Letter | Published:

Three-dimensional magnetization structures revealed with X-ray vector nanotomography

Nature volume 547, pages 328331 (20 July 2017) | Download Citation


In soft ferromagnetic materials, the smoothly varying magnetization leads to the formation of fundamental patterns such as domains, vortices and domain walls1. These have been studied extensively in thin films of thicknesses up to around 200 nanometres, in which the magnetization is accessible with current transmission imaging methods that make use of electrons or soft X-rays. In thicker samples, however, in which the magnetization structure varies throughout the thickness and is intrinsically three dimensional, determining the complex magnetic structure directly still represents a challenge1,3. We have developed hard-X-ray vector nanotomography with which to determine the three-dimensional magnetic configuration at the nanoscale within micrometre-sized samples. We imaged the structure of the magnetization within a soft magnetic pillar of diameter 5 micrometres with a spatial resolution of 100 nanometres and, within the bulk, observed a complex magnetic configuration that consists of vortices and antivortices that form cross-tie walls and vortex walls along intersecting planes. At the intersections of these structures, magnetic singularities—Bloch points—occur. These were predicted more than fifty years ago4 but have so far not been directly observed. Here we image the three-dimensional magnetic structure in the vicinity of the Bloch points, which until now has been accessible only through micromagnetic simulations, and identify two possible magnetization configurations: a circulating magnetization structure5 and a twisted state that appears to correspond to an ‘anti-Bloch point’. Our imaging method enables the nanoscale study of topological magnetic structures6 in systems with sizes of the order of tens of micrometres. Knowledge of internal nanomagnetic textures is critical for understanding macroscopic magnetic properties and for designing bulk magnets for technological applications7.

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X-ray measurements were performed at the cSAXS beamline at the Swiss Light Source, Paul Scherrer Institut, Switzerland. We thank R. M. Galera for providing and performing magnetic characterizations of the GdCo2 nugget, and S. Stutz and E. Müller for the sample fabrication, as well as K. Metlov, A. Arrott and G. Hrkac for discussions. S.G. was funded by the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement number 708674.

Author information


  1. Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland

    • Claire Donnelly
    • , Valerio Scagnoli
    •  & Laura J. Heyderman
  2. Paul Scherrer Institute, 5232 Villigen, Switzerland

    • Claire Donnelly
    • , Manuel Guizar-Sicairos
    • , Valerio Scagnoli
    • , Mirko Holler
    • , Jörg Raabe
    •  & Laura J. Heyderman
  3. SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK

    • Sebastian Gliga


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J.R. and L.J.H. conceived the project. C.D., M.G.-S., V.S., M.H. and J.R. designed the experiment. M.H. and J.R. modified the instrument for the 30° tilt measurement. C.D., M.G.-S., V.S., M.H. and J.R. performed the experiment. C.D. and M.G.-S. developed the vector tomography reconstruction algorithm. C.D. performed the data analysis (with support from M.G.-S. and V.S.). C.D., S.G. and J.R. interpreted the magnetic results. C.D., M.G.-S. and S.G. wrote the manuscript with contributions from all authors.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Claire Donnelly or Manuel Guizar-Sicairos or Sebastian Gliga.

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Extended data

Supplementary information


  1. 1.

    Circulating Bloch point

    The magnetic configuration in the vicinity of an energetically stable circulating Bloch point. The magnetic structure is shown in a radius of 125 nm.

  2. 2.

    Twisted magnetic structure surrounding an anti-Bloch point

    The magnetic configuration in the vicinity of an energetically unstable anti-Bloch point. The magnetisation is twisted to shield the Bloch point structure at length scales greater than the exchange length. The magnetic structure is shown in a radius of 125 nm.

  3. 3.

    Intersection of a magnetic vortex with a vortex domain wall

    The intersection of a magnetic vortex (purple-orange tube) with a vortex domain wall (white surface with a blue-red core). Across the intersection points the direction of the magnetisation in the core of the vortex (indicated by the colour) reverses (from red to blue, and orange to purple). At these points, magnetic singularities occur.

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