Simulation of ferroelectric properties of barium titanate

We compute the ferroelectric properties of barium titanate on a microscopic scale by calculating the local electric fields. In contrast to macroscopic or medium field calculations the method of local fields considers all electric fields within the sample taking account of the electrodes by the method of images. In our model, the barium and the oxygen ions are assumed to be fixed point charges with an additional induced dipole moment proportional to the local field. The titanium ions fluctuate in double well potentials, with switching times depending on the local field and on the intrinsic barrier height. The three dimensional model simulations yield a temperature dependent spontaneous polarization and a hysteresis loop of the polarization. We find layers close to the electrodes which are not switchable by external fields. These layers are the nuclei for the polarization reversal after reversal of the external field. In the bulk between these boundary layers, we find ferroelectric as well as antiferroelectric states, depending on the choice of parameters like polarizabilities. In the ferroelectric situation, the total spontaneous polarization may vary, since domains of different sizes and orientations can occur.