Electric polarization of BiFeO3 (procedure in obtaining net polarization)

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Electric polarization of BiFeO3 (procedure in obtaining net polarization)

Date: 2024/10/29 17:41
Name: Amran Yatmeidhy <yatmeidhy.amran@nims.go.jp>: Dear all,

I tried to calculate the electric polarization of BiFeO3 along [111] direction.
Here are my results using polB of OpenMX:

1) Electric polarization

***************************************************************
Electric polarization (muC/cm^2) : Berry phase
***************************************************************

Background Core Electron Total

Px -0.00000000 -0.00000000 -0.00000093 -0.00000093
Py -0.00000000 -0.00000000 -0.00000172 -0.00000172
Pz -0.00000000 7492.03744942 12.95572100 7504.99317042

I used this input for polB calculation:

11 11 11 #k-grid
1 1 1 #target direction

And this is the quantum polarization based on my cell structure:

2) Quantum polarization (muC/cm^2)

eRix/V 35.41736768 20.44822676 59.40232721
eRiy/V -35.41736768 20.44822676 59.40232721
eRiz/V 0 -40.89645353 59.40232721

I want to know how to properly obtain the net electric polarization by considering the electric polarization from polB calculation and the quantum polarization.

A previous thread (https://www.openmx-square.org/forum/patio.cgi?mode=view&no=2690) discussed the relation between electric and quantum polarizations for obtaining net electric polarization. However, I still do not understand how to get the arbitrary parts of N1, N2, and N3.

Px(net)=Px(Total)+N1*eR1x/V+N2*eR2x/V+N3*eR3x/V
Py(net)=Py(Total)+N1*eR1y/V+N2*eR2y/V+N3*eR3y/V
Pz(net)=Pz(Total)+N1*eR1z/V+N2*eR2z/V+N3*eR3z/V

I hope someone can answer my question.
Thank you very much.

*)
For additional reference, I used this input file of BiFeO3 structure to obtain the *.scfout file:

3) input.dat for the SCF calculation

#
# File Name
#

System.CurrrentDirectory ./ # default=./
System.Name bifeo3
level.of.stdout 1 # default=1 (1-3)
level.of.fileout 0 # default=1 (0-2)
DATA.PATH /home/amranmy/openmx3.9/DFT_DATA19

#
# Definition of Atomic Species
#

Species.Number 3
<Definition.of.Atomic.Species
Fe Fe10.0H-s2p2d2 Fe_PBE19H
Bi Bi10.0-s2p2d2 Bi_PBE19
O O7.0-s2p2 O_PBE19
Definition.of.Atomic.Species>

#
# Atoms
#

Atoms.Number 10
Atoms.SpeciesAndCoordinates.Unit Frac # Ang|AU
<Atoms.SpeciesAndCoordinates
1 Bi 0.0036899999999989 0.0036899999999989 0.0036899999999989 7.5 7.5 off
2 Bi 0.5036899999999989 0.5036899999999989 0.5036899999999989 7.5 7.5 off
3 Fe 0.2232600000000033 0.2232600000000033 0.2232600000000033 10.5 5.5 off
4 Fe 0.7232600000000033 0.7232600000000033 0.7232600000000033 5.5 10.5 off
5 O 0.8891899999999993 0.4349199999999982 0.0330399999999997 3.0 3.0 off
6 O 0.4349199999999982 0.0330399999999997 0.8891899999999993 3.0 3.0 off
7 O 0.0330399999999997 0.8891899999999993 0.4349199999999982 3.0 3.0 off
8 O 0.9349199999999982 0.3891899999999993 0.5330399999999997 3.0 3.0 off
9 O 0.5330399999999997 0.9349199999999982 0.3891899999999993 3.0 3.0 off
10 O 0.3891899999999993 0.5330399999999997 0.9349199999999982 3.0 3.0 off
Atoms.SpeciesAndCoordinates>
Atoms.UnitVectors.Unit Ang # Ang|AU
<Atoms.UnitVectors
2.7903465736272248 1.6110073454160283 4.6799943377191253
-2.7903465736272248 1.6110073454160283 4.6799943377191253
0.0000000000000000 -3.2220146908320566 4.6799943377191253
Atoms.UnitVectors>

#
# SCF or Electronic System
#

scf.XcType GGA-PBE # LDA|LSDA-CA|LSDA-PW|GGA-PBE
scf.SpinPolarization on # On|Off|NC
scf.ElectronicTemperature 300.0 # default=300 (K)
scf.energycutoff 400.0 # default=150 (Ry)
scf.maxIter 300 # default=40
scf.EigenvalueSolver band # DC|GDC|Cluster|Band
scf.Kgrid 11 11 11 # means n1 x n2 x n3
scf.ProExpn.VNA off # default=on
scf.Mixing.Type rmm-diish # Simple|Rmm-Diis|Gr-Pulay|Kerker|Rmm-Diisk
scf.Init.Mixing.Weight 0.001 # default=0.30
scf.Min.Mixing.Weight 0.0001 # default=0.001
scf.Max.Mixing.Weight 0.300 # default=0.40
scf.Mixing.History 40 # default=5
scf.Mixing.StartPulay 30 # default=6
scf.Mixing.EveryPulay 1 # default=5
scf.criterion 1.0e-8 # default=1.0e-6 (Hartree)
#scf.lapack.dste dstevx # dstevx|dstedc|dstegr,default=dstevx

HS.fileout on # on|off, default=off

scf.Hubbard.U on # on|off, default=off
scf.DFTU.Type 1 # 1:Simplified(Dudarev)|2:General, default=1

<Hubbard.U.values # eV
Fe 1s 0.0 2s 0.0 1p 0.0 2p 0.0 1d 4.0 2d 0.0
Bi 1s 0.0 2s 0.0 1p 0.0 2p 0.0 1d 0.0 2d 0.0
O 1s 0.0 2s 0.0 1p 0.0 2p 0.0
Hubbard.U.values>

#
# MD or Geometry Optimization
#

MD.Type Nomd # Nomd|Opt|NVE|NVT_VS|NVT_NH
#MD.Opt.DIIS.History 3 # default=7
#MD.Opt.StartDIIS 20 # default=5
#MD.Opt.EveryDIIS 1000 # default=10
MD.maxIter 1 # default=1
MD.Opt.criterion 1.0e-4 # default=1.0e-4 (Hartree/bohr)

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Re: Electric polarization of BiFeO3 (procedure in obtaining net polarization) ( No.1 )

Date: 2024/10/30 14:29
Name: Naoya Yamaguchi

Dear Amran-san,

It is not clear what the circumstances are since the original case was not left in the previous thread, but my explanation of the earlier discussion seems to lack generality, but basically there is a 2π arbitrariness in the inner product of the reciprocal lattice vector and the electronic contribution to the electric polarization: G_i・P_e=2πe/V, that is, (R_j×R_k)/|R_j×R_k|・P_e=e/|R_j×R_k|=e|R_i||cosθ|/V, where θ is the angle between R_i and R_j×R_k.

Also, the electric polarization in solids can be well defined only by its difference.

Regards,
Naoya Yamaguchi

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