Fractional antiferromagnetic skyrmion lattice induced by anisotropic couplings

This article has been updated (view changelog)


Magnetic skyrmions are topological solitons with a nanoscale winding spin texture that hold promise for spintronics applications1,2,3,4. Skyrmions have so far been observed in a variety of magnets that exhibit nearly parallel alignment for neighbouring spins, but theoretically skyrmions with anti-parallel neighbouring spins are also possible. Such antiferromagnetic skyrmions may allow more flexible control than conventional ferromagnetic skyrmions5,6,7,8,9,10. Here, by combining neutron scattering measurements and Monte Carlo simulations, we show that a fractional antiferromagnetic skyrmion lattice is stabilized in MnSc2S4 through anisotropic couplings. The observed lattice is composed of three antiferromagnetically coupled sublattices, and each sublattice is a triangular skyrmion lattice that is fractionalized into two parts with an incipient meron (half-skyrmion) character11,12. Our work demonstrates that the theoretically proposed antiferromagnetic skyrmions can be stabilized in real materials and represents an important step towards their implementation in spintronic devices.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Spin dynamics in a powder sample of MnSc2S4.
Fig. 2: Spin dynamics in a single-crystal sample of MnSc2S4.
Fig. 3: Anisotropic-coupling-induced triple-q phase in MnSc2S4.
Fig. 4: Fractional antiferromagnetic skyrmion lattice in MnSc2S4.

Data availability

The data that support the findings of this study are available at and from the corresponding author upon reasonable request.

Code availability

The codes for the spin-wave calculations and the Monte Carlo simulations that support the findings of this study are available from the corresponding author upon reasonable request.

Change history

  • 08 October 2020

    This Article was amended to correct the Peer review information in the Additional information section.


  1. 1.

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

    ADS  PubMed  Google Scholar 

  2. 2.

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

    ADS  CAS  PubMed  Google Scholar 

  3. 3.

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

    ADS  CAS  PubMed  Google Scholar 

  4. 4.

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

    ADS  CAS  Google Scholar 

  5. 5.

    Baltz, V. et al. Antiferromagnetic spintronics. Rev. Mod. Phys. 90, 015005 (2018).

    ADS  MathSciNet  CAS  Google Scholar 

  6. 6.

    Barker, J. & Tretiakov, O. A. Static and dynamical properties of antiferromagnetic skyrmions in the presence of applied current and temperature. Phys. Rev. Lett. 116, 147203 (2016).

    ADS  PubMed  Google Scholar 

  7. 7.

    Zhang, X., Zhou, Y. & Ezawa, M. Antiferromagnetic skyrmion: stability, creation and manipulation. Sci. Rep. 6, 24795 (2016).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  8. 8.

    Rosales, H. D., Cabra, D. C. & Pujol, P. Three-sublattice skyrmion crystal in the antiferromagnetic triangular lattice. Phys. Rev. B 92, 214439 (2015).

    ADS  Google Scholar 

  9. 9.

    Díaz, S. A., Klinovaja, J. & Loss, D. Topological magnons and edge states in antiferromagnetic skyrmion crystals. Phys. Rev. Lett. 122, 187203 (2019).

    ADS  PubMed  Google Scholar 

  10. 10.

    Kamiya, Y. & Batista, C. D. Magnetic vortex crystals in frustrated Mott insulator. Phys. Rev. X 4, 011023 (2014).

    Google Scholar 

  11. 11.

    Lin, S.-Z., Saxena, A. & Batista, C. D. Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy. Phys. Rev. B 91, 224407 (2015).

    ADS  Google Scholar 

  12. 12.

    Yu, X. Z. et al. Transformation between meron and skyrmion topological spin textures in a chiral magnet. Nature 564, 95–98 (2018).

    ADS  CAS  PubMed  Google Scholar 

  13. 13.

    Wen, X.-G. Zoo of quantum-topological phases of matter. Rev. Mod. Phys. 89, 041004 (2017).

    ADS  MathSciNet  Google Scholar 

  14. 14.

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

    ADS  CAS  PubMed  Google Scholar 

  15. 15.

    Yu, X. et al. Skyrmion ow near room temperature in an ultralow current density. Nat. Commun. 3, 988 (2012).

    ADS  CAS  PubMed  Google Scholar 

  16. 16.

    White, J. S. et al. Electric field control of the skyrmion lattice in Cu2OSeO3. J. Phys. Condens. Matter 24, 432201 (2012).

    CAS  PubMed  Google Scholar 

  17. 17.

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

    ADS  PubMed  Google Scholar 

  18. 18.

    Kurumaji, T. et al. Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet. Science 365, 914–918 (2019).

    ADS  CAS  PubMed  Google Scholar 

  19. 19.

    Hirschberger, M. et al. Skyrmion phase and competing magnetic orders on a breathing kagomé lattice. Nat. Commun. 10, 5831 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  20. 20.

    Khanh, N. D. et al. Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet. Nat. Nanotechnol. 15, 444–449 (2020).

    ADS  CAS  PubMed  Google Scholar 

  21. 21.

    Sokolov, D. A. et al. Metamagnetic texture in a polar antiferromagnet. Nat. Phys. 15, 671–677 (2019).

    CAS  Google Scholar 

  22. 22.

    Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010).

    ADS  CAS  PubMed  Google Scholar 

  23. 23.

    Okubo, T., Chung, S. & Kawamura, H. Multiple-q states and the skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields. Phys. Rev. Lett. 108, 017206 (2012).

    ADS  PubMed  Google Scholar 

  24. 24.

    Leonov, A. O. & Mostovoy, M. Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet. Nat. Commun. 6, 8275 (2015).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  25. 25.

    Sutcliffe, P. Skyrmion knots in frustrated magnets. Phys. Rev. Lett. 118, 247203 (2017).

    ADS  PubMed  Google Scholar 

  26. 26.

    Rybakov, F. N. et al. Magnetic hopfions in solids. Preprint at (2019).

  27. 27.

    Lohani, V., Hickey, C., Masell, J. & Rosch, A. Quantum skyrmions in frustrated ferromagnets. Phys. Rev. X 9, 041063 (2019).

    CAS  Google Scholar 

  28. 28.

    Fritsch, V. et al. Spin and orbital frustration in MnSc2S4 and FeSc2S4. Phys. Rev. Lett. 92, 116401 (2004).

    ADS  CAS  PubMed  Google Scholar 

  29. 29.

    Gao, S. et al. Spiral spin-liquid and the emergence of a vortex-like state in MnSc2S4. Nat. Phys. 13, 157–161 (2017).

    CAS  Google Scholar 

  30. 30.

    Bergman, D., Alicea, J., Gull, E., Trebst, S. & Balents, L. Order-by-disorder and spiral spin liquid in frustrated diamond-lattice antiferromagnets. Nat. Phys. 3, 487–491 (2007).

    CAS  Google Scholar 

  31. 31.

    Lee, S. & Balents, L. Theory of the ordered phase in A-site antiferromagnetic spinels. Phys. Rev. B 78, 144417 (2008).

    ADS  Google Scholar 

  32. 32.

    Iqbal, Y., Müller, T., Jeschke, H. O., Thomale, R. & Reuther, J. Stability of the spiral spin liquid in MnSc2S4. Phys. Rev. B 98, 064427 (2018).

    ADS  CAS  Google Scholar 

  33. 33.

    Zaharko, O. et al. Spin liquid in a single crystal of the frustrated diamond lattice antiferromagnet CoAl2O4. Phys. Rev. B 84, 094403 (2011).

    ADS  Google Scholar 

  34. 34.

    MacDougall, G. J. et al. Revisiting the ground state of CoAl2O4: comparison to the conventional antiferromagnet MnAl2O4. Phys. Rev. B 94, 184422 (2016).

    ADS  Google Scholar 

  35. 35.

    Ge, L. et al. Spin order and dynamics in the diamond-lattice Heisenberg antiferromagnets CuRh2O4 and CoRh2O4. Phys. Rev. B 96, 064413 (2017).

    ADS  Google Scholar 

  36. 36.

    Watanabe, H. On the ground level splitting of Mn++ and Fe+++ in nearly cubic crystalline field. Prog. Theor. Phys. 18, 405–420 (1957).

    ADS  CAS  Google Scholar 

  37. 37.

    Akagi, Y., Udagawa, M. & Motome, Y. Hidden multiple-spin interactions as an origin of spin scalar chiral order in frustrated Kondo lattice models. Phys. Rev. Lett. 108, 096401 (2012).

    ADS  PubMed  Google Scholar 

  38. 38.

    Hayami, S., Ozawa, R. & Motome, Y. Effective bilinear–biquadratic model for noncoplanar ordering in itinerant magnets. Phys. Rev. B 95, 224424 (2017).

    ADS  Google Scholar 

  39. 39.

    Milde, P. et al. Unwinding of a skyrmion lattice by magnetic monopoles. Science 340, 1076–1080 (2013).

    ADS  CAS  PubMed  Google Scholar 

  40. 40.

    Karube, K. et al. Robust metastable skyrmions and their triangular-square lattice structural transition in a high-temperature chiral magnet. Nat. Mater. 15, 1237–1242 (2016).

    ADS  CAS  PubMed  Google Scholar 

  41. 41.

    Attig, J. & Trebst, S. Classical spin spirals in frustrated magnets from free-fermion band topology. Phys. Rev. B 96, 085145 (2017).

    ADS  Google Scholar 

  42. 42.

    Balla, P., Iqbal, Y. & Penc, K. Affine lattice construction of spiral surfaces in frustrated Heisenberg models. Phys. Rev. B 100, 140402 (2019).

    ADS  CAS  Google Scholar 

  43. 43.

    Göbel, B., Mook, A., Henk, J. & Mertig, I. Antiferromagnetic skyrmion crystals: generation, topological Hall, and topological spin Hall effect. Phys. Rev. B 96, 060406 (2017).

    ADS  Google Scholar 

  44. 44.

    Bessarab, P. F. et al. Stability and lifetime of antiferromagnetic skyrmions. Phys. Rev. B 99, 140411 (2019).

    ADS  CAS  Google Scholar 

  45. 45.

    van Hoogdalem, K. A., Tserkovnyak, Y. & Loss, D. Magnetic texture-induced thermal Hall effects. Phys. Rev. B 87, 024402 (2013).

    ADS  Google Scholar 

  46. 46.

    Daniels, M. W., Yu, W., Cheng, R., Xiao, J. & Xiao, D. Topological spin Hall effects and tunable skyrmion Hall effects in uniaxial antiferromagnetic insulators. Phys. Rev. B 99, 224433 (2019).

    ADS  CAS  Google Scholar 

  47. 47.

    Roldán-Molina, A., Nunez, A. S. & Fernández-Rossier, J. Topological spin waves in the atomic-scale magnetic skyrmion crystal. New J. Phys. 18, 045015 (2016).

    ADS  Google Scholar 

  48. 48.

    Krimmel, A. et al. Magnetic ordering and spin excitations in the frustrated magnet MnSc2S4. Phys. Rev. B 73, 014413 (2006).

    ADS  Google Scholar 

  49. 49.

    Boehm, M. et al. ThALES—three axis low energy spectroscopy for highly correlated electron systems. Neutron News 26, 18–21 (2015).

    Google Scholar 

  50. 50.

    Zaharko, O. et al. Spin dynamics in the order-by-disorder candidate MnSc2S4. Report (Institut Laue-Langevin, 2016).

  51. 51.

    Schneidewind, A. & Čermák, P. PANDA: cold three axes spectrometer. J. Large-Scale Res. Facilities 1, A12 (2015).

    Google Scholar 

  52. 52.

    Utschick, C., Skoulatos, M., Schneidewind, A. & Böni, P. Optimizing the triple-axis spectrometer PANDA at the MLZ for small samples and complex sample environment conditions. Nucl. Instr. Meth. Phys. Res. A 837, 88–91 (2016).

    ADS  CAS  Google Scholar 

  53. 53.

    Toth, S. & Lake, B. Linear spin wave theory for single-Q incommensurate magnetic structures. J. Phys. Condens. Matter 27, 166002 (2015).

    ADS  CAS  PubMed  Google Scholar 

  54. 54.

    Johnston, D. C. et al. Magnetic exchange interactions in BaMn2As2: a case study of the J 1-J 2-J c Heisenberg model. Phys. Rev. B 84, 094445 (2011).

    ADS  Google Scholar 

  55. 55.

    Kézsmárki, I. et al. Néel type skyrmion lattice with confined orientation in the polar magnetic semiconductor GaV4S8. Nat. Mater. 14, 1116–1122 (2015).

    ADS  PubMed  Google Scholar 

Download references


We acknowledge S. Tóth and S. Ward for help in the analysis of the neutron spectra. We thank A. Scaramucci for the initial trial of the Monte Carlo simulations. We acknowledge discussions with M. Pregelj, S. B. Lee, T.-h. Arima, T. Nakajima, J. S. White and Y. Su. S.G. acknowledges discussions at RIKEN CEMS. F.A.G.A. and H.D.R thank R. Borzi for discussions. H.D.R. thanks M. Zhitomirsky for discussions about the Monte Carlo simulations. Our neutron scattering experiments were performed at the SINQ, PSI, Villigen, Switzerland, at MLZ, Garching, Germany and at ILL, Grenoble, France. This work was supported by the Swiss National Science Foundation under grant numbers 20021-140862 and 20020-152734, by the SCOPES project number IZ73Z0-152734/1 and by Centro Latinoamericano-Suizo under the Seed money grant number SMG1811. Our work was additionally supported by Deutsche Forschungsgemeinschaft of the Transregional Collaborative Research Center TRR 80. D.C.C., F.A.G.A. and H.D.R. are partially supported by CONICET (PIP 2015-813), SECyT UNLP PI+D X792 and X788, PPID X039. H.D.R. acknowledges support from PICT 2016-4083.

Author information




O.Z. designed and coordinated the project. V.T. prepared the single crystals. S.G., O.Z. and C.R. performed the INS experiments with T.F. as the local contact for FOCUS, P.S. and M.B. for ThALES and P.C. and A.S. for PANDA. S.G. analysed the neutron spectra with input from O.Z., T.F. and C.R. Neutron diffraction experiments were performed by G.K. and O.Z, with E.R. as the local contact. Theoretical analysis and Monte Carlo simulations were performed by H.D.R., F.A.G.A. and D.C.C. The manuscript was prepared by S.G., H.D.R. and O.Z. with input from all co-authors.

Corresponding author

Correspondence to Oksana Zaharko.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Yoshitomo Kamiya and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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 Fig. 1 Comparison of different spin models.

a, INS spectra S(Q, ω) collected on FOCUS at T = 1.3 K using a powder sample of MnSc2S4. bd, INS spectra calculated using the linear spin-wave theory for the J1J2J3 model with J1 = −0.31 K, J2 = 0.46 K and J3 = 0.087 K, as discussed in the main text (b), for the J1J2 model with J1 = −0.71 K, J2 = −0.85 × J1 = 0.60 K (c), and for the J1J2J3 model with parameters calculated from the DFT calculations32, J1 = −0.378 K, J2 = 0.621 K and J3 = 0.217 K. Note the different energy ranges in different panels.

Extended Data Fig. 2 Spiral surface above the long-range order transition.

Spin correlations in the (hk0) plane calculated by Monte Carlo simulations using the J1J2J3 model and the anisotropic perturbation terms with coupling strength listed in the main text. Calculations were performed at T = 2.9 K. Calculations with zero anisotropic perturbations do not affect the results.

Extended Data Fig. 3 Calculated phase diagram with perturbations J|| = −0.01 K and A4 = 0.0016 K.

Phase diagram for MnSc2S4 obtained from Monte Carlo simulations with a field applied along the [111] direction as in the experiment. The colour map shows the calculated absolute value of the total scalar spin chirality, χtot. Squares indicate the phase boundary obtained from the peak position of the calculated magnetic susceptibility in field along the [111] direction. Up-pointing triangles on the boundary of the antiferromagnetic skyrmion lattice (AF-SkL) phase are the middle points of the steep rise/drop in χtot as a function of magnetic field at constant T, and their errors are estimated using the half-width of the transitional region. Left-pointing triangles mark the sudden rise in χtot(T) in constant field. Error bars representing the standard deviations are not shown if their length is smaller than the marker size.

Extended Data Fig. 4 Identifying the triple-q phase.

Magnetic structure factor obtained by simulations in the triple-q phase at T = 1.25 K and B111 = 5.6 T in the (hk0) (a) and (111) (b) planes.

Extended Data Fig. 5 Dependence of the triple-q phase stability on the perturbation terms J||.

ad, Calculated phase diagrams with perturbations J|| = 0.01 K (a), −0.005 K (b), −0.01 K (c) and −0.02 K (d). The single-ion anisotropy A4 is fixed at 0.0016 K. The colour map shows the absolute value of the total scalar spin chirality as in Extended Data Fig. 3. eh, Field dependence of the domain population at T = 0.1 K. Red circles and blue triangles indicate domains with q in and out of the (111) plane, respectively. Yellow squares are the calculated absolute values of the scalar spin chirality. Error bars representing the standard deviations of the mean are smaller than the marker size.

Extended Data Fig. 6 Analytical ansatz for the antiferromagnetic skyrmion lattice.

a, Schematic for the moment directions in each q component of the triple-q structure at ϕ111 = −π (helical), −3π/2 (collinear) and −9π/8 (distorted helical). b, Comparison between the representative magnetic texture for one sublattice in the (111) plane obtained by the analytical ansatz (left) and Monte Carlo simulations (right) performed at T = 0.5 K and B111 = 5 T. The colour scheme indicates the spin component along the [111] direction, and the arrows show the spin component in the (111) plane.

Extended Data Fig. 7 Refinement of the neutron diffraction dataset collected in the triple-q phase.

a, Comparison of observed and calculated intensities for the fractional antiferromagnetic skyrmion lattice. The dataset was collected in the triple-q phase under a magnetic field of 3.5 T along the [111] direction. b, Dependence of the RF2 factor on the phase factor ϕ111. The arrows indicate results for ϕ111 = −π, −3π/2 and −9π/8, which correspond to the triple-q structures with helical, collinear and distorted helical components, respectively. The error bars correspond to the standard deviations of the measured neutron intensities (a) and the refined phase factor (b). c, Magnetic textures for one sublattice in the (111) plane with ϕ111 = −9π/8, −π and −7π/8, showing that in the region −9π/8 ≤ ϕ111 ≤ −7π/8 the triple-q structure always realizes a fractional antiferromagnetic skyrmion lattice, and only the proportion of fractionalization is varied. The colour scheme indicates the spin component along the [111] direction, and the arrows show the spin component in the (111) plane.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gao, S., Rosales, H.D., Gómez Albarracín, F.A. et al. Fractional antiferromagnetic skyrmion lattice induced by anisotropic couplings. Nature 586, 37–41 (2020).

Download citation


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.


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