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the last few days I've tried to calculate the phonon-dispersion of SrTiO3 (STO) and EuTiO3 (ETO) using the PHonon package of QE. SCF, DOS, PDOS and Bandsctructure calculation worked well on these materials, I've used a Hubbard-correction for both. My scf.in file for STO looks as follows:

STO:

&CONTROL
    calculation = 'scf'
    outdir = './out/'
    prefix      = 'STO_gamma'
    pseudo_dir  = './nc-sr-04_pbe_stringent_upf/'
/

&SYSTEM
  ! a = 3.94513 # old value before vc-relax.x
  A = 3.93795
  degauss =   0.005
  ecutwfc =   80
  lda_plus_u=.true.
  lda_plus_u_kind = 0
  hubbard_u(1) = 0
  hubbard_u(2) = 5.6
  hubbard_u(3) = 4
  ibrav = 0
  nbnd = 33
  nat = 5
  nosym = .false.
  nspin = 2
  ntyp = 3
  occupations = 'smearing'
  starting_magnetization(1) =   1.0d-01
  starting_magnetization(2) =   1.0d-01
  starting_magnetization(3) =   4.16d-01
/

&ELECTRONS
    conv_thr =  1.d-10
    mixing_beta = 0.7
/

ATOMIC_SPECIES
Sr    87.62000  Sr.upf
Ti   47.86700  Ti.upf
O   15.99940  O.upf

CELL_PARAMETERS {alat}
   0.998180509   0.000000000   0.000000000
   0.000000000   0.998180509   0.000000000
   0.000000000   0.000000000   0.998180509

ATOMIC_POSITIONS {crystal}
Sr           0.0000000000       0.0000000000       0.0000000000
Ti           0.5000000000       0.5000000000       0.5000000000
O            0.5000000000       0.0000000000       0.5000000000
O            0.5000000000       0.5000000000       0.0000000000
O            0.0000000000       0.5000000000       0.5000000000

K_POINTS {automatic}
16 16 16

The pesudopotentials are the norm conserving potentials from pseudo-dojo.org. The bandstructure shows an energy gap of about 3.2 eV with these settings. STO Bandstructure

The ph.x input looks like:

phonon calculation at Gamma point.
&inputph
  outdir = './out/'
  prefix      = 'STO_gamma'
  tr2_ph = 1.0d-3
  nmix_ph = 10
  epsil = .false.
  amass(1) = 87.62000
  amass(2) = 47.86700
  amass(3)  = 15.99940
  fildyn = 'STO_phonon.dyn'
/
0 0 0

The output generated by dynmat.x after applying the acustic sum rule = crystal looks like:

# mode   [cm-1]    [THz]      IR
    1  -6235.76 -186.9435    0.0000
    2  -6235.76 -186.9435    0.0000
    3  -6235.76 -186.9435    0.0000
    4  -4352.85 -130.4953    0.0000
    5  -4352.85 -130.4953    0.0000
    6  -4352.85 -130.4953    0.0000
    7  -4105.78 -123.0883    0.0000
    8  -4105.78 -123.0883    0.0000
    9  -4105.78 -123.0883    0.0000
   10  -2138.73  -64.1174    0.0000
   11  -2138.73  -64.1174    0.0000
   12  -2138.73  -64.1174    0.0000
   13      0.00    0.0000    0.0000
   14      0.00    0.0000    0.0000
   15      0.00    0.0000    0.0000

This calculation alone took over 3 hours only for the gamma point. The input file for my scf calculation of ETO looks like

ETO:

&CONTROL
  calculation = 'scf'
  outdir = './out/'
  prefix = 'EuTiO3'
  pseudo_dir = './pseudo/'
/

&SYSTEM
  a = 3.9611945300
  degauss = 0.01
  ecutrho =   600
  ecutwfc =   75
  lda_plus_u=.true.
  lda_plus_u_kind = 0
  hubbard_u(1) = 9
  hubbard_u(2) = 0
  hubbard_u(3) = 0
  ibrav = 1
  nat = 5
  nosym = .false.
  nspin = 2
  ntyp = 3
  occupations = 'smearing'
  smearing = 'mv'
  starting_magnetization(1) =   4.1176470588d-01
  starting_magnetization(2) =   1.0000000000d-01
  starting_magnetization(3) =   4.1666666667d-01
/

&ELECTRONS
  conv_thr =   1.0000000000d-06
  electron_maxstep = 1000
  mixing_beta =   4.0000000000d-01
/

ATOMIC_SPECIES
Eu     151.964 Eu.GGA-PBE-paw-v1.0.UPF
O      15.9994 O.pbe-n-kjpaw_psl.0.1.UPF
Ti     47.867 ti_pbe_v1.4.uspp.F.UPF

ATOMIC_POSITIONS {crystal}
Eu           0.0000000000       0.0000000000       0.0000000000 
Ti           0.5000000000       0.5000000000       0.5000000000 
O            0.5000000000       0.5000000000       0.0000000000 
O            0.5000000000       0.0000000000       0.5000000000 
O            0.0000000000       0.5000000000       0.5000000000 

K_POINTS {automatic}
6 6 6 0 0 0

Bandstructure with band gap of about 1.05 eV:enter image description here The ph.x input is:

!phonons of EuTiO3 at Gamma
&inputph
  prefix = 'EuTiO3'
  outdir = './out/'
  tr2_ph = 1.0d-14
  amass(1) = 151.964
  amass(2) = 15.9994
  amass(3) =  47.867
  ! epsil = .true.
  ! lraman .true.
  fildyn='EuTiO3.dynG'
 /
0.000000000000000   0.000000000000000   0.000000000000000

Which got me the following phonon frequencies (again asr = crystal):

# mode   [cm-1]    [THz]      IR
    1   -636.90  -19.0939    0.0000
    2   -636.90  -19.0939    0.0000
    3   -636.90  -19.0939    0.0000
    4   -547.18  -16.4041    0.0000
    5   -547.18  -16.4041    0.0000
    6   -547.18  -16.4041    0.0000
    7   -401.41  -12.0340    0.0000
    8   -401.41  -12.0340    0.0000
    9   -401.41  -12.0340    0.0000
   10     -0.00   -0.0000    0.0000
   11     -0.00   -0.0000    0.0000
   12      0.00    0.0000    0.0000
   13     64.61    1.9371    0.0000
   14     64.61    1.9371    0.0000
   15     64.61    1.9371    0.0000

I have a question about these results:

Why is it not possible to set epsil = .true., lraman .true. ?

I hope you are still around and thank you for reading :)

Have a nice day,

Simon

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    $\begingroup$ Although cubic STO is not dynamically stable, I would only expect a subset of frequencies to be imaginary. In your case all frequencies (apart from the three acoustic modes) are imaginary, which suggests that there is something wrong either with the structure or the calculation. $\endgroup$
    – ProfM
    Jun 17 at 20:09

1 Answer 1

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Follow up: Using a fixed occupation it was possible to get the dielectric constant since then QE won't treat the system as a metal anymore. Since STO is not stable at 0K, ph.x only showed imaginary frequencies (see https://arxiv.org/pdf/1506.02382.pdf). As for ETO it might be similar but I am not sure yet.

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