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.

Towards control of the size and helicity of skyrmions in helimagnetic alloys by spin–orbit coupling

Abstract

Chirality—that is, left- or right-handedness—is an important concept in a broad range of scientific areas. In condensed matter, chirality is found not only in molecular or crystal forms, but also in magnetic structures. A magnetic skyrmion1,2,3,4,5,6,7,8 is a topologically stable spin vortex structure, as observed in chiral-lattice helimagnets, and is one example of such a structure. The spin swirling direction (skyrmion helicity) should be closely related to the underlying lattice chirality via the relativistic spin–orbit coupling. Here, we report on the correlation between skyrmion helicity and crystal chirality in alloys of helimagnets Mn1−xFexGe with varying compositions by Lorentz transmission electron microscopy and convergent-beam electron diffraction over a broad range of compositions (x = 0.3–1.0). The skyrmion lattice constant shows non-monotonous variation with composition x, with a divergent behaviour around x = 0.8, where the correlation between magnetic helicity and crystal chirality changes sign. This originates from continuous variation of the spin–orbit coupling strength and its sign reversal in the metallic alloys as a function of x. Controllable spin–orbit coupling may offer a promising way to tune skyrmion size and helicity.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Definitions of Γc and γm, and observation of skyrmions by Lorentz TEM.
Figure 2: Dependence of skyrmion size on x, obtained in a microcrystal of Mn1−xFexGe with varying composition (x ≈ 0.7).
Figure 3: Lorentz TEM images of magnetic helix and skyrmion, and CBED disk patterns used for determination of Γc.
Figure 4: Composition dependence of helical-magnetic properties of Mn1–xFexGe.

References

  1. Bogdanov, A. N. & Yablonskii, D. A. Thermodynamically stable ‘vortices’ in magnetically ordered crystals. The mixed state of magnets. Sov. Phys. JETP 68, 101–103 (1989).

    Google Scholar 

  2. Rößler, U. K., Bogdanov, A. N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797–801 (2006).

    Article  Google Scholar 

  3. Binz, B., Vishwanath, A. & Aji, V. Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi. Phys. Rev. Lett. 96, 207202 (2006).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  7. Tonomura, A. et al. Real-space observation of skyrmion lattice in helimagnet MnSi thin samples. Nano Lett. 12, 1673–1677 (2012).

    Article  CAS  Google Scholar 

  8. Seki, S., Yu, X. Z., Ishiwata, S. & Tokura, Y. Observation of skyrmions in a multiferroic material. Science 336, 198–201 (2012).

    Article  CAS  Google Scholar 

  9. Kanazawa, N. et al. Possible skyrmion-lattice ground state in the B20 chiral-lattice magnet MnGe as seen via small-angle neutron scattering. Phys. Rev. B 86, 134425 (2012).

    Article  Google Scholar 

  10. Nagaosa, N., Yu, X. Z. & Tokura, Y. Gauge fields in real and momentum spaces in magnets: monopoles and skyrmions. Philos. Trans. A Math. Phys. Eng. Sci. 370, 5806–5819 (2012).

    Article  CAS  Google Scholar 

  11. Fert, A., Cros, V. & Sampaio, J. Skyrmions on the track. Nature Nanotech. 8, 152–156 (2013).

    Article  CAS  Google Scholar 

  12. Lee, M., Kang, W., Onose, Y., Tokura, Y. & Ong, N. P. Unusual Hall anomaly in MnSi under pressure. Phys. Rev. Lett. 102, 186601 (2009).

    Article  Google Scholar 

  13. Neubauer, A. et al. Topological Hall effect in the A phase of MnSi. Phys. Rev. Lett. 102, 186602 (2009).

    Article  CAS  Google Scholar 

  14. Kanazawa, N. et al. Large topological Hall effect in a short-period helimagnet MnGe. Phys. Rev. Lett. 106, 156603 (2011).

    Article  CAS  Google Scholar 

  15. Schulz, T. et al. Emergent electrodynamics of skyrmions in a chiral magnet. Nature Phys. 8, 301–304 (2012).

    Article  CAS  Google Scholar 

  16. Yu, X. Z. et al. Skyrmion flow near room temperature in an ultralow current density. Nature Commun. 3, 988 (2012).

    Article  CAS  Google Scholar 

  17. Grigoriev, S. V. et al. Crystal handedness and spin helix chirality in Fe1−xCoxSi. Phys. Rev. Lett. 102, 037204 (2009).

    Article  CAS  Google Scholar 

  18. Grigoriev, S. V. et al. Interplay between crystalline chirality and magnetic structure in Mn1−xFexSi. Phys. Rev. B 81, 012408 (2010).

    Article  Google Scholar 

  19. Landau, L. D., Lifshitz, E. M. & Pitaevskii, L. P. in Electrodynamics of Continuous Media Vol. 8 (eds Lifshitz, E. M. & Pitaevskii, L. P.) 178–179 (Elsevier, 2008).

    Google Scholar 

  20. Uchida, M., Onose, Y., Matsui, Y. & Tokura, Y. Real-space observation of helical spin order. Science 311, 359–361 (2006).

    Article  CAS  Google Scholar 

  21. Bajt, S. et al. Quantitative phase-sensitive imaging in a transmission electron microscope. Ultramicroscopy 83, 67–73 (2000).

    Article  CAS  Google Scholar 

  22. Ishizuka, K. & Allman, B. Phase measurement of atomic resolution image using transport of intensity equation. J. Electron Microsc. 54, 191–197 (2005).

    CAS  Google Scholar 

  23. Tanaka, M., Takayoshi, H., Ishida, M. & Endoh, Y. Crystal chirality and helicity of the helical spin density wave in MnSi. I. Convergent-beam electron diffraction. J. Phys. Soc. Jpn 54, 2970–2974 (1985).

    Article  CAS  Google Scholar 

  24. Tsuda, K. & Tanaka, M. Refinement of crystal structural parameters using two-dimensional energy-filtered CBED patterns. Acta Crystallogr. A 55, 939–954 (1999).

    Article  CAS  Google Scholar 

  25. Ishida, M., Endoh, Y., Mitsuda, S., Ishikawa, Y. & Tanaka, M. Crystal chirality and helicity of the helical spin density wave in MnSi. II. Polarized neutron diffraction. J. Phys. Soc. Jpn 54, 2975–2982 (1985).

    Article  CAS  Google Scholar 

  26. Morikawa, D., Shibata, K., Kanazawa, N., Yu, X. Z. & Tokura, Y. Crystal chirality and skyrmion helicity in MnSi and (Fe, Co)Si as determined by transmission electron microscopy. Phys. Rev. B 88, 024408 (2013).

    Article  Google Scholar 

  27. Grigoriev, S. V. et al. Chiral properties of structure and magnetism in Mn1−xFexGe compounds: when the left and the right are fighting, who wins? Phys. Rev. Lett. 110, 207201 (2013).

    Article  CAS  Google Scholar 

  28. Lebech, B., Bernhard, J. & Freltoft, T. Magnetic structures of cubic FeGe studied by small-angle neutron scattering. J. Phys. Condens. Matter 1, 6105–6122 (1989).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors thank N. Nagaosa, S. Seki, T. Kurumaji and Y. Okamura for helpful discussions. This study was supported by a Grant-in-Aid for Scientific Research (grant no. 24224009) from MEXT, and by the Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program).

Author information

Authors and Affiliations

Authors

Contributions

K.S. synthesized the polycrystalline samples, prepared the TEM samples, carried out the Lorentz TEM observations, and applied the CBED method. X.Z.Y. measured the EELS thickness map. T.H. measured the EDX composition map. D.M. analysed the CBED patterns. N.K. and S.I. contributed to the synthesis of polycrystalline samples. K.K. and Y.M. contributed to the EELS and EDX studies. Y.T. conceived the project and wrote the manuscript with K.S. and N.K.

Corresponding authors

Correspondence to K. Shibata or Y. Tokura.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary Information (PDF 1227 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Shibata, K., Yu, X., Hara, T. et al. Towards control of the size and helicity of skyrmions in helimagnetic alloys by spin–orbit coupling. Nature Nanotech 8, 723–728 (2013). https://doi.org/10.1038/nnano.2013.174

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2013.174

This article is cited by

Search

Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research