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
Open Access articles citing this article.
npj Quantum Materials Open Access 08 April 2022
Nature Communications Open Access 07 September 2021
Scientific Reports Open Access 04 March 2020
Subscribe to Journal
Get full journal access for 1 year
only $9.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
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).
Rößler, U. K., Bogdanov, A. N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797–801 (2006).
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).
Mühlbauer, S. et al. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009).
Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010).
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).
Tonomura, A. et al. Real-space observation of skyrmion lattice in helimagnet MnSi thin samples. Nano Lett. 12, 1673–1677 (2012).
Seki, S., Yu, X. Z., Ishiwata, S. & Tokura, Y. Observation of skyrmions in a multiferroic material. Science 336, 198–201 (2012).
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).
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).
Fert, A., Cros, V. & Sampaio, J. Skyrmions on the track. Nature Nanotech. 8, 152–156 (2013).
Lee, M., Kang, W., Onose, Y., Tokura, Y. & Ong, N. P. Unusual Hall anomaly in MnSi under pressure. Phys. Rev. Lett. 102, 186601 (2009).
Neubauer, A. et al. Topological Hall effect in the A phase of MnSi. Phys. Rev. Lett. 102, 186602 (2009).
Kanazawa, N. et al. Large topological Hall effect in a short-period helimagnet MnGe. Phys. Rev. Lett. 106, 156603 (2011).
Schulz, T. et al. Emergent electrodynamics of skyrmions in a chiral magnet. Nature Phys. 8, 301–304 (2012).
Yu, X. Z. et al. Skyrmion flow near room temperature in an ultralow current density. Nature Commun. 3, 988 (2012).
Grigoriev, S. V. et al. Crystal handedness and spin helix chirality in Fe1−xCoxSi. Phys. Rev. Lett. 102, 037204 (2009).
Grigoriev, S. V. et al. Interplay between crystalline chirality and magnetic structure in Mn1−xFexSi. Phys. Rev. B 81, 012408 (2010).
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).
Uchida, M., Onose, Y., Matsui, Y. & Tokura, Y. Real-space observation of helical spin order. Science 311, 359–361 (2006).
Bajt, S. et al. Quantitative phase-sensitive imaging in a transmission electron microscope. Ultramicroscopy 83, 67–73 (2000).
Ishizuka, K. & Allman, B. Phase measurement of atomic resolution image using transport of intensity equation. J. Electron Microsc. 54, 191–197 (2005).
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).
Tsuda, K. & Tanaka, M. Refinement of crystal structural parameters using two-dimensional energy-filtered CBED patterns. Acta Crystallogr. A 55, 939–954 (1999).
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).
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).
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).
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).
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).
The authors declare no competing financial interests.
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
This article is cited by
Nature Reviews Physics (2022)
npj Quantum Materials (2022)
Rare Metals (2022)
Rare Metals (2022)
Nature Communications (2021)