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Weyl-mediated helical magnetism in NdAlSi


Emergent relativistic quasiparticles in Weyl semimetals are the source of exotic electronic properties such as surface Fermi arcs, the anomalous Hall effect and negative magnetoresistance, all observed in real materials. Whereas these phenomena highlight the effect of Weyl fermions on the electronic transport properties, less is known about what collective phenomena they may support. Here, we report a Weyl semimetal, NdAlSi, that offers an example. Using neutron diffraction, we found a long-wavelength helical magnetic order in NdAlSi, the periodicity of which is linked to the nesting vector between two topologically non-trivial Fermi pockets, which we characterize using density functional theory and quantum oscillation measurements. We further show the chiral transverse component of the spin structure is promoted by bond-oriented Dzyaloshinskii–Moriya interactions associated with Weyl exchange processes. Our work provides a rare example of Weyl fermions driving collective magnetism.

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Fig. 1: Crystal structure of NdAlSi.
Fig. 2: Magnetic phase transitions in NdAlSi.
Fig. 3: Commensurate ferrimagnetic spin structure of NdAlSi.
Fig. 4: Quantum oscillations in NdAlSi.
Fig. 5: DFT + U electronic structure for the ferromagnetic phase of NdAlSi including spin–orbit coupling.
Fig. 6: Nesting vector and the \((\frac{2}{3}+\delta ,\frac{2}{3}+\delta ,0)\) magnetic order in NdAlSi.

Data availability

All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Information. Additional data related to this paper may be requested from the authors.


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This work was supported as part of the Institute for Quantum Matter, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences under award no. DE-SC0019331. The work at Boston College was funded by the National Science Foundation under award no. DMR-1708929. C.L.B. and J.G. were supported by the Gordon and Betty Moore Foundation through GBMF9456. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement no. DMR-1644779 and the state of Florida. We also acknowledge the support of the National Institute of Standards and Technology, US Department of Commerce. The identification of any commercial product or trade name does not imply endorsement or recommendation by the National Institute of Standards and Technology. Access to MACS was provided by the Center for High Resolution Neutron Scattering, a partnership between the National Institute of Standards and Technology and the National Science Foundation under agreement no. DMR-1508249. A portion of this research used resources at the Spallation Neutron Source, a Department of Energy Office of Science User Facility operated by the Oak Ridge National Laboratory. S.B. thanks J. Kim for fruitful discussions on the symmetric Wannier function generations from Wannier90. We thank Y. Li for useful discussions. We are also grateful to Y. Chen, Y. Luo, C. Lygouras and Y. Vekhov for their help during neutron scattering experiments.

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Authors and Affiliations



The project was conceived by F.T., J.G., D.V. and C.L.B. Sample synthesis was done by H.-Y.Y. and F.T., and D.H.T. and B.L. performed and analysed the second harmonic generation experiments. The heat capacity and bulk susceptibility measurements were carried out by H.-Y.Y. and analysed by J.G. Neutron scattering experiments were performed by J.G., C.L.B., G.X., Y.Z., J.A.R.-R. and C.M.H. The neutron analysis was performed by J.G. Quantum oscillation measurements were conducted and analysed by H.-Y.Y., F.T. and D.E.G. The DFT calculations were carried out by S.B. and D.V.; P.N. interpreted the data in terms of his theory of exchange interactions mediated by Weyl electrons. The first draught of the paper was written by J.G., H.-Y.Y. and S.B., and all authors contributed with comments and edits.

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Correspondence to Jonathan Gaudet.

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

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Supplementary Information

Supplementary Figs. 1–7 and Tables 1 and 2.

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Gaudet, J., Yang, HY., Baidya, S. et al. Weyl-mediated helical magnetism in NdAlSi. Nat. Mater. 20, 1650–1656 (2021).

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