Historical research guide · 0737 · 2010

Production and application of electron vortex beams

J. Verbeeck · H. Tian · P. Schattschneider

In one minute

Shine a laser through the right piece of glass and the wavefront stops being flat and starts spiralling, like the thread of a screw. A beam shaped that way carries angular momentum about its own direction of travel, and optical tweezers have used it for years to spin particles. Jo Verbeeck, He Tian and Peter Schattschneider did the same thing to electrons. Their method is a hologram: a tiny fork-shaped grating machined into a film, placed in the beam of an ordinary transmission electron microscope, which diffracts the electron wave into beams whose phase winds once around the axis in one direction, once in the other, and not at all. That is a reproducible way to make twisted electrons on any conventional microscope, not a one-off. Then they used them: because a twisted electron carries orbital angular momentum, and therefore a magnetic moment, its energy-loss spectrum can read out the magnetic state of the material it passes through.

Connection

Chapter 10 is about what the phase of a field can do on its own, with no extra energy and no force in the classical sense — the Aharonov-Bohm line of thought. This is that idea made into an instrument: the phase structure of an electron beam, and nothing else, carries angular momentum and reads magnetism. Chapter 5 treats the vacuum as a quantum fluid, and quantised circulation around a phase singularity is exactly the signature such a fluid is defined by.

From the source

Vortex beams — beams with a phase singularity — consist of spiralling wavefronts that give rise to angular momentum around the propagation direction. Photon vortex beams are already in wide use in optical tweezers to manipulate micrometre-sized particles, in micro-motors to supply angular momentum, and to increase channel capacity in optical and radio-wave information transfer.Abstract, sentences 1 and 2
The paper creates vortex electron beams using a versatile holographic reconstruction technique in a transmission electron microscope, and the authors’ own emphasis is on reproducibility: this is a repeatable method of creating vortex electron beams in a conventional electron microscope, rather than a single realisation.Abstract, sentences 4 and 5
The beams are then used, not merely made. The authors demonstrate their use in electron energy-loss spectroscopy to detect the magnetic state of materials, and describe the beams’ properties — so the twisted electron becomes a magnetic probe inside an instrument that is already in thousands of laboratories.Abstract, sentence 6
Context, from the collaboration’s immediate follow-up rather than from this paper: the holographic mask is a circular aperture carrying a fork-shaped grating, and the exit wave splits into three orders — topological charge minus one, zero and plus one. Unlike an optical vortex, an electron vortex carries a magnetic moment even when the beam is not spin-polarised, and that is what makes it a probe of magnetic transitions in the ferromagnetic 3d metals.Schattschneider, Stöger-Pollach, Löffler, Steiger-Thirsfeld, Hell and Verbeeck, arXiv 1106.1726, introduction and Equations 1 and 2
Context on scale, from the same follow-up: the first holographic-mask vortices were several micrometres across, and a changed scattering geometry then produced a series of well separated electron vortices with a beam waist of about 0.2 nanometres — free electrons carrying topological charge, focused below the nanometre range.Schattschneider et al., arXiv 1106.1726, introduction, paragraph 4
What to watch: the application the authors name for the technique is analysing and manipulating nanomaterials — transferring quantised angular momentum from a beam to individual particles, clusters and molecules. Quantised circulation about a phase singularity is the defining excitation of a quantum fluid, and here it is produced on demand in free space with a diffraction grating; how far that control extends is the open question.Abstract, final sentence

The way in

https://doi.org/10.1038/nature09366

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

SOURCE NOT REACHED IN FULL. Published as Nature 467, issue 7313, pages 301 to 304, 16 September 2010, under the Nature journal licence; the only licence Crossref carries for it is Springer’s text-and-data-mining licence, which is not a Creative Commons licence, so no text of the paper is reproduced here. OpenAlex, Unpaywall and Semantic Scholar all report the article closed with no repository copy, and there is no arXiv preprint of it: the arXiv author search for Verbeeck with vortex in the abstract, run on 2026-09-08, returns the 2011 follow-up and later work but not this paper. The authors’ own abstract was read from the National Library of Medicine record for PubMed 20844532, and the summary and the first three claims are written from it; their locators point to sentences of that abstract. Claims four and five are context and are labelled as such: they come from the immediate follow-up by the same collaboration, Schattschneider, Stöger-Pollach, Löffler, Steiger-Thirsfeld, Hell and Verbeeck, ’Sub-nanometer free electrons with topological charge’, arXiv 1106.1726, which was downloaded and read, and which describes the holographic-mask technique and the scale of these first vortices. Affiliation as printed on the paper: J. Verbeeck at Electron Microscopy for Materials Science (EMAT), University of Antwerp; P. Schattschneider at the Institute of Solid State Physics, Vienna University of Technology.

How to cite it

J. Verbeeck, H. Tian, P. Schattschneider (2010) Production and application of electron vortex beams doi:10.1038/nature09366

Where it sits in the curriculum

Scalar waves and the field behind the fields