Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Geometrically stabilized skyrmionic vortex in FeGe tetrahedral nanoparticles

Abstract

The concept of topology has dramatically expanded the research landscape of magnetism, leading to the discovery of numerous magnetic textures with intriguing topological properties. A magnetic skyrmion is an emergent topological magnetic texture with a string-like structure in three dimensions and a disk-like structure in one and two dimensions. Skyrmions in zero dimensions have remained elusive due to challenges from many competing orders. Here, by combining electron holography and micromagnetic simulations, we uncover the real-space magnetic configurations of a skyrmionic vortex structure confined in a B20-type FeGe tetrahedral nanoparticle. An isolated skyrmionic vortex forms at the ground state and this texture shows excellent robustness against temperature without applying a magnetic field. Our findings shed light on zero-dimensional geometrical confinement as a route to engineer and manipulate individual skyrmionic metastructures.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Morphology and crystallography of FeGe tetrahedral particles.
Fig. 2: Skyrmionic vortex confined in a 145 nm FeGe tetrahedral particle.
Fig. 3: Observed and simulated projections of non-trivial magnetic states.
Fig. 4: Chiral edge state in a tetrahedron.
Fig. 5: Magnetic phase diagram of the FeGe tetrahedral particle system.

Data availability

The data that support the findings of this study are available within the article and its Supplementary Information. Any other relevant data are also available upon reasonable request from the corresponding authors.

References

  1. Allwood, D. A. et al. Magnetic domain-wall logic. Science 309, 1688–1692 (2005).

    CAS  Google Scholar 

  2. Parkin, S. S., Hayashi, M. & Thomas, L. Magnetic domain-wall racetrack memory. Science 320, 190–194 (2008).

    CAS  Google Scholar 

  3. Wolf, D., Lubk, A., Röder, F. & Lichte, H. Electron holographic tomography. Curr. Opin. Solid State Mater. Sci. 17, 126–134 (2013).

    CAS  Google Scholar 

  4. Wolf, D. et al. 3D magnetic induction maps of nanoscale materials revealed by electron holographic tomography. Chem. Mater. 27, 6771–6778 (2015).

    CAS  Google Scholar 

  5. Wolf, D. et al. Holographic vector field electron tomography of three-dimensional nanomagnets. Commun. Phys. 2, 87 (2019).

    Google Scholar 

  6. Hilger, A. et al. Tensorial neutron tomography of three-dimensional magnetic vector fields in bulk materials. Nat. Commun. 9, 4023 (2018).

    CAS  Google Scholar 

  7. Donnelly, C. et al. Three-dimensional magnetization structures revealed with X-ray vector nanotomography. Nature 547, 328–331 (2017).

    CAS  Google Scholar 

  8. Donnelly, C. et al. Tomographic reconstruction of a three-dimensional magnetization vector field. New J. Phys. 20, 083009 (2018).

    Google Scholar 

  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).

    Google Scholar 

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

    CAS  Google Scholar 

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

    Google Scholar 

  12. Lai, G. et al. Three-dimensional reconstruction of magnetic vector fields using electron-holographic interferometry. J. Appl. Phys. 75, 4593–4598 (1994).

    CAS  Google Scholar 

  13. Gubin, S. P. Magnetic Nanoparticles (Wiley-VCH, 2009).

  14. Mühlbauer, S. et al. Magnetic small-angle neutron scattering. Rev. Mod. Phys. 91, 015004 (2019).

    Google Scholar 

  15. Skyrme, T. H. R. A unified field theory of mesons and baryons. Nucl. Phys. 31, 556–569 (1962).

    CAS  Google Scholar 

  16. Mühlbauer, S. et al. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009).

    Google Scholar 

  17. Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010).

    CAS  Google Scholar 

  18. Jonietz, F. et al. Spin transfer torques in MnSi at ultralow current densities. Science 330, 1648–1651 (2010).

    CAS  Google Scholar 

  19. Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8, 899–911 (2013).

    CAS  Google Scholar 

  20. Fert, A., Cros, V. & Sampaio, J. Skyrmions on the track. Nat. Nanotechnol. 8, 152–156 (2013).

    CAS  Google Scholar 

  21. Parkin, S. & Yang, S. H. Memory on the racetrack. Nat. Nanotechnol. 10, 195–198 (2015).

    CAS  Google Scholar 

  22. Liang, D., DeGrave, J. P., Stolt, M. J., Tokura, Y. & Jin, S. Current-driven dynamics of skyrmions stabilized in MnSi nanowires revealed by topological Hall effect. Nat. Commun. 6, 8217 (2015).

    CAS  Google Scholar 

  23. Fert, A., Reyren, N. & Cros, V. Magnetic skyrmions: advances in physics and potential applications. Nat. Rev. Mater. 2, 17031 (2017).

    CAS  Google Scholar 

  24. Sampaio, J., Cros, V., Rohart, S., Thiaville, A. & Fert, A. Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures. Nat. Nanotechnol. 8, 839–844 (2013).

    CAS  Google Scholar 

  25. Jiang, W. et al. Magnetism. Blowing magnetic skyrmion bubbles. Science 349, 283–286 (2015).

    CAS  Google Scholar 

  26. Du, H. et al. Edge-mediated skyrmion chain and its collective dynamics in a confined geometry. Nat. Commun. 6, 8504 (2015).

    CAS  Google Scholar 

  27. Jin, C. et al. Control of morphology and formation of highly geometrically confined magnetic skyrmions. Nat. Commun. 8, 15569 (2017).

    CAS  Google Scholar 

  28. Iwasaki, J., Mochizuki, M. & Nagaosa, N. Current-induced skyrmion dynamics in constricted geometries. Nat. Nanotechnol. 8, 742–747 (2013).

    CAS  Google Scholar 

  29. Mathur, N., Stolt, M. J. & Jin, S. Magnetic skyrmions in nanostructures of non-centrosymmetric materials. APL Mater. 7, 120703 (2019).

    Google Scholar 

  30. Yu, X. Z. et al. Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe. Nat. Mater. 10, 106–109 (2011).

    CAS  Google Scholar 

  31. Zhao, X. et al. Direct imaging of magnetic field-driven transitions of skyrmion cluster states in FeGe nanodisks. Proc. Natl Acad. Sci. USA 113, 4918–4923 (2016).

    CAS  Google Scholar 

  32. Matsumoto, T., So, Y. G., Kohno, Y., Ikuhara, Y. & Shibata, N. Stable magnetic skyrmion states at room temperature confined to corrals of artificial surface pits fabricated by a focused electron beam. Nano Lett. 18, 754–762 (2018).

    CAS  Google Scholar 

  33. Rohart, S. & Thiaville, A. Skyrmion confinement in ultrathin film nanostructures in the presence of Dzyaloshinskii–Moriya interaction. Phys. Rev. B 88, 184422 (2013).

    Google Scholar 

  34. Beg, M. et al. Ground state search, hysteretic behaviour, and reversal mechanism of skyrmionic textures in confined helimagnetic nanostructures. Sci. Rep. 5, 17137 (2015).

    Google Scholar 

  35. Zheng, F. et al. Direct imaging of a zero-field target skyrmion and its polarity switch in a chiral magnetic nanodisk. Phys. Rev. Lett. 119, 197205 (2017).

    Google Scholar 

  36. Stolt, M. J. et al. Selective chemical vapor deposition growth of cubic FeGe nanowires that support stabilized magnetic skyrmions. Nano Lett. 17, 508–514 (2017).

    CAS  Google Scholar 

  37. Hou, Z. et al. Creation of single chain of nanoscale skyrmion bubbles with record-high temperature stability in a geometrically confined nanostripe. Nano Lett. 18, 1274–1279 (2018).

    CAS  Google Scholar 

  38. Moon, K. et al. Spontaneous interlayer coherence in double-layer quantum Hall systems: charged vortices and Kosterlitz–Thouless phase transitions. Phys. Rev. B 51, 5138–5170 (1995).

    CAS  Google Scholar 

  39. Rybakov, F., Borisov, A. & Bogdanov, A. Three-dimensional skyrmion states in thin films of cubic helimagnets. Phys. Rev. B 87, 094424 (2013).

    Google Scholar 

  40. Tchernyshyov, O. & Chern, G. W. Fractional vortices and composite domain walls in flat nanomagnets. Phys. Rev. Lett. 95, 197204 (2005).

    Google Scholar 

  41. Almeida, T. P. et al. Direct visualization of the thermomagnetic behavior of pseudo-single-domain magnetite particles. Sci. Adv. 2, e1501801 (2016).

    Google Scholar 

  42. Bogdanov, A. N. & Rössler, U. K. Chiral symmetry breaking in magnetic thin films and multilayers. Phys. Rev. Lett. 87, 037203 (2001).

    CAS  Google Scholar 

  43. Cubukcu, M. et al. Dzyaloshinskii–Moriya anisotropy in nanomagnets with in-plane magnetization. Phys. Rev. B 93, 020401 (2016).

    Google Scholar 

  44. Volkov, M. O. et al. Mesoscale Dzyaloshinskii–Moriya interaction: geometrical tailoring of the magnetochirality. Sci. Rep. 8, 866 (2018).

    Google Scholar 

  45. Harada, K., Tonomura, A., Togawa, Y., Akashi, T. & Matsuda, T. Double-biprism electron interferometry. Appl. Phys. Lett. 84, 3229–3231 (2004).

    CAS  Google Scholar 

  46. Shindo, D. & Murakami, Y. Electron holography of magnetic materials. J. Phys. D 41, 183002 (2008).

    Google Scholar 

  47. Vansteenkiste, A. et al. The design and verification of MuMax3. AIP Adv. 4, 107133 (2014).

    Google Scholar 

  48. Dyadkin, V. A. et al. Control of chirality of transition-metal monosilicides by the Czochralski method. Phys. Rev. B 84, 014435 (2011).

    Google Scholar 

  49. Morikawa, D. et al. Determination of crystallographic chirality of MnSi thin film grown on Si(111) substrate. Phys. Rev. Mater. 4, 014407 (2020).

    CAS  Google Scholar 

Download references

Acknowledgements

K.N. was supported by a Grant-in-Aid for Scientific Research (B) (number 19H02418) and for Challenging Research (Exploratory) (number 19K22052) from the JSPS. X.Y. was supported by a Grant-in-Aid for Scientific Research (A) (number 19H00660) from the JSPS and JST CREST (grant number JPMJCR20T1). N.N. was supported by JST CREST (grant number JPMJCR1874). A.C.B. and J.Z. acknowledge support from the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under award number DE-SC0020221. Y.L. was supported by the Special Postdoctoral Researcher programme of RIKEN. N.M., M.J.S. and S.J. were supported by US NSF grant ECCS-1609585. M.J.S. also acknowledges support from the NSF Graduate Research Fellowship Program.

Author information

Authors and Affiliations

Authors

Contributions

S.J. and Y.T. conceived the project. N.M., M.J.S. and S.J. synthesized the FeGe particles. Y.L., A.C.B. and J.Z. performed the micromagnetic simulations. K.N. performed the EH observations and model-based simulations. K.N., Y.L. and J.Z. wrote the manuscript. All authors discussed the data and revised the manuscript.

Corresponding authors

Correspondence to Kodai Niitsu or Jiadong Zang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Materials thanks Shawn D. Pollard and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

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

Supplementary information

Supplementary Information

Supplementary notes 1–5, references 1–7, Figs. 1–22 and captions of Movies 1–4.

Supplementary Video 1

Simulated 3D view of the skyrmionic vortex in a 145 nm tetrahedron (in-plane (xy plane) magnetic component).

Supplementary Video 2

Simulated 3D view of the skyrmionic vortex in a 145 nm tetrahedron (out-of-plane (z axis) magnetic component).

Supplementary Video 3

Sliced vector plots of the skyrmionic vortex in a 145 nm tetrahedron.

Supplementary Video 4

Sliced vector plots of the skyrmionic vortex in a 185 nm tetrahedron.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Niitsu, K., Liu, Y., Booth, A.C. et al. Geometrically stabilized skyrmionic vortex in FeGe tetrahedral nanoparticles. Nat. Mater. 21, 305–310 (2022). https://doi.org/10.1038/s41563-021-01186-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-021-01186-x

Further reading

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