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.

Weyl-mediated helical magnetism in NdAlSi

Nature Materials volume 20, pages 1650–1656 (2021)Cite this article

Subjects

Abstract

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.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

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.

References

  1. Armitage, N. P., Mele, E. J. & Ashvin, V. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).

    Article  CAS  Google Scholar 

  2. Wan, X., Turner, M. A., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2015).

    Article  Google Scholar 

  3. Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).

    Google Scholar 

  4. Yang, L. X. et al. Weyl semimetal phase in the non-centrosymmetric compound TaAs. Nat. Phys. 11, 728–732 (2015).

    Article  CAS  Google Scholar 

  5. Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).

    Article  CAS  Google Scholar 

  6. Nakatsuji, S., Kiyohara, N. & Higo, T. Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature. Nature 527, 212–215 (2015).

    Article  CAS  Google Scholar 

  7. Kim, K. et al. Large anomalous Hall current induced by topological nodal lines in a ferromagnetic van der Waals semimetal. Nat. Mater. 17, 794–799 (2018).

    Article  CAS  Google Scholar 

  8. Sakai, A. et al. Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal. Nat. Phys. 14, 1119–1124 (2018).

    Article  CAS  Google Scholar 

  9. Liu, D. F. et al. Magnetic Weyl semimetal phase in a Kagomé crystal. Science 365, 1282–1285 (2019).

    Article  CAS  Google Scholar 

  10. Liu, E. et al. Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal. Nat. Phys. 14, 1125–1131 (2018).

    Article  CAS  Google Scholar 

  11. Belopolski, I. et al. Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet. Science 365, 1278–1281 (2019).

    Article  CAS  Google Scholar 

  12. Chang, G. et al. Magnetic and noncentrosymmetric Weyl fermion semimetals in the RAlGe family of compounds (R = rare earth). Phys. Rev. B 97, 041104 (2018).

    Article  CAS  Google Scholar 

  13. Suzuki, T. et al. Singular angular magnetoresistance in a magnetic nodal semimetal. Science 365, 377–381 (2019).

    Article  CAS  Google Scholar 

  14. Puphal, P. et al. Topological magnetic phase in the candidate Weyl semimetal CeAlGe. Phys. Rev. Lett. 124, 017202 (2020).

    Article  CAS  Google Scholar 

  15. Yang, H. Y. et al. Noncollinear ferromagnetic Weyl semimetal with anisotropic anomalous Hall effect. Phys. Rev. B 103, 115143 (2021).

    Article  CAS  Google Scholar 

  16. Wei, H. et al. Crystal structural refinement for NdAlSi. Rare Metals 25, 355–358 (2006).

    Google Scholar 

  17. Lin, H., Rebelsky, L., Collins, M. F., Garret, J. D. & Buyers, W. J. L. Magnetic structure of UNi2Si2. Phys. Rev. B 43, 13232 (1991).

    Article  CAS  Google Scholar 

  18. Wu, S. et al. Incommensurate magnetism near quantum criticality in CeNiAsO. Phys. Rev. Lett. 122, 197203 (2019).

    Article  CAS  Google Scholar 

  19. Rossat-Mignod, J. et al. Phase diagram and magnetic structures of CeSb. Phys. Rev. B 16, 440–461 (1977).

    Article  CAS  Google Scholar 

  20. Gignoux, D. & Schmitt, D. Competition between commensurate and incommensurate phases in rare-earth systems: effects on H-T magnetic phase diagrams. Phys. Rev. B 48, 12682 (1993).

    Article  CAS  Google Scholar 

  21. Taylor, K. N. R. Intermetallic rare-earth compounds. Adv. Phys. 20, 551–660 (1971).

    Article  CAS  Google Scholar 

  22. Jensen, J. & Mackintosh, A. R. Rare Earth Magnetism (Clarendon Press, 1991).

  23. Anisimov, V. I., Aryasetiawan, F. & Lichtenstein, A. I. First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+ U method. J. Phys. Condens. Matter 9, 767 (1997).

    Article  CAS  Google Scholar 

  24. Pizzi, G. et al. Wannier90 as a community code: new features and applications. J. Phys. Condens. Matter 31, 165902 (2020).

    Article  Google Scholar 

  25. Hosseini, M. V. & Askari, M. Ruderman-Kittel-Kasuya-Yosida interaction in Weyl semimetals. Phys. Rev. B 92, 224435 (2015).

    Article  Google Scholar 

  26. Chang, H.-R., Zhou, J., Wang, S.-X., Shan, W.-Y. & Di, X. RKKY interaction of magnetic impurities in Dirac and Weyl semimetals. Phys. Rev. B 92, 241103(R) (2015).

    Article  Google Scholar 

  27. Araki, Y. & Nomura, K. Spin textures and spin-wave excitations in doped Dirac-Weyl semimetals. Phys. Rev. B 93, 094438 (2016).

    Article  Google Scholar 

  28. Wang, S.-X., Hao-Ran Chang, H.-R. & Chang, H.-R. RKKY interaction in three-dimensional electron gases with linear spin-orbit coupling. Phys. Rev. B 96, 115204 (2017).

    Article  Google Scholar 

  29. Nikolić, P. Quantum field theory of topological spin dynamics. Phys. Rev. B 102, 075131 (2020).

    Article  Google Scholar 

  30. Nikolić, P. Dynamics of local magnetic moments induced by itinerant Weyl electrons. Phys. Rev. B 103, 155151 (2021).

    Article  Google Scholar 

  31. Schultz, A. J. et al. Integration of neutron time-of-flight single-crystal Bragg peaks in reciprocal space. J. Appl. Crystallogr. 47, 915–921 (2014).

    Article  CAS  Google Scholar 

  32. Toby, G. H. & Von Dreele, R. B. GSAS-II: the genesis of a modern open-source all purpose crystallography software package. J. Appl. Crystallogr. 46, 544–549 (2013).

    Article  CAS  Google Scholar 

  33. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).

    Article  CAS  Google Scholar 

  34. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 11758 (1999).

    Google Scholar 

  35. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 11758 (1996).

    Article  Google Scholar 

  36. Wu, Q., Zhang, S., Song, H.-F., Troyer, M. & Soluyanov, A. A. WannierTools: an open-source software package for novel topological materials. Comput. Phys. Commun. 224, 405–416 (2018).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy and Institute for Quantum Matter, The Johns Hopkins University, Baltimore, MD, USA

    Jonathan Gaudet, Predrag Nikolić & Collin L. Broholm

  2. NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA

    Jonathan Gaudet, Guangyong Xu, Yang Zhao, Jose A. Rodriguez-Rivera & Collin L. Broholm

  3. Department of Materials Science and Engineering, University of Maryland, College Park, MD, USA

    Jonathan Gaudet, Yang Zhao & Jose A. Rodriguez-Rivera

  4. Department of Physics, Boston College, Chestnut Hill, MA, USA

    Hung-Yu Yang & Fazel Tafti

  5. Department of Physics and Astronomy, Rutgers University, Piscataway, NJ, USA

    Santu Baidya & David Vanderbilt

  6. Department of Physics, Temple University, Philadelphia, PA, USA

    Baozhu Lu & Darius H. Torchinsky

  7. Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    Christina M. Hoffmann

  8. National High Magnetic Field Laboratory, Tallahassee, FL, USA

    David E. Graf

  9. Department of Physics and Astronomy, George Mason University, Fairfax, VA, USA

    Predrag Nikolić

Authors
  1. Jonathan Gaudet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hung-Yu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Santu Baidya
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Baozhu Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Guangyong Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yang Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Jose A. Rodriguez-Rivera
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Christina M. Hoffmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. David E. Graf
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Darius H. Torchinsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Predrag Nikolić
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. David Vanderbilt
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Fazel Tafti
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. Collin L. Broholm
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

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.

Corresponding author

Correspondence to Jonathan Gaudet.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Materials thanks Philippe Bourges 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.

Supplementary information

Supplementary Information

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

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gaudet, J., Yang, HY., Baidya, S. et al. Weyl-mediated helical magnetism in NdAlSi. Nat. Mater. 20, 1650–1656 (2021). https://doi.org/10.1038/s41563-021-01062-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-021-01062-8

This article is cited by

Search

Advanced search

Quick links

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