Neutrons reveal distribution of flux-tube islands

Neutrons visualize vortex domains in superconductors. Experiments were funded by NMI3.

Source: and

Usually, superconductors expel magnetic fields. In type II superconductors, however, thin channels – so-called flux tubes – are formed. The magnetic field is guided through these tubes while the rest of the material remains field-free and superconducting. In the metal niobium, the flux tubes bunch together into small islands that create complex patterns, which are common to other forms found in nature. A team of researchers from the Paul Scherrer Institute PSI and the Technische Universität München were the first to conduct neutron experiments to study these structures in niobium and determine the distribution of the islands in detail. The researchers hope their experimental approach will help understand the origins of such universal structures better. The results of their study were published in the journal Nature Communications.


PSI researcher Christian Grünzweig mounting the sample for an experiment on flux tubes in the superconducting metal niobium at the ICON measuring station at the Swiss Spallation Neutron Source SINQ. (Photo: Paul Scherrer Institute/Markus Fischer)

Superconductors conduct electrical current without any resistance whatsoever, which makes them promising materials for any applications where electricity needs to be transported over long distances with little loss. Nonetheless, superconductors have other properties that make them exciting objects for basic research. For instance, they expel magnetic fields. A superconductor placed near a magnet, will not be penetrated by the magnetic field. Instead, the magnetic field will be deflected around the superconductor. If the external magnetic field is increased further, the material loses its superconductive properties from a certain value of the magnetic field. In so-called type II superconductors, however, there is a compromise between superconductivity and field expulsion. Thin channels – called flux tubes or vortices – form inside the superconductor, where the magnetic field can flow through the material. Outside the flux tubes, the material remains superconducting.

Flux-tube islands


In the superconductive metal niobium, the flux tubes that form when an external magnetic field is applied do not necessarily fill the sample evenly. At certain temperature and magnetic field values, the flux tubes form “islands”. In the figure, the individual dots represent the flux tubes from above. (Nature Communications, CC BY 4.0)

Researchers from the Paul Scherrer Institute (PSI) and the Technische Universität München (TUM) studied the arrangement and distribution of the flux tubes in the superconductive metal niobium and, for the first time, determined their arrangement and distribution deep inside the superconductor, as opposed to merely on the surface as done previously. In niobium, flux tubes behave in a special way: they are not necessarily evenly distributed in the material, but group together to form complex-shaped islands – called “vortex domains” by experts. Between the islands, there are areas without any flux tubes. This situation is known as an “intermediate mixed state”.

The researchers directly imaged the areas of the niobium sample where the flux-tube islands appear and showed how their structure changes with increasing magnetic field. At PSI’s neutron source SINQ and TUM’s research neutron source FRM-II, they used neutrons as a measuring probe in various experiments. They sent a beam of neutrons through the material and observed how the neutrons were deflected from their path. In the initial experiments, the researchers measured this deflection highly accurately, which enabled them to estimate the size of the islands and determine the arrangement of the flux tubes. The method used is known by the name “small-angle neutron scattering” as the neutrons are only slightly deflected here. However, the scientists were unable to ascertain whether the islands are distributed evenly across the entire material or concentrated in individual areas.

Fine gratings render micrometre structures visible

In order to render the distribution of the flux tubes visible, the researchers from PSI and TUM used a new method based on the principle of neutron grating interferometry. During the experiment, the neutrons are sent through several gratings, for example arrangements of fine strips that are alternately permeable and non-permeable for neutrons. An overlay pattern forms behind the lattices, which alternates between areas with many or few neutrons. By observing how the pattern changes when a sample is placed in the beam, the structures inside the sample can be deduced. “Grating interferometry enables us to study structures with a length-scale of a few micrometres – for example the size of the vortex islands”, explains Christian Grünzweig, who is responsible for the experiment at PSI, where he helped develop the grating interferometry technique. Thanks to this method, it was possible to determine the spatial distribution of the vortex islands, despite the fact that they are smaller than the detector’s individual pixels and therefore cannot normally be rendered visible. Surprisingly, it transpired that the islands initially start to form deep inside the sample, and not at the edges.


The result of the experiment: the sample was exposed to an increasingly strong magnetic field (from left to right) and probed with neutron beams applied parallel to the flux tubes. The light areas represent where the flux tubes appear in islands. If the fields are weaker, the islands fill the interior of the sample while no flux tubes appear at the edge. (Nature Communications, CC BY 4.0)

Islands as a model system

“In niobium, the flux tubes and the islands form typical structures and patterns, which appear in a similar way in many physical and chemical systems on a wide variety of length and time scales”, explains Tommy Reimann, a doctoral student at TUM and first author on the study. “These include magnetic domains, alloys in microstructures or chemical diffusion reactions. By changing the magnetic field or temperature, we can study the origins of such patterns in the ‘model system’ niobium in a unique way and draw very general conclusions about the formation of such patterns.” At the same time, as the authors stress, the experimental approach presented in this project is just the ticket for studying almost any system that develops structures on a micrometre scale.

Additional information

Neutron Imaging and Activation Group at the Paul Scherrer Institute PSI
Heinz Maier-Leibnitz Zentrum in Garching


Dr. Christian Grünzweig, Neutron Imaging and Activation Group,
Paul Scherrer Institute, Switzerland
Telephone: +41 56 310 4662, e-mail:

M.Sc. Tommy Reimann, research neutron source Heinz Maier-Leibnitz, Technische Universität München, Germany
Telephone: +49 89 289 11769, e-mail:

Original Publication

Visualizing the morphology of vortex lattice domains in a bulk type-II superconductor, T. Reimann, S. Mühlbauer, M. Schulz, B. Betz, A. Kaestner, V. Pipich, P. Böni und C. Grünzweig, Nature Communications 2. November 2015, DOI: 10.1038/ncomms9813

T. Reimann from the MLZ in Germany has received NMI3 support to conduct experiments.