On the possibility of magnetic Weyl fermions in non-symmorphic compound PtFeSb

  • Maia G. VergnioryEmail author
  • Luis Elcoro
  • Fabio Orlandi
  • Benjamin Balke
  • Yang-Hao Chan
  • Juergen Nuss
  • Andreas P. Schnyder
  • Leslie M. Schoop
Regular Article
Part of the following topical collections:
  1. Topical issue: Special issue in honor of Hardy Gross


Weyl fermions are expected to exhibit exotic physical properties such as the chiral anomaly, large negative magnetoresistance or Fermi arcs. Recently a new platform to realize these fermions has been introduced based on the appearance of a three-fold band crossing at high symmetry points of certain space groups. These band crossings are composed of two linearly dispersed bands that are topologically protected by a Chern number, and a flat band with no topological charge. In this paper, we present a new way of inducing two kinds of Weyl fermions, based on two- and three-fold band crossings, in the non-symmorphic magnetic material PtFeSb. By means of density functional theory calculations and group theory analysis, we show that magnetic order can split a six-fold degeneracy enforced by non-symmoprhic symmetry to create three- or two-fold degenerate Weyl nodes. We also report on the synthesis of a related phase potentially containing two-fold degenerate magnetic Weyl points and extend our group theory analysis to that phase. This is the first study showing that magnetic ordering has the potential to generate new three-fold degenerate Weyl nodes, advancing the understanding of magnetic interactions in topological materials.


  1. 1.
    X. Wan, A.M. Turner, A. Vishwanath, S.Y. Savrasov, Phys. Rev. B 83, 205101 (2011) ADSCrossRefGoogle Scholar
  2. 2.
    H. Weng, C. Fang, Z. Fang, B.A. Bernevig, X. Dai, Phys. Rev. X 5, 011029 (2015) Google Scholar
  3. 3.
    S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, M.Z. Hasan, Nat. Commun. 6, 7373 (2015) CrossRefGoogle Scholar
  4. 4.
    B.Q. Lv, H.M. Weng, B.B. Fu, X.P. Wang, H. Miao, J. Ma, P. Richard, X.C. Huang, L.X. Zhao, G.F. Chen, Z. Fang, X. Dai, T. Qian, H. Ding, Phys. Rev. X 5, 031013 (2015) Google Scholar
  5. 5.
    S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D.S. Sanchez, B. Wang, A. Bansil, F. Chou, P.P. Shibayev, H. Lin, S. Jia, M.Z. Hasan, Science 349, 613 (2015) ADSCrossRefGoogle Scholar
  6. 6.
    H. Nielsen, M. Ninomiya, Phys. Lett. B 130, 389 (1983) ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    J. Xiong, S.K. Kushwaha, T. Liang, J.W. Krizan, M. Hirschberger, W. Wang, R.J. Cava, N.P. Ong, Science 350, 413 (2015) ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    X. Huang, L. Zhao, Y. Long, P. Wang, D. Chen, Z. Yang, H. Liang, M. Xue, H. Weng, Z. Fang, X. Dai, G. Chen, Phys. Rev. X 5, 031023 (2015) Google Scholar
  9. 9.
    J. Liu, D. Vanderbilt, Phys. Rev. B 90, 155316 (2014) ADSCrossRefGoogle Scholar
  10. 10.
    M. Hirayama, R. Okugawa, S. Ishibashi, S. Murakami, T. Miyake, Phys. Rev. Lett. 114, 206401 (2015) ADSCrossRefGoogle Scholar
  11. 11.
    T.c.v. Bzduš, A. Rüegg, M. Sigrist, Phys. Rev. B 91, 165105 (2015) ADSCrossRefGoogle Scholar
  12. 12.
    A. Cortijo, D. Kharzeev, K. Landsteiner, M.A.H. Vozmediano, Phys. Rev. B 94, 241405 (2016) ADSCrossRefGoogle Scholar
  13. 13.
    A.A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, B.A. Bernevig, Nature 527, 495 (2015) ADSCrossRefGoogle Scholar
  14. 14.
    G. Bian, T.-R. Chang, R. Sankar, S.-Y. Xu, H. Zheng, T. Neupert, C.-K. Chiu, S.-M. Huang, G. Chang, I. Belopolski, D.S. Sanchez, M. Neupane, N. Alidoust, C. Liu, B. Wang, C.-C. Lee, H.-T. Jeng, C. Zhang, Z. Yuan, S. Jia, A. Bansil, F. Chou, H. Lin, M.Z. Hasan, Nat. Commun. 7, 10556 (2016) ADSCrossRefGoogle Scholar
  15. 15.
    S. Singh, A.C. Garcia-Castro, I. Valencia-Jaime, F. Muñoz, A.H. Romero, Phys. Rev. B 94, 161116 (2016) ADSCrossRefGoogle Scholar
  16. 16.
    J. Sánchez-Barriga, M.G. Vergniory, D. Evtushinsky, I. Aguilera, A. Varykhalov, S. Blügel, O. Rader, Phys. Rev. B 94, 161401 (2016) ADSCrossRefGoogle Scholar
  17. 17.
    B. Bradlyn, L. Elcoro, J. Cano, M.G. Vergniory, Z. Wang, C. Felser, M.I. Aroyo, B.A. Bernevig, Nature 547, 298 (2017) ADSCrossRefGoogle Scholar
  18. 18.
    L.M. Schoop, F. Pielnhofer, B.V. Lotsch, Chem. Mater. 30, 3155 (2018) CrossRefGoogle Scholar
  19. 19.
    G. Xu, H. Weng, Z. Wang, X. Dai, Z. Fang, Phys. Rev. Lett. 107, 186806 (2011) ADSCrossRefGoogle Scholar
  20. 20.
    A.A. Burkov, L. Balents, Phys. Rev. Lett. 107, 127205 (2011) ADSCrossRefGoogle Scholar
  21. 21.
    D. Bulmash, C.-X. Liu, X.-L. Qi, Phys. Rev. B 89, 081106 (2014) ADSCrossRefGoogle Scholar
  22. 22.
    M. Hirschberger, S. Kushwaha, Z. Wang, Q. Gibson, S. Liang, C.A. Belvina, B. Bernevig, R. Cava, N. Ong, Nat. Mater. 15, 1161 (2016) ADSCrossRefGoogle Scholar
  23. 23.
    Z. Wang, M.G. Vergniory, S. Kushwaha, M. Hirschberger, E.V. Chulkov, A. Ernst, N.P. Ong, R.J. Cava, B.A. Bernevig, Phys. Rev. Lett. 117, 236401 (2016) ADSCrossRefGoogle Scholar
  24. 24.
    Q. Xu, E. Liu, W. Shi, L. Muechler, C. Felser, Y. Sun, (2018)
  25. 25.
    J.L. Mañes, Phys. Rev. B 85, 155118 (2012) ADSCrossRefGoogle Scholar
  26. 26.
    B.J. Wieder, Y. Kim, A.M. Rappe, C.L. Kane, Phys. Rev. Lett. 116, 186402 (2016) ADSCrossRefGoogle Scholar
  27. 27.
    B. Bradlyn, J. Cano, Z. Wang, M.G. Vergniory, C. Felser, R.J. Cava, B.A. Bernevig, Science 353, aaf5037 (2016) CrossRefGoogle Scholar
  28. 28.
    A. Topp, J.M. Lippmann, A. Varykhalov, V. Duppel, B.V. Lotsch, C.R. Ast, L.M. Schoop, New J. Phys. 18, 125014 (2016) ADSCrossRefGoogle Scholar
  29. 29.
    M. Hellenbrandt, Crystallogr. Rev. 10, 17 (2014) CrossRefGoogle Scholar
  30. 30.
    S. Zhong, J.E. Moore, I. Souza, Phys. Rev. Lett. 116, 077201 (2016) ADSCrossRefGoogle Scholar
  31. 31.
    F. de Juan, A.G. Grushin, T. Morimoto, J.E. Moore, Nat. Commun. 8, 15995 (2017) ADSCrossRefGoogle Scholar
  32. 32.
    G. Chang, S.-Y. Xu, B.J. Wieder, D.S. Sanchez, S.-M. Huang, I. Belopolski, T.-R. Chang, S. Zhang, A. Bansil, H. Lin, M.Z. Hasan, Phys. Rev. Lett. 119, 206401 (2017) ADSCrossRefGoogle Scholar
  33. 33.
    A. Cortijo, Phys. Rev. B 94, 241105 (2016) ADSCrossRefGoogle Scholar
  34. 34.
    L.M. Schoop, A. Topp, J. Lippmann, F. Orlandi, L. Müchler, M.G. Vergniory, Y. Sun, A.W. Rost, V. Duppel, M. Krivenkov, S. Sheoran, P. Manuel, A. Varykhalov, B. Yan, R.K. Kremer, C.R. Ast, B.V. Lotsch, Sci. Adv. 4, eaar2317 (2018) ADSCrossRefGoogle Scholar
  35. 35.
    A. Topp, M. G. Vergniory, M. Krivenkov, A. Varykhalov, F. Rodolakis, J.L. McChesney, B.V. Lotsch, C.R. Ast, L.M. Schoop, J. Phys. Chem. Solids (2017) DOI:
  36. 36.
    B. Bradlyn, M.G. Vergniory, J. Cano, in preparation Google Scholar
  37. 37.
    K.H.J. Buschow, J.H.N. van Vucht, P.G. van Engen, D.B. de Mooij, A.M. van der Kraan, Physica Status Solidi (a) 75, 617 (1983) ADSCrossRefGoogle Scholar
  38. 38.
    P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964) ADSCrossRefGoogle Scholar
  39. 39.
    W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965) ADSCrossRefGoogle Scholar
  40. 40.
    G. Kresse, J. Furthmueller, Comput. Mater. Sci. 6, 15 (1996) CrossRefGoogle Scholar
  41. 41.
    G. Kresse, J. Hafner, Phys. Rev. B 48, 13115 (1993) ADSCrossRefGoogle Scholar
  42. 42.
    G. Kresse, D. Joubert, Phys. Rev. B 59, 1758 (1999) ADSCrossRefGoogle Scholar
  43. 43.
    J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) ADSCrossRefGoogle Scholar
  44. 44.
    D. Hobbs, G. Kresse, J. Hafner, Phys. Rev. B 62, 11556 (2000) ADSCrossRefGoogle Scholar
  45. 45.
    L. Elcoro, B. Bradlyn, Z. Wang, M.G. Vergniory, J. Cano, C. Felser, B.A. Bernevig, D. Orobengoa, G. de la Flor, M.I. Aroyo, J. Appl. Crystallogr. 50, 1457 (2017) CrossRefGoogle Scholar
  46. 46.
    M.G. Vergniory, L. Elcoro, Z. Wang, J. Cano, C. Felser, M.I. Aroyo, B.A. Bernevig, B. Bradlyn, Phys. Rev. E 96, 023310 (2017) ADSCrossRefGoogle Scholar
  47. 47.
    M.I. Aroyo, J.M. Perez-Mato, D. Orobengoa, E. Tasci, G. de la Flor, A. Kirov, Bulg. Chem. Commun. 43, 183 (2011) Google Scholar
  48. 48.
    M.I. Aroyo, J.M. Perez-Mato, C. Capillas, E. Kroumova, S. Ivantchev, G. Madariaga, A. Kirov, H. Wondratschek, Z. Krist. 221, 15 (2006) Google Scholar
  49. 49.
    M.I. Aroyo, A. Kirov, C. Capillas, J.M. Perez-Mato, H. Wondratschek, Acta Cryst. A62, 115 (2006) CrossRefGoogle Scholar
  50. 50.
    H.T. Stokes, D.M. Hatch, B.J. Campbell, D.E. Tanner, J. Appl. Crystallogr. 39, 607 (2006) CrossRefGoogle Scholar
  51. 51.
    J.M. Perez-Mato, S.V. Gallego, L. Elcoro, E. Tasci, M.I. Aroyo, J. Phys.: Condens. Matter 28, 286001 (2016) Google Scholar
  52. 52.
    J. Perez-Mato, S. Gallego, E. Tasci, L. Elcoro, G. de la Flor, M. Aroyo, Ann. Rev. Mater. Res. 45, 217 (2015) ADSCrossRefGoogle Scholar
  53. 53.
    K. Buschow, J. van Vucht, P. van Engen, B. de Mooij, A. van der Kraan, Phys. Status Solidi A 75, 617 (1983) ADSCrossRefGoogle Scholar
  54. 54.
    V.N. Antonov, P.M. Oppeneer, A.N. Yaresko, A.Y. Perlov, T. Kraft, Phys. Rev. B 56, 13012 (1997) ADSCrossRefGoogle Scholar
  55. 55.
    Y. Kim, B. J. Wieder, C.L. Kane, A.M. Rappe, Phys. Rev. Lett. 115, 036806 (2015) ADSCrossRefGoogle Scholar
  56. 56.
    P. Tang, Q. Zhou, S.-C. Zhang, Phys. Rev. Lett. 119, 206402 (2017) ADSCrossRefGoogle Scholar
  57. 57.
    T. Eriksson, R. Lizárraga, S. Felton, L. Bergqvist, Y. Andersson, P. Nordblad, O. Eriksson, Phys. Rev. B 69, 054422 (2004) ADSCrossRefGoogle Scholar
  58. 58.
    S.C. Miller, W.F. Love, Tables of Irreducible Representations of Space Groups and Co-Representations of Magnetic Space Groups (Pruett Press, Boulder, Colorado, 1967) Google Scholar
  59. 59.
    S. Furuseth, K. Selte, A. Kjekshus, Acta Chem. Scand. 19, 735 (1965) CrossRefGoogle Scholar
  60. 60.
    N. Spaldin, Magnetic Materials, Fundamentals and Applications (Cambridge University Press, Cambridge, 2010) Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Maia G. Vergniory
    • 1
    • 2
    • 3
    Email author
  • Luis Elcoro
    • 4
  • Fabio Orlandi
    • 5
  • Benjamin Balke
    • 6
  • Yang-Hao Chan
    • 7
  • Juergen Nuss
    • 8
  • Andreas P. Schnyder
    • 8
  • Leslie M. Schoop
    • 9
  1. 1.Donostia International Physics CenterDonostia-San SebastiánSpain
  2. 2.IKERBASQUE, Basque Foundation for ScienceBilbaoSpain
  3. 3.Department of Applied Physics IIFaculty of Science and Technology, University of the Basque Country UPV/EHUBilbaoSpain
  4. 4.Condensed Matter Physics Department, Faculty of Science and Technology, University of the Basque Country UPV/EHUBilbaoSpain
  5. 5.ISIS Neutron Pulsed Facility, Science and Technology Facilities Council, Rutherford Appleton LaboratoryOxfordUK
  6. 6.Universität Stuttgart, Institut für Materialwissenschaft - Chemische MaterialsyntheseStuttgartGermany
  7. 7.Institute of Atomic and Molecular Sciences, Academia SinicaTaipeiTaiwan
  8. 8.Max-Planck-Institut für FestkörperforschungStuttgartGermany
  9. 9.Department of ChemistryPrinceton UniversityPrincetonUSA

Personalised recommendations