[Pw_forum] Convergence of Magnetization in Graphene Monovacancy Supercell

[Haricharan Padmanabhan]

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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20141021/f8246c69/attachment.html>