Circularly polarized x-rays are sensitive to the local magnetization in a material and in principle images obtained using x-rays can be interpreted to infer the state of the magnetization. In the past, low energy x-rays have been used to investigate the magnetization in thin films. For certain geometries, the three-dimensional (3D) magnetization has also been studied in thicker films (ca. 200 nm thick), where the geometry allows for certain assumptions and/or constraints that simplify the analysis. The problem becomes challenging when one attempts to probe the magnetization in a bulk sample: in order to probe greater depths high-energy (hard) x-rays must be used, which implies a significant loss of contrast.  In a recent issue of Nature, Claire Donnelly and Laura Heyderman of the ETH Zurich, Manuel Guizar-Sicairos of the Paul Scherrer Institute, Sebastian Gliga of the University of Glasgow, and their colleagues report the development of an x-ray tomography technique that can be used to measure the 3D magnetization structure within a bulk sample. According to the researchers, their method makes it possible to study topological magnetic structures at the nanoscale in systems with sizes of the order of 10 µm.

The magnetization structure in a bulk sample is intrinsically 3D and its different components can be probed depending on the relative orientation of the sample and the x-rays. X-ray images were obtained by rotating the sample in small steps with a full 360° revolution around two distinct axes (oriented at 30° with respect to each other). For each angle, the object is scanned across a coherent x-ray beam and the corresponding diffraction patterns are measured in the far field for each scanning position, a technique termed ptychography. By using circularly polarized x-rays, the recorded data is sensitive to the sample magnetization structure. The reconstructed absorption images have both electronic and magnetic contributions. These two-dimensional images are assembled using an in-house developed algorithm to reconstruct the magnetization vector field (see figure). The technique was demonstrated for a gadolinium-cobalt (GdCo₂) 5-μm-diameter pillar to a spatial resolution of about 100 nm (the resolution is presently limited by the available photon flux). The negligible magnetocrystalline anisotropy of polycrystalline GdCo₂ results in a slowly varying magnetization. The researchers could thus probe the magnetization structure of fundamental micromagnetic structures such as domain walls and vortices.

The reconstructed magnetization over a smaller region of the sample is shown in the figure, panel (c). Three-dimensional structures such as a vortex domain wall were identified. At the intersections of the core V_i of the vortex with the core V_d of the vortex wall, the magnetization vanishes in all directions, leading to the formation of singularities in the magnetization, called Bloch points. Given that the singularity itself is a point and cannot be measured, its existence is inferred by studying the nanoscale magnetization structure surrounding it. These experiments are the first known to directly probe the magnetization structure surrounding a Bloch point. A second singularity, an anti-Bloch point, was also identified, which differs in its surrounding magnetization structure.

Denys Makarov of Helmholtz-Zentrum Dresden-Rossendorf, Germany (who is not associated with the present work) emphasizes that in addition to this study being the first measurement of a complex magnetic texture in a bulk material, the resolution (down to 100 nm) is remarkable. He further suggests that the reported approach closes the gap between magnetic soft x-ray tomography and neutron tomography. He anticipates that the technique will improve rapidly given commensurate advances in synchrotron sources, and more intricate structures such as non-collinear magnetic textures, for example, spin spirals or skyrmionic textures will soon be probed. Additionally, he envisions that the method can be rapidly adopted to study complicated sample shapes and resulting 3D magnetic architectures.

The method opens new possibilities for the investigation of bulk magnetic materials. For example, the insights gained with this new technique could be used to tailor magnet fabrication in order to optimize a magnet’s microstructure and thus performance, or to be able to spot and avoid undesirable defects.

Read the abstract in Nature.