Magnetic monopole field exposed by electrons

The experimental search for magnetic monopole particles1–3 has, so far, been in vain. Nevertheless, these elusive particles of magnetic charge have fuelled a rich field of theoretical study4–10. Here, we created an approximation of a magnetic monopole in free space at the end of a long, nanoscopically thin magnetic needle11. We experimentally demonstrate that the interaction of this approximate magnetic monopole field with a beam of electrons produces an electron vortex state, as theoretically predicted for a true magnetic monopole3,11–18. This fundamental quantum mechanical scattering experiment is independent of the speed of the electrons and has consequences for all situations where electrons meet such monopole magnetic fields, as, for example, in solids. The set-up not only shows an attractive way to produce electron vortex states but also provides a unique insight into monopole fields and shows that electron vortices might well occur in unexplored solid-state physics situations. Magnetic monopoles have provided a rich field of study, leading to a wide area of research in particle physics4–6, solidstate physics7, ultra-cold gases8, superconductors9, cosmology4 and gauge theory10. As electric charges can be seen as monopole sources and sinks of electric field lines, the strong symmetry with magnetic and electrical fields for example in the free-space Maxwell equations19–21 hints at the possible existence of magnetic monopoles as well. So far, the search for such magnetic monopoles has been unsuccessful. However, an effective monopole field can be produced at the tip of a nanoscopic magnetized ferromagnetic needle11,17. The Aharanov–Bohm effect12 can be used to understand the effects of such a monopole field on its surroundings, which is crucial to its observation and provides a better grasp of fundamental physical theory. Previous studies have been limited to theoretical semiclassical optical calculations of the motion of electrons in such a monopole field13. Solid-state systems such as the recently studied ‘spin ice’ provide a constrained system to study similar fields, but make it impossible to separate the monopole from the material7. Here, we realize the diffraction of fast electrons on the magnetic monopole field generated by the extremity of a long magnetic needle. Free-space propagation of the electrons helps in the understanding of the dynamics of the electron–monopole system without the complexity of a solid-state system and will allow various areas of physics to use the effects of monopole fields. Various predictions about angular momentum, paths of travel and general field effects can readily be studied using the available equipment. The experiment performed here shows that even without a true magnetic monopole particle, the theoretical background onmonopoles serves as a basis for experiments. Indeed, it has been predicted that when a plane electron wave interacts with a hypothetical magnetic monopole, a vortex electron state Ψout would arise3,11–18: