Fig. 3
From: An automatically curated first-principles database of ferroelectrics
Examples of improper (left) and proper (right) polarization curves for BaTiO3 along the \({\hat{c}}\) direction versus distortion from the nonpolar to polar structure, showing the importance of calculating the proper polarization. Due to the change in lattice parameters and volume across the distortion, the quantum of polarization defined for each structure along the \({\hat{c}}\) direction is different. Using these different quanta causes the improper spontaneous polarization predicted by different branches to differ, as can be seen in the polarization values given in the right of the image. In contrast for the proper polarization (right), we re-scale the polarization of each intermediate structure to be in the polar structure’s polarization lattice and use the quantum of polarization as defined by the polar structure. This results in predictions that are branch independent, which is what we use to assess candidates. Note that while, in this specific case, the calculated polarization values for all interpolations were on the same branch, this need not generally be the case.
