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2015] [Revised: 05/28/2015] [Accepted: 06/04/2015] [Indexed: 11/29/2022]
Abstract
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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Affiliation(s)
- T Schachinger
- Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria; University Service Centre for Transmission Electron Microscopy, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Wien, Austria.
| | - S Löffler
- Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria; University Service Centre for Transmission Electron Microscopy, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
| | - M Stöger-Pollach
- University Service Centre for Transmission Electron Microscopy, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
| | - P Schattschneider
- Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria; LMSSMat (CNRS UMR 8579) Ecole Centrale Paris, F-92295 Châtenay-Malabry, France
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19
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Shiloh R, Tsur Y, Remez R, Lereah Y, Malomed BA, Shvedov V, Hnatovsky C, Krolikowski W, Arie A. Unveiling the orbital angular momentum and acceleration of electron beams. PHYSICAL REVIEW LETTERS 2015; 114:096102. [PMID: 25793830 DOI: 10.1103/physrevlett.114.096102] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2013] [Indexed: 05/21/2023]
Abstract
New forms of electron beams have been intensively investigated recently, including vortex beams carrying orbital angular momentum, as well as Airy beams propagating along a parabolic trajectory. Their traits may be harnessed for applications in materials science, electron microscopy, and interferometry, and so it is important to measure their properties with ease. Here, we show how one may immediately quantify these beams' parameters without need for additional fabrication or nonstandard microscopic tools. Our experimental results are backed by numerical simulations and analytic derivation.
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Affiliation(s)
- Roy Shiloh
- Department of Physical Electronics, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Yuval Tsur
- Department of Physical Electronics, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Roei Remez
- Department of Physical Electronics, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Yossi Lereah
- Department of Physical Electronics, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Boris A Malomed
- Department of Physical Electronics, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Vladlen Shvedov
- Laser Physics Centre, The Australian National University, Canberra ACT 0200, Australia
| | - Cyril Hnatovsky
- Laser Physics Centre, The Australian National University, Canberra ACT 0200, Australia
| | - Wieslaw Krolikowski
- Laser Physics Centre, The Australian National University, Canberra ACT 0200, Australia
| | - Ady Arie
- Department of Physical Electronics, Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv 6997801, Israel
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20
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Grillo V, Gazzadi GC, Mafakheri E, Frabboni S, Karimi E, Boyd RW. Holographic generation of highly twisted electron beams. PHYSICAL REVIEW LETTERS 2015; 114:034801. [PMID: 25659003 DOI: 10.1103/physrevlett.114.034801] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2014] [Indexed: 05/21/2023]
Abstract
Free electrons can possess an intrinsic orbital angular momentum, similar to those in an electron cloud, upon free-space propagation. The wave front corresponding to the electron's wave function forms a helical structure with a number of twists given by the 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 conventional electron beam into a helical form with large values of angular momentum. Here, we propose and manufacture a nanofabricated phase hologram for generating a beam of this kind with an orbital angular momentum up to 200ℏ. Based on a novel technique the value of orbital angular momentum of the generated beam is measured and 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 nanoparticles.
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Affiliation(s)
- Vincenzo Grillo
- CNR-Istituto Nanoscienze, Centro S3, Via G. Campi 213/a, I-41125 Modena, Italy and CNR-IMEM Parco Area delle Scienze 37/A, I-43124 Parma, Italy
| | - Gian Carlo Gazzadi
- CNR-Istituto Nanoscienze, Centro S3, Via G. Campi 213/a, I-41125 Modena, Italy
| | - Erfan Mafakheri
- CNR-Istituto Nanoscienze, Centro S3, Via G. Campi 213/a, I-41125 Modena, Italy and Dipartimento FIM, Universitá di Modena e Reggio Emilia, Via G. Campi 213/a, I-41125 Modena, Italy
| | - Stefano Frabboni
- CNR-Istituto Nanoscienze, Centro S3, Via G. Campi 213/a, I-41125 Modena, Italy and Dipartimento FIM, Universitá di Modena e Reggio Emilia, Via G. Campi 213/a, I-41125 Modena, Italy
| | - Ebrahim Karimi
- Department of Physics, University of Ottawa, 25 Templeton, Ottawa, Ontario, K1N 6N5 Canada
| | - Robert W Boyd
- Department of Physics, University of Ottawa, 25 Templeton, Ottawa, Ontario, K1N 6N5 Canada and Institute of Optics, University of Rochester, Rochester, New York 14627, USA
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21
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Rusz J, Idrobo JC, Bhowmick S. Achieving atomic resolution magnetic dichroism by controlling the phase symmetry of an electron probe. PHYSICAL REVIEW LETTERS 2014; 113:145501. [PMID: 25325649 DOI: 10.1103/physrevlett.113.145501] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Indexed: 06/04/2023]
Abstract
The calculations presented here reveal that an electron probe carrying orbital angular momentum is just a particular case of a wider class of electron beams that can be used to measure electron magnetic circular dichroism (EMCD) with atomic resolution. It is possible to obtain an EMCD signal with atomic resolution by simply breaking the symmetry of the electron probe phase distribution using the aberration-corrected optics of a scanning transmission electron microscope. The required phase distribution of the probe depends on the magnetic symmetry and crystal structure of the sample. The calculations indicate that EMCD signals utilizing the phase of the electron probe are as strong as those obtained by nanodiffraction methods.
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Affiliation(s)
- Ján Rusz
- Department of Physics and Astronomy, Uppsala University, P.O. Box 516, 75120 Uppsala, Sweden
| | - Juan-Carlos Idrobo
- Center of Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Somnath Bhowmick
- Department of Materials Science and Engineering, Indian Institute of Technology, Kanpur 208016, India
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22
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Imaging the dynamics of free-electron Landau states. Nat Commun 2014; 5:4586. [PMID: 25105563 PMCID: PMC4143940 DOI: 10.1038/ncomms5586] [Citation(s) in RCA: 70] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2014] [Accepted: 07/03/2014] [Indexed: 11/27/2022] Open
Abstract
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. Landau states are associated with the quantised orbits of charged particles in magnetic fields. By manipulating electron vortex beams in a magnetic field, this study reconstructs the internal quantum dynamics of free-electron Landau states, which differs strongly from the classical cyclotron rotation.
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23
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Schattschneider P, Löffler S, Stöger-Pollach M, Verbeeck J. Is magnetic chiral dichroism feasible with electron vortices? Ultramicroscopy 2014; 136:81-5. [PMID: 24012939 PMCID: PMC3866682 DOI: 10.1016/j.ultramic.2013.07.012] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2013] [Revised: 07/15/2013] [Accepted: 07/19/2013] [Indexed: 11/02/2022]
Abstract
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 ∼1 nm. This is confirmed by a key experiment with nanometer-sized vortices.
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Affiliation(s)
- P Schattschneider
- Institut für Festkörperphysik, Technische Universität Wien, A-1040 Wien, Austria.
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24
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Creating arrays of electron vortices. Ultramicroscopy 2014; 136:165-70. [DOI: 10.1016/j.ultramic.2013.10.002] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2013] [Revised: 09/24/2013] [Accepted: 10/08/2013] [Indexed: 11/21/2022]
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25
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Rusz J, Bhowmick S. Boundaries for efficient use of electron vortex beams to measure magnetic properties. PHYSICAL REVIEW LETTERS 2013; 111:105504. [PMID: 25166681 DOI: 10.1103/physrevlett.111.105504] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2013] [Indexed: 05/14/2023]
Abstract
Development of experimental techniques for characterization of magnetic properties at high spatial resolution is essential for progress in miniaturization of magnetic devices, for example, in data storage media. Inelastic scattering of electron vortex beams (EVBs) was recently reported to contain atom-specific magnetic information. We develop a theoretical description of inelastic scattering of EVBs on crystals and perform simulations for EVBs of different diameters. We show that use of an EVB wider than an interatomic distance does not provide any advantage over an ordinary convergent beam without angular momentum. On the other hand, in the atomic-resolution limit, electron energy loss spectra measured by EVBs are strongly sensitive to the spin and orbital magnetic moments of studied matter, when channeling through or very close to the atomic columns. Our results demonstrate the boundaries for efficient use of EVBs in measurement of magnetic properties.
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Affiliation(s)
- Ján Rusz
- Department of Physics and Astronomy, Uppsala University, Post Office Box 516, 75120 Uppsala, Sweden and Institute of Physics, Czech Academy of Sciences, Na Slovance 2, 182 21 Prague, Czech Republic
| | - Somnath Bhowmick
- Department of Physics and Astronomy, Uppsala University, Post Office Box 516, 75120 Uppsala, Sweden and Department of Materials Science and Engineering, Indian Institute of Technology, Kanpur 208016, India
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26
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Clark L, Béché A, Guzzinati G, Lubk A, Mazilu M, Van Boxem R, Verbeeck J. Exploiting lens aberrations to create electron-vortex beams. PHYSICAL REVIEW LETTERS 2013; 111:064801. [PMID: 23971578 DOI: 10.1103/physrevlett.111.064801] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2013] [Indexed: 05/21/2023]
Abstract
A model for a new electron-vortex beam production method is proposed and experimentally demonstrated. The technique calls on the controlled manipulation of the degrees of freedom of the lens aberrations to achieve a helical phase front. These degrees of freedom are accessible by using the corrector lenses of a transmission electron microscope. The vortex beam is produced through a particular alignment of these lenses into a specifically designed astigmatic state and applying an annular aperture in the condenser plane. Experimental results are found to be in good agreement with simulations.
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Affiliation(s)
- L Clark
- EMAT, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium.
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27
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Chu MW, Chen CH. Chemical mapping and quantification at the atomic scale by scanning transmission electron microscopy. ACS NANO 2013; 7:4700-4707. [PMID: 23799301 DOI: 10.1021/nn4023558] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
With innovative modern material-growth methods, a broad spectrum of fascinating materials with reduced dimensions-ranging from single-atom catalysts, nanoplasmonic and nanophotonic materials to two-dimensional heterostructural interfaces-is continually emerging and extending the new frontiers of materials research. A persistent central challenge in this grand scientific context has been the detailed characterization of the individual objects in these materials with the highest spatial resolution, a problem prompting the need for experimental techniques that integrate both microscopic and spectroscopic capabilities. To date, several representative microscopy-spectroscopy combinations have become available, such as scanning tunneling microscopy, tip-enhanced scanning optical microscopy, atom probe tomography, scanning transmission X-ray microscopy, and scanning transmission electron microscopy (STEM). Among these tools, STEM boasts unique chemical and electronic sensitivity at unparalleled resolution. In this Perspective, we elucidate the advances in STEM and chemical mapping applications at the atomic scale by energy-dispersive X-ray spectroscopy and electron energy loss spectroscopy with a focus on the ultimate challenge of chemical quantification with atomic accuracy.
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Affiliation(s)
- Ming-Wen Chu
- Center for Condensed Matter Sciences, National Taiwan University, Taipei 106, Taiwan.
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28
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Guzzinati G, Schattschneider P, Bliokh KY, Nori F, Verbeeck J. Observation of the Larmor and Gouy rotations with electron vortex beams. PHYSICAL REVIEW LETTERS 2013; 110:093601. [PMID: 23496708 DOI: 10.1103/physrevlett.110.093601] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2012] [Indexed: 05/14/2023]
Abstract
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.
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Affiliation(s)
- Giulio Guzzinati
- EMAT, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium
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29
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Electron Tweezers as a Tool for High-Precision Manipulation of Nanoobjects. ADVANCES IN IMAGING AND ELECTRON PHYSICS 2013. [DOI: 10.1016/b978-0-12-407700-3.00003-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
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