[Pw_forum] Convergence of Magnetization in Graphene Monovacancy Supercell

[BARRETEAU Cyrille]

Dear Haricharan Padmanabhan

The magnetization asociated with a vacancy is known to converge very slowly. As you will see in the following detailed study: PHYSICAL REVIEW B 85, 245443 (2012)
the 6x6 supercell in in fact very small... if you want to get your magnetization converged.

2d systems can have some advantages but also some serious drawbacks due to the very slow convergence of certain quantities related to the bi-dimensionality. This is also why tight-binding is very popular in graphene :-)

good luck

Cyrille



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Cyrille Barreteau
CEA Saclay, IRAMIS, SPEC Bat. 771
91191 Gif sur Yvette Cedex, FRANCE
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DTU Nanotech
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email:     cyrille.barreteau at cea.fr  /  cyrbar at nanotech.dtu.dk
Web:     http://iramis.cea.fr/Pisp/cyrille.barreteau/
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________________________________
De : pw_forum-bounces at pwscf.org [pw_forum-bounces at pwscf.org] de la part de Haricharan Padmanabhan [hari00968 at gmail.com]
Envoyé : mardi 21 octobre 2014 10:43
À : pw_forum at pwscf.org
Objet : [Pw_forum] Convergence of Magnetization in Graphene Monovacancy Supercell

Dear Quantum ESPRESSO users,

I am attempting to estimate the value of the magnetism in Graphene with a mono-vacancy, using supercells of different sizes.

Some background -

- One would expect (from literature) the magnetism to converge to around 1.5 bohr magnetons (uB) as the supercell size is increased.

- Since vacancies result in localized states at the Fermi level (flat bands, or peaks in the DOS), a dense k-point mesh is usually required to accurately estimate (N.up - N.down), and hence the magnetism.

I first obtained convergence with respect to k-point sampling, for a 4x4 supercell (31 atoms + 1 vacancy)

K-point mesh    Total Energy (Ry)
        Total magnetization (uB)

16x16   -355.586        1.29

20x20   -355.586        1.21

24x24   -355.586        1.25

32x32   -355.586        1.27

36x36   -355.586        1.27


A larger 6x6 supercell (71 atoms + 1 vacancy), by conventional wisdom, would require a less dense k-point mesh for convergence. However, even with a dense 32x32 k-point mesh, I get a non-converged value of 0.59 uB for the magnetism. Different calculations with different k-point meshes give me values that oscillate between 0.59 and 1.45 uB, with no apparent pattern. It does not make sense to me to further increase the k-point mesh density.

Clearly, the flat bands at the Fermi level are causing trouble depending on whether they've been bumped slightly above or below the Fermi level, due to inadequate k-point sampling in different calculations. How can I fix this problem? Will doing a manual k-point sampling help?



A part of the input file -


 &system
    ibrav=  4, celldm(1) =27.9, celldm(3) = 1, nat=  71, ntyp= 1,
    ecutwfc =30.0,
    ecutrho = 250.0,
    occupations='smearing', smearing='gaussian', degauss=0.001
    nspin = 2,  starting_magnetization(1)=0.7
 /
 &electrons
    diagonalization='cg'
    mixing_mode = 'plain'
    mixing_beta = 0.1
    conv_thr =  1.0d-6
    electron_maxstep = 200
 /

ATOMIC_SPECIES
 C 12.011  c_pbe_v1.2.uspp.F.UPF

K_POINTS {automatic}
  32 32 1 0 0 0


A part of the output file -


     the Fermi energy is    -1.9682 ev

     total energy              =    -815.17816366 Ry
     Harris-Foulkes estimate   =    -815.17815922 Ry
     estimated scf accuracy    <       0.00000077 Ry

     The total energy is the sum of the following terms:

     one-electron contribution =   -5427.83442348 Ry
     hartree contribution      =    2763.25828072 Ry
     xc contribution           =    -257.55564014 Ry
     ewald contribution        =    2106.95386447 Ry
     smearing contrib. (-TS)   =      -0.00024524 Ry

     total magnetization       =     0.59 Bohr mag/cell
     absolute magnetization    =     0.79 Bohr mag/cell


Thank you.

Haricharan Padmanabhan

Indian Institute of Technology Madras
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