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Shortcomings of meta-GGA functionals when describing magnetism

Fabien Tran, Guillaume Baudesson, Jesús Carrete, Georg K. H. Madsen, Peter Blaha, Karlheinz Schwarz, and David J. Singh
Phys. Rev. B 102, 024407 – Published 6 July 2020
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  • INTRODUCTION
  • METHODS
  • RESULTS
  • DISCUSSION
  • SUMMARY
  • ACKNOWLEDGMENTS
    • References

    Abstract

    Several recent studies have shown that SCAN, a functional belonging to the meta-generalized gradient approximation (MGGA) family, leads to significantly overestimated magnetic moments in itinerant ferromagnetic metals. However, this behavior is not inherent to the MGGA level of approximation since TPSS, for instance, does not lead to such severe overestimations. In order to provide a broader view of the accuracy of MGGA functionals for magnetism, we extend the assessment to more functionals but also to antiferromagnetic solids. The results show that to describe magnetism there is overall no real advantage in using a MGGA functional compared to GGAs. For both types of approximation, an improvement in ferromagnetic metals is necessarily accompanied by a deterioration (underestimation) in antiferromagnetic insulators, and vice versa. We also provide some analysis in order to understand in more detail the relation between the mathematical form of the functionals and the results.

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    • Received 9 April 2020
    • Revised 2 June 2020
    • Accepted 22 June 2020

    DOI:https://doi.org/10.1103/PhysRevB.102.024407

    ©2020 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    AntiferromagnetismFerromagnetism
    1. Physical Systems
    Charge-transfer insulatorsIntermetallic compoundsMott insulatorsStrongly correlated systemsTransition metals
    1. Techniques
    Density functional theory
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Fabien Tran1, Guillaume Baudesson1,2, Jesús Carrete1, Georg K. H. Madsen1, Peter Blaha1, Karlheinz Schwarz1, and David J. Singh3

    • 1Institute of Materials Chemistry, Vienna University of Technology, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria
    • 2Univ Rennes, ENSCR, CNRS, ISCR (Institut des Sciences Chimiques de Rennes) - UMR 6226, F-35000 Rennes, France
    • 3Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211-7010, USA

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    Issue

    Vol. 102, Iss. 2 — 1 July 2020

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    Images

    • Figure 1
      Figure 1

      Magnetic energy ΔEtot as a function of the magnetic moment μS in Fe (a), Ni (b), ZrZn2 (c), and Ni3Al (d).

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    • Figure 2
      Figure 2

      Magnetic energy ΔEtot as a function of the magnetic moment μS in V.

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    • Figure 3
      Figure 3

      Difference ΔεxcSCAN-L−ΔεxcSCAN between the xc magnetic energy density obtained with SCAN and SCAN-L within a (110) plane in Fe (left panel) and FeCo (right panel, the middle atom is Co). The FM states correspond to μS=2.0 and 4.5 μB for Fe and FeCo, respectively. Blue and red regions correspond to negative and positive values, respectively. The regions with the most intense blue/red colors correspond to absolute values above 0.02Ry/bohr3.

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    • Figure 4
      Figure 4

      Valence electron density ρval=ρval↑+ρval↓ in FM Fe plotted from the atom at (0,0,0) until the mid-distance to the atom at (1/2,1/2,1/2). The maximum near d=0.5 bohr is due to the 3d electrons and the spike at the nucleus due to the 4s electrons.

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    • Figure 5
      Figure 5

      Difference ΔεxcPBE−ΔεxcF between the xc magnetic energy density within a (110) plane in Fe obtained with PBE and another functional F. The FM state corresponds to μS=2.0μB. Blue and red regions correspond to negative and positive values, respectively. The regions with the most intense blue/red colors correspond to absolute values above 0.02Ry/bohr3.

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    • Figure 6
      Figure 6

      Difference ΔεxcPBE−ΔεxcHLE17 between the xc magnetic energy density within a (110) plane in Fe obtained with PBE and HLE17. ΔεxcHLE17 is evaluated with the density/KED generated from either the mRPBE (left panel) or the PBE potential (right panel). The FM state corresponds to μS=2.0μB. Blue and red regions correspond to negative and positive values, respectively. The regions with the most intense blue/red colors correspond to absolute values above 0.02Ry/bohr3.

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    • Figure 7
      Figure 7

      xc magnetic energy ΔExc as a function of the magnetic moment μS in Ni.

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    • Figure 8
      Figure 8

      Difference ΔεxcSCAN-L−ΔεxcSCAN between the xc magnetic energy density obtained with SCAN and SCAN-L within a (110) plane in CrSb (left panel, the left atoms are Cr) and within a (100) plane in NiO (right panel, the upper left atom is Ni). The AFM states correspond to an atomic moment (defined according to the Bader volume) of 3.0 μB (Cr) and 1.5 μB (Ni). Blue and red regions correspond to negative and positive values, respectively. The regions with the most intense blue/red colors correspond to absolute values above 0.01Ry/bohr3.

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    • Figure 9
      Figure 9

      Difference ΔεxcPBE−ΔεxcF between the xc magnetic energy density within a (110) plane in CrSb obtained with PBE and another functional F. The AFM state corresponds to a Cr (left atoms) atomic moment of μS=3.0μB (defined according to the Bader volume). Blue and red regions correspond to negative and positive values, respectively. The regions with the most intense blue/red colors correspond to absolute values above 0.01Ry/bohr3.

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    • Figure 10
      Figure 10

      rs,σ, sσ, and ασ for σ=↑ (majority spin) as a function of the distance d for FM Fe plotted along the direction from (0,0,0) to (1/2,1/2,1/2) or (1/2,1/2,0).

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    • Figure 11
      Figure 11

      Enhancement factors Fxc plotted as a function of s (left panels), α (middle panels), or rs (right panels). The value of the two other variables (that are kept fixed) are indicated in the respective panels. Note the different scales on the vertical axis.

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    • Figure 12
      Figure 12

      Spatial average of rs,σ, sσ, ασ, and αL,σ inside a sphere of radius 1.25 bohr centered on the atom in Fe plotted as a function of μS. σ=↑ corresponds to the majority spin.

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