ABINIT Discussion Forums

Dear all

I am now trying about the calculations of spontaneous polarization of PbTiO3 and BiGaO3 using Berry phase method. First, I calculated the polarization of PbTiO3 (equilibrium structure). After atomic positions and lattice parameters have been relaxed (first relax only atomic positions and then full optimize), the relaxation results agree well with experimental data and other DFT calculations. So, It give me the confidence to go to the next step, the calculation of polarization using Berry phase method ( which I used berryopt -1, rfdir 1 1 1 within hgh pseudopotential and abinit-6.12.3 as well as ecut 120, ngkpt 8x8x8). After the polarization calculation has been done, ABINIT reported the results as shown below

Polarization in cartesian coordinates (C/m^2):
(the sum of the electronic and ionic Berry phase has been fold into [-1, 1])
Electronic berry phase: 0.305174856E-32 -0.457762284E-32 -0.940815754E+00
Expectation value (PAW only): 0.000000000E+00 0.000000000E+00 0.000000000E+00
Ionic: -0.175921327E-14 -0.175921327E-14 0.157405518E+00
Total: -0.175921327E-14 -0.175921327E-14 -0.783410236E+00

So, I have -0.7834 C/m^2 (only z-direction is significant) for PbTiO3 polarization but the value from reference (Solid State Communications Vo. 152, Issue 17, 2012, pp 1707–1710) is 0.814 C/m^2 which is inconsistent in direction. If I take my side by ignoring the sign and trust only the acceptable amplitude. This calculation may be not the problem. However, when i performed the calculation of BiGaO3 polarization (with equilibrium structure which is hypothetical tetragonal structure). a and c lattice parameters agree well with Chem. Mater., 2005, 17 (6), pp 1376–1380 reference. So, the structural relaxation is clear and can skip to polarization calculation of that equilibrium structure. The polarization results for BiGaO3 (I used PAW with convergence tested i.e., ecut, ecutdg, and mesh grid).

Polarization in cartesian coordinates (C/m^2):
(the sum of the electronic and ionic Berry phase has been fold into [-1, 1])
Electronic berry phase: -0.941827427E+00 -0.941827427E+00 -0.514838897E+00
Expectation value (PAW only): 0.000000000E+00 0.000000000E+00 -0.706390224E-02
Ionic: 0.470913746E+00 0.470913746E+00 0.811720979E+00
Total: -0.470913812E+00 -0.470913812E+00 0.289818180E+00

If I consider only along [100] direction, I then have -0.470913812 C/m^2 which both sign and magnetude is inconsistent with the results form above Ref. (1.519 C/m^2). If this is because the sum of the electronic and ionic Berry phase has been fold into [-1, 1], How can I know the total polarization is really in [-1,1] or implicitly in [-1,1] due to it has been fold ? and I am not clear about the definition of Polarization Direction within Berry phase method. Anyone, please advice me.

Any help and comment will be very appreciated.


Sittichain Pramchu
Ph.D. student
Applied Physics, Department of Physics and Materials Science,
Faculty of science,Chiang Mai University,
Thailand