Abstract
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.
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Data availability
The data that support the findings of this study are available at https://doi.org/10.5281/zenodo.3902757 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.
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Acknowledgements
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.
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Contributions
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.
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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. b–d, INS spectra calculated using the linear spin-wave theory for the J1–J2–J3 model with J1 = −0.31 K, J2 = 0.46 K and J3 = 0.087 K, as discussed in the main text (b), for the J1–J2 model with J1 = −0.71 K, J2 = −0.85 × J1 = 0.60 K (c), and for the J1–J2–J3 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 J1–J2–J3 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||.
a–d, 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. e–h, 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.
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Gao, S., Rosales, H.D., Gómez Albarracín, F.A. et al. Fractional antiferromagnetic skyrmion lattice induced by anisotropic couplings. Nature 586, 37–41 (2020). https://doi.org/10.1038/s41586-020-2716-8
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DOI: https://doi.org/10.1038/s41586-020-2716-8
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