“Although it was possible to image the arrangement of magnetic moments in 3D before now in films of up to around 200 nm thick using soft X-rays and electrons, it was not possible to study the internal micromagnetic structure of larger, bulk, systems,” explains team member Claire Donnelly of the PSI. “In general, it is not possible to slice down a magnet to investigate its structure because the magnetic configuration will change accordingly. Scientists have tried to overcome this problem in the past using neutron magnetic imaging, but they were only able to achieve a spatial resolution of tens to hundreds of microns using this approach.

“In our new work, we are able to study the internal magnetization within a micron-sized system with 100 nm spatial resolution and observe micromagnetic details within the bulk for the first time.”

The researchers, led by Laura Heyderman, imaged the internal magnetic structure of a micron-sized pillar made of the magnetic material gadolinium-cobalt using hard X-ray magnetic tomography, a technique developed at PSI during the course of this study. “We had to make a number of advances in developing this method,” explains Donnelly. ‘First, we developed hard X-ray magnetic imaging with nanoscale magnetic resolution (this work was published last year). Hard X-rays have a much higher energy than soft X-rays and thus a much larger penetration depth, which allows us to study thicker samples with high spatial resolution.

“The imaging itself involves using circularly polarized X-rays with which we probe the magnetization of our sample parallel to the X-ray beam,” she adds. These 2D images form the ‘raw data’ in the experiment – that is, 2D projections of the magnetization that we measured at many different angles about a rotation axis (which is similar to what is done in normal tomography). We measured such projections around two tomographic axes to probe all three components of the magnetization.”

The challenges did not end there. The researchers say that they were then faced with the question of how to obtain their 3D magnetic configuration from this 2D data. “Unlike traditional scalar tomography, in which you recover one value for each pixel, here we had to recover three components of the magnetization for each pixel within our tomogram. To do this, we developed our own iterative reconstruction algorithm, which does not assume anything about the magnetic properties or magnetic configuration of a sample. This is in contrast to other algorithms that have been used before in soft X-ray magnetic tomography.”

The team observed a number of magnetic structures, interacting throughout the bulk of the material. “In particular, we saw large domains of uniform magnetization, separated by transition regions, or ‘domain walls’,” explains Donnelly. “These walls contain vortices and, at the intersections of these structures, we observed magnetic singularities known as Bloch points.”

At a Bloch point, the magnetic moments abruptly change their direction, and the usual “continuum” description, of magnetism breaks down. Bloch points in fact comprise monopoles in the magnetization and were first predicted in 1965.

The new work is a step forward in understanding the relationship between the magnetic structure and the behaviour and performance of bulk magnets, says team member Sebastian Gliga.

“The magnetic microstructure plays a fundamental role in the macroscopic properties and the performance of bulk magnets,” explains Donnelly. “For example, the structure and mobility of the domain wall defines the performance of soft magnets with high permeability, essential for inductive applications, such as motors or sensors. We can now measure the detailed structure of these walls and therefore better understand their behaviour. The findings from such measurements could lead to improvements in these magnets’ efficiency.

Towards better magnets

“The magnetic tomography described in the work could also be used to directly study the internal structure of permanent magnets, which are widely employed in motors and energy generation, as well as softer materials, such as the write-heads in your computer hard drive,” she adds.

The researchers, reporting their work in Nature doi:10.1038/nature23006, say that they would now like to make use of the increase in X-ray flux that will come with the next generation of X-ray synchrotron sources to obtain even higher spatial resolution. This will allow them to study even smaller features of the magnetization, below 100 nm in size, and so approach fundamental magnetic length scales. One such length is the “exchange length” of a material, which is around a few nanometres and typically the smallest length at which the magnetization can be inhomogeneous. These studies could be used to determine how physical defects, for example, affect magnetic structure.

“Not only can we use hard X-ray tomography to study magnetic materials for the types of applications mentioned above, it might also be used to study fundamental magnetic structures, like the one we looked at in our present work,” says Donnelly. “Determining how these structures behave, and whether they can be controlled by applying magnetic fields, could help further our understanding of magnetic systems in general.”