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

Abstract

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: X-ray magnetic tomography.
Figure 2: Axial tomographic slice of the reconstructed magnetization vector field.
Figure 3: Details of the reconstructed magnetization.

References

  1. 1

    Hubert, A. & Schäfer, R. Magnetic Domains: The Analysis of Magnetic Microstructures (Springer, 1998)

  2. 2

    Arrott, A. S., Heinrich, B. & Aharoni, A. Point singularities and magnetization reversal in ideally soft ferromagnetic cylinders. IEEE Trans. Magn. 15, 1228–1235 (1979)

    ADS  Article  Google Scholar 

  3. 3

    Shin, S., Schäfer, R. & De Cooman, B. C. Three-dimensional visualization of the magnetic microstructure in bulk Fe-6.6 pct Si. Metall. Mater. Trans. A 44, 4239–4247 (2013)

    CAS  Article  Google Scholar 

  4. 4

    Feldtkeller, E. Mikromagnetisch Stetige und Unstetige Magnetisierungskonfigurationen. Z. Angew. Phys. 19, 530 (1965)

    Google Scholar 

  5. 5

    Elías, R. G. & Verga, A. Magnetization structure of a Bloch point singularity. Eur. Phys. J. B 82, 159 (2011)

    ADS  Article  CAS  Google Scholar 

  6. 6

    Braun, H.-B. Topological effects in nanomagnetism: from superparamagnetism to chiral quantum solitons. Adv. Phys. 61, 1–116 (2012)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Gutfleisch, O. et al. Magnetic materials and devices for the 21st century: stronger, lighter, and more energy efficient. Adv. Mater. 23, 821–842 (2011)

    CAS  PubMed  Article  Google Scholar 

  8. 8

    Streubel, R. et al. Retrieving spin textures on curved magnetic thin films with full-field soft X-ray microscopies. Nat. Commun. 6, 7612 (2015)

    ADS  PubMed  PubMed Central  Article  Google Scholar 

  9. 9

    Phatak, C., Petford-Long, A. K. & De Graef, M. Three-dimensional study of the vector potential of magnetic structures. Phys. Rev. Lett. 104, 253901 (2010)

    ADS  PubMed  Article  CAS  Google Scholar 

  10. 10

    Phatak, C. et al. Visualization of the magnetic structure of sculpted three-dimensional cobalt nanospirals. Nano Lett. 14, 759–764 (2014)

    ADS  CAS  PubMed  Article  Google Scholar 

  11. 11

    Tanigaki, T. et al. Three-dimensional observation of magnetic vortex cores in stacked ferromagnetic discs. Nano Lett. 15, 1309–1314 (2015)

    ADS  CAS  PubMed  Article  Google Scholar 

  12. 12

    Hertel, R. Curvature-induced magnetochirality. Spin 3, 134009 (2013)

    Article  CAS  Google Scholar 

  13. 13

    Streubel, R. et al. Magnetism in curved geometries. J. Phys. D 49, 363001 (2016)

    Article  CAS  Google Scholar 

  14. 14

    Arrott, A. S. Visualization and interpretation of magnetic configurations using magnetic charge. IEEE Magn. Lett. 7, 1108505 (2016)

    Article  Google Scholar 

  15. 15

    Andreas, C., Kákay, A. & Hertel, R. Multiscale and multimodel simulation of Bloch-point dynamics. Phys. Rev. B 89, 134403 (2014)

    ADS  Article  CAS  Google Scholar 

  16. 16

    Hertel, R. & Schneider, C. M. Exchange explosions: magnetization dynamics during vortex–antivortex annihilation. Phys. Rev. Lett. 97, 177202 (2006)

    ADS  PubMed  Article  CAS  Google Scholar 

  17. 17

    Thiaville, A. et al. Micromagnetic study of Bloch-point-mediated vortex core reversal. Phys. Rev. B 67, 094410 (2003)

    ADS  Article  CAS  Google Scholar 

  18. 18

    Hertel, R. Ultrafast domain wall dynamics in magnetic nanotubes and nanowires. J. Phys. Condens. Matter 28, 483002 (2016)

    CAS  PubMed  Article  Google Scholar 

  19. 19

    Kardjilov, N. et al. Three-dimensional imaging of magnetic fields with polarized neutrons. Nat. Phys. 4, 399–403 (2008)

    CAS  Article  Google Scholar 

  20. 20

    Manke, I. et al. Three-dimensional imaging of magnetic domains. Nat. Commun. 1, 125 (2010)

    ADS  CAS  PubMed  Article  Google Scholar 

  21. 21

    Holler, M. et al. High-resolution non-destructive three-dimensional imaging of integrated circuits. Nature 543, 402–406 (2017)

    ADS  CAS  Article  PubMed  Google Scholar 

  22. 22

    Donnelly, C. et al. High-resolution hard x-ray magnetic imaging with dichroic ptychography. Phys. Rev. B 94, 064421 (2016)

    ADS  Article  CAS  Google Scholar 

  23. 23

    Phatak, C., Beleggia, M. & De Graef, M. Vector field electron tomography of magnetic materials: theoretical development. Ultramicroscopy 108, 503–513 (2008)

    CAS  PubMed  Article  Google Scholar 

  24. 24

    Burzo, E. Paramagnetic behavior of some rare-earth cobalt compounds. Phys. Rev. B 6, 2882–2887 (1972)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Chukazumi, S. in Physics of Ferromagnetism Ch. 7.2 (Oxford Univ. Press, 2009)

  26. 26

    Stoehr, J. & Siegmann, H. Magnetism: From Fundamentals to Nanoscale Dynamics Ch. 9 (Springer, 2006)

  27. 27

    Scagnoli, V. et al. Linear polarization scans for resonant X-ray diffraction with a double-phase-plate configuration. J. Synchrotron Radiat. 16, 778–787 (2009)

    CAS  PubMed  Article  Google Scholar 

  28. 28

    Schäfer, R. Domains in ‘extremely’ soft magnetic materials. J. Magn. Magn. Mater. 215–216, 652–663 (2000)

    ADS  Article  Google Scholar 

  29. 29

    Chen, Y.-T. et al. Full-field hard x-ray microscopy below 30 nm: a challenging nanofabrication achievement. Nanotechnology 19, 395302 (2008)

    PubMed  Article  CAS  Google Scholar 

  30. 30

    Cloetens, P. et al. Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays. Appl. Phys. Lett. 75, 2912–2914 (1999)

    ADS  CAS  Article  Google Scholar 

  31. 31

    Eriksson, M., van der Veen, J. F. & Quitmann, C. Diffraction-limited storage rings—a window to the science of tomorrow. J. Synchrotron Radiat. 21, 837–842 (2014)

    CAS  PubMed  Article  Google Scholar 

  32. 32

    Thibault, P., Guizar-Sicairos, M. & Menzel, A. Coherent imaging at the diffraction limit. J. Synchrotron Radiat. 21, 1011–1018 (2014)

    PubMed  PubMed Central  Article  Google Scholar 

  33. 33

    Holler, M. et al. X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution. Sci. Rep. 4, 3857 (2014)

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  34. 34

    Rodenburg, J. M. et al. Hard-x-ray lensless imaging of extended objects. Phys. Rev. Lett. 98, 034801 (2007)

    ADS  CAS  PubMed  Article  Google Scholar 

  35. 35

    Thibault, P. et al. High-resolution scanning x-ray diffraction microscopy. Science 321, 379–382 (2008)

    ADS  CAS  PubMed  Article  Google Scholar 

  36. 36

    Tripathi, A. et al. Dichroic coherent diffractive imaging. Proc. Natl Acad. Sci. USA 108, 13393–13398 (2011)

    ADS  CAS  PubMed  Article  Google Scholar 

  37. 37

    Giles, C. et al. Energy-dispersive phase plate for magnetic circular-dichroism experiments in the X-ray range. J. Appl. Cryst. 27, 232–240 (1994)

    CAS  Article  Google Scholar 

  38. 38

    Dierolf, M. et al. Ptychographic X-ray computed tomography at the nanoscale. Nature 467, 436–439 (2010)

    ADS  CAS  PubMed  Article  Google Scholar 

  39. 39

    Henrich, B. et al. PILATUS: A single photon counting pixel detector for X-ray applications. Nucl. Instrum. Meth. A 607, 247–249 (2009)

    ADS  CAS  Article  Google Scholar 

  40. 40

    Kraft, P. et al. Characterization and calibration of PILATUS detectors. IEEE Trans. Nucl. Sci. 56, 758–764 (2009)

    ADS  CAS  Article  Google Scholar 

  41. 41

    Guizar-Sicairos, M. & Fienup, J. R. Phase retrieval with transverse translation diversity: a nonlinear optimization approach. Opt. Express 16, 7264–7278 (2008)

    ADS  PubMed  Article  Google Scholar 

  42. 42

    Thibault, P. & Guizar-Sicairos, M. Maximum-likelihood refinement for coherent diffractive imaging. New J. Phys. 14, 063004 (2012)

    ADS  Article  Google Scholar 

  43. 43

    Bouchenoire, L. et al. Performance of phase plates on the XMaS beamline at the ESRF. J. Synchrotron Radiat. 10, 172–176 (2003)

    CAS  PubMed  Article  Google Scholar 

  44. 44

    Guizar-Sicairos, M., Thurman, S. T. & Fienup, J. R. Efficient subpixel image registration algorithms. Opt. Lett. 33, 156–158 (2008)

    ADS  PubMed  Article  Google Scholar 

  45. 45

    Guizar-Sicairos, M. et al. High-throughput ptychography using Eiger: scanning X-ray nano-imaging of extended regions. Opt. Express 22, 14859–14870 (2014)

    ADS  PubMed  Article  Google Scholar 

  46. 46

    Guizar-Sicairos, M. et al. Phase tomography from x-ray coherent diffractive imaging projections. Opt. Express 19, 21345–21357 (2011)

    ADS  PubMed  Article  Google Scholar 

  47. 47

    Guizar-Sicairos, M. et al. Quantitative interior x-ray nanotomography by a hybrid imaging technique. Optica 2, 259–266 (2015)

    ADS  Article  Google Scholar 

  48. 48

    Hannon, J. P. et al. X-ray resonance exchange scattering. Phys. Rev. Lett. 61, 1245–1248 (1988)

    ADS  CAS  PubMed  Article  Google Scholar 

  49. 49

    van Heel, M. & Schatz, M. Fourier shell correlation threshold criteria. J. Struct. Biol. 151, 250–262 (2005)

    CAS  PubMed  Article  Google Scholar 

  50. 50

    Howells, M. R. et al. An assessment of the resolution limitation due to radiation-damage in x-ray diffraction microscopy. J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009)

    CAS  Article  Google Scholar 

Download references

Acknowledgements

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

Affiliations

Authors

Contributions

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.

Corresponding authors

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

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Figure 1 Transmission spectrum obtained with spectroscopic ptychography.

a, Absorption part of a ptychographic reconstruction of the pillar measured at 7.203 keV. Regions of air and material are highlighted by the blue and red boxes, respectively. These regions were used to obtain the transmission of the sample at different energies. Such images were measured for a range of energies between 7.203 keV and 7.282 keV in steps of 1.5 eV. b, The transmission spectrum obtained from the range of images is shown, and the difference in absorption across the absorption edge, Δedge, is indicated.

Extended Data Figure 2 Validation of the magnetic reconstruction.

Single polarization images for different angles about the rotation axis (0°, 30° and 60°) in the 30° tilt geometry are shown in the left-hand column. In the central column, XMCD projections obtained by taking the difference between images measured with circular left and right polarization are given, which are the integrals of the magnetic component along the path of the X-ray beam. The equivalent projections obtained from the reconstructed magnetic tomogram are given in the right-hand column. When we compare the images in the central and right columns, the contrast and projection of the magnetization match well. This good agreement provides a validation for the magnetic reconstruction.

Extended Data Figure 3 Structure of the magnetization surrounding the singularity shown in Fig. 3f.

a, View parallel to the plane of the domain wall shown in Fig. 3c; b, view perpendicular to the plane of the domain wall shown in Fig. 3c. The observed magnetic structure does not show a one-to-one correspondence to any of the Bloch point configurations in Fig. 3g–i. While circulating Bloch points have been shown to minimize the magnetostatic energy as result of their swirling magnetization, this is not the case for other Bloch point configurations, where the magnetization in the vicinity of the singularity is predicted to deform in order to minimize the magnetostatic energy. We therefore attribute the structure above to the redistribution of the magnetization in order to screen the magnetostatic charge associated with the monopole generated by the diverging magnetization at the Bloch point.

Extended Data Figure 4 Estimation of the spatial resolution obtained by resolving nearby structures.

ac, Streamlines showing the direction of the magnetization for three xz slices at heights of 0 nm (midway through the pillar), +20 nm and +40 nm. A vortex–antivortex pair draw closer together as the height increases until they merge and can barely be resolved. df, The absolute value of the magnetization is shown for the same areas as ac, where the cores of the vortex and antivortex are minima. gi, The line profiles along the dotted lines in df, where we show that we are able to resolve features in the vector field that are separated by approximately 126 nm (h), the structure of which can be seen clearly in b, whereas in i the two structures can no longer be resolved.

Extended Data Figure 5 Estimation of the spatial resolution using FSC.

ac, The spatial resolution of the single components of the magnetization vector— mx (a), my (b) and mz (c)—are found to be 195 nm, 250 nm and 196 nm, respectively. The spatial resolution of my is lower because of lower sampling resulting from the experimental geometry, as explained in the text. df, To estimate the spatial resolution of the vector field, the FSC values are calculated for (d), (e) and (f) to be 125 nm, 97 nm and 127 nm, respectively. The x–y and y–z planes exhibit lower spatial resolution, owing to the low sampling of my caused by the experimental geometry.

Extended Data Figure 6 The correspondence of the three-dimensional region in Fig. 3c with the axial slice of Fig. 2a.

a, From above; b, from the side. The core of vortex (i) is mapped with an isosurface in b. The relative positions of the slice in Fig. 3a and the three-dimensional region in Fig. 3c are given in c.

Supplementary information

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. (AVI 11026 kb)

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. (AVI 10087 kb)

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. (AVI 16733 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Donnelly, C., Guizar-Sicairos, M., Scagnoli, V. et al. Three-dimensional magnetization structures revealed with X-ray vector nanotomography. Nature 547, 328–331 (2017). https://doi.org/10.1038/nature23006

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing