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From one to three, exploring the rungs of Jacob’s ladder in magnetic alloys

  • Aldo H. Romero
  • Matthieu J. Verstraete
Regular Article
  • 40 Downloads
Part of the following topical collections:
  1. Topical issue: Special issue in honor of Hardy Gross

Abstract

Magnetic systems represent an important challenge for electronic structure methods, in particular Density Functional Theory (DFT), which uses a single determinant wavefunction. To assess the predictions obtained by DFT in this type of materials, we benchmark different exchange correlation functionals with respect to each other, and with respect to available experimental data, on two families of binary iron alloys which are metallic and magnetic. We climb three rungs in Jacob’s ladder of DFT (i) the local density approximation, (ii) the industry standard approximation due to Perdew, Burke and Ernzerhof, and the revised version for solids, PBEsol (iii) and finally a very accurate meta-GGA functional SCAN, which corresponds to the third rung. More than 350 structures in ferromagnetic and antiferromagnetic configurations were considered. We compare the Convex Hull, the calculated magnetic moment, crystal structure, formation energy and electronic gap if present. We conclude that none of the functionals work in all conditions: whereas PBE and PBEsol can give a fair description of the crystal structure and the energetics, SCAN strongly overestimates the formation energy – giving values which are at least twice as large as PBE (and experiment). Magnetic moments are better predicted by PBE as well. Our results show that magnetic and strongly correlated materials are a tough litmus test for DFT, and that they represent the next frontier in the development of a truly universal exchange correlation functionals.

References

  1. 1.
    P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964) ADSCrossRefGoogle Scholar
  2. 2.
    W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965) ADSCrossRefGoogle Scholar
  3. 3.
    Y. Zhao, D.G. Truhlar, Acc. Chem. Res. 41, 157 (2008) CrossRefGoogle Scholar
  4. 4.
    G.E. Scuseria, V.N. Staroverov, in Theory and applications of computational chemistry (Elsevier, 2005), pp. 669–724 Google Scholar
  5. 5.
    C. Fiolhais, F. Nogueira, M.A. Marques, in A primer in density functional theory (Springer Science & Business Media, 2003), Vol. 620 Google Scholar
  6. 6.
    E.K. Gross, R.M. Dreizler, in Density functional theory (Springer Science & Business Media, 2013), Vol. 337 Google Scholar
  7. 7.
    S. Grimme, Wiley Interdiscip Rev. Comput. Mol. Sci. 1, 211 (2011) CrossRefGoogle Scholar
  8. 8.
    A. Tkatchenko, M. Scheffler, Phys. Rev. Lett. 102, 073005 (2009) ADSCrossRefGoogle Scholar
  9. 9.
    M. Dion, H. Rydberg, E. Schröder, D.C. Langreth, B.I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004) ADSCrossRefGoogle Scholar
  10. 10.
    A.D. Becke, J. Chem. Phys. 140, 18A301 (2014) CrossRefGoogle Scholar
  11. 11.
    J.P. Perdew, K. Schmidt, Jacobs ladder of density functional approximations for the exchange-correlation energy, in AIP Conference Proceedings (AIP, 2001), Vol. 577, pp. 1–20 Google Scholar
  12. 12.
    M.G. Medvedev, I.S. Bushmarinov, J. Sun, J.P. Perdew, K.A. Lyssenko, Science 355, 49 (2017) ADSCrossRefGoogle Scholar
  13. 13.
    M.A. Marques, M.J. Oliveira, T. Burnus, Comp. Phys. Commun. 183, 2272 (2012) ADSCrossRefGoogle Scholar
  14. 14.
    S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58, 1200 (1980) ADSCrossRefGoogle Scholar
  15. 15.
    J.P. Perdew, A. Ruzsinszky, J. Tao, V.N. Staroverov, G.E. Scuseria, G.I. Csonka, J. Chem. Phys. 123, 062201 (2005) ADSCrossRefGoogle Scholar
  16. 16.
    J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) ADSCrossRefGoogle Scholar
  17. 17.
    J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, K. Burke, Phys. Rev. Lett. 100, 136406 (2008) ADSCrossRefGoogle Scholar
  18. 18.
    U. von Barth, L. Hedin, J. Phys. C 5, 1629 (1972) ADSCrossRefGoogle Scholar
  19. 19.
    F.G. Eich, E.K.U. Gross, Phys. Rev. Lett. 111, 156401 (2013) ADSCrossRefGoogle Scholar
  20. 20.
    J. Heyd, G.E. Scuseria, M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003) ADSCrossRefGoogle Scholar
  21. 21.
    J. Heyd, G.E. Scuseria, J. Chem. Phys. 120, 7274 (2004) ADSCrossRefGoogle Scholar
  22. 22.
    A. Becke, E. Johnson, J. Chem. Phys. 124, 221101 (2006) ADSCrossRefGoogle Scholar
  23. 23.
    F. Tran, P. Blaha, Phys. Rev. Lett. 102, 226401 (2009) ADSCrossRefGoogle Scholar
  24. 24.
    J.P. Perdew, S. Kurth, A. Zupan, P. Blaha, Phys. Rev. Lett. 82, 2544 (1999) ADSCrossRefGoogle Scholar
  25. 25.
    J. Sun, A. Ruzsinszky, J.P. Perdew, Phys. Rev. Lett. 115, 036402 (2015) ADSCrossRefGoogle Scholar
  26. 26.
    J. Sun, R.C. Remsing, Y. Zhang, Z. Sun, A. Ruzsinszky, H. Peng, Z. Yang, A. Paul, U. Waghmare, X. Wu et al., Nat. Chem. 8, 831 (2016) CrossRefGoogle Scholar
  27. 27.
    H. Peng, Z.H. Yang, J.P. Perdew, J. Sun, Phys. Rev. X 6, 041005 (2016) Google Scholar
  28. 28.
    O. Levy, R.V. Chepulskii, G.L. Hart, S. Curtarolo, J. Am. Chem. Soc. 132, 833 (2009) CrossRefGoogle Scholar
  29. 29.
    S. Curtarolo, W. Setyawan, S. Wang, J. Xue, K. Yang, R.H. Taylor, L.J. Nelson, G.L. Hart, S. Sanvito, M. Buongiorno-Nardelli et al., Comput. Mat. Sci. 58, 227 (2012) CrossRefGoogle Scholar
  30. 30.
    G. Kresse, J. Furthmüller, Phys. Rev. B 54, 11169 (1996) ADSCrossRefGoogle Scholar
  31. 31.
    G. Kresse, D. Joubert, Phys. Rev. B 59, 1758 (1999) ADSCrossRefGoogle Scholar
  32. 32.
    P.E. Blöchl, Phys. Rev. B 50, 17953 (1994) ADSCrossRefGoogle Scholar
  33. 33.
    M. Sternik, S. Couet, J. Łażewski, P. Jochym, K. Parlinski, A. Vantomme, K. Temst, P. Piekarz, J. Alloys Comp. 651, 528 (2015) CrossRefGoogle Scholar
  34. 34.
    A.B. Shick, O.N. Mryasov, Phys. Rev. B 67, 172407 (2003) ADSCrossRefGoogle Scholar
  35. 35.
    M. Annaorazov, S. Nikitin, A. Tyurin, K. Asatryan, A.K. Dovletov, J. Appl. Phys. 79, 1689 (1996) ADSCrossRefGoogle Scholar
  36. 36.
    J. Kudrnovskỳ, V. Drchal, I. Turek, Phys. Rev. B 91, 014435 (2015) ADSCrossRefGoogle Scholar
  37. 37.
    J.M. Jani, M. Leary, A. Subic, M.A. Gibson, Mater. Des. 56, 1078 (2014) CrossRefGoogle Scholar
  38. 38.
    M. Wuttig, J. Li, C. Craciunescu, Scr. Mater. 44, 2393 (2001) CrossRefGoogle Scholar
  39. 39.
    T. Kakeshita, T. Takeuchi, T. Fukuda, M. Tsujiguchi, T. Saburi, R. Oshima, S. Muto, Appl. Phys. Lett. 77, 1502 (2000) ADSCrossRefGoogle Scholar
  40. 40.
    G. Kim, S. Meschel, P. Nash, W. Chen, Sci. Data 4, 170162 (2017) CrossRefGoogle Scholar
  41. 41.
    M.J. Mehl, D. Hicks, C. Toher, O. Levy, R.M. Hanson, G. Hart, S. Curtarolo, Comput. Mater. Sci. 136, S1 (2017) CrossRefGoogle Scholar
  42. 42.
    H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13, 5188 (1976) ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    S. Lany, Phys. Rev. B 78, 245207 (2008) ADSCrossRefGoogle Scholar
  44. 44.
    O. Gutfleisch, J. Lyubina, K.H. Müller, L. Schultz, Adv. Eng. Mater. 7, 208 (2005) CrossRefGoogle Scholar
  45. 45.
    M. Rajagopalan, A. Kashyap, S. Auluck, G. Kalpana, J. Alloys Comp. 240, 124 (1996) CrossRefGoogle Scholar
  46. 46.
    T.B. Massalski, H. Okamoto, P. Subramanian, L. Kacprzak, ASM Int. 1990, 1485 (1990) Google Scholar
  47. 47.
    H. Okamoto, L. Kacprzak, P. Subramanian, Binary alloy phase diagrams (ASM international, 1996) Google Scholar
  48. 48.
    J. Hesse, G. Nölle, H. Körner, Solid State Commun. 46, 721 (1983) ADSCrossRefGoogle Scholar
  49. 49.
    B. Wang, D. Berry, Y. Chiari, K. Barmak, J. Appl. Phys. 110, 013903 (2011) ADSCrossRefGoogle Scholar
  50. 50.
    C.S. Wang, B.M. Klein, H. Krakauer, Phys. Rev. Lett. 54, 1852 (1985) ADSCrossRefGoogle Scholar
  51. 51.
    A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996) ADSCrossRefGoogle Scholar
  52. 52.
    G. Kotliar, S.Y. Savrasov, K. Haule, V.S. Oudovenko, O. Parcollet, C. Marianetti, Rev. Mod. Phys. 78, 865 (2006) ADSCrossRefGoogle Scholar
  53. 53.
    J.M. Tomczak, M. van Schilfgaarde, G. Kotliar, Phys. Rev. Lett. 109, 237010 (2012) ADSCrossRefGoogle Scholar
  54. 54.
    S. Biermann, J. Phys.: Condens. Matter 26, 173202 (2014) Google Scholar
  55. 55.
    S. Kulagin, N. Prokof’ev, O. Starykh, B. Svistunov, C.N. Varney, Phys. Rev. B 87, 024407 (2013) ADSCrossRefGoogle Scholar
  56. 56.
    F. Alet, P. Dayal, A. Grzesik, A. Honecker, M. Körner, A. Läuchli, S. R. Manmana, I. P. McCulloch, F. Michel, R. M. Noack et al., J. Phys. Soc. Japan 74, 30 (2005) CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Physics and AstronomyWest Virginia UniversityMorgantownUSA
  2. 2.European Theoretical Spectroscopy Facility and Nanomat/Q-MAT/CESAM, Université de LiègeLiègeBelgium

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