Effect of an electric field on ferroelectric and piezoelectric properties of brownmillerite Ca2Al2O5

Brownmillerites ${A}_{2}{B}_{2}{\mathrm{O}}_{5}$ are oxides possessing a crystallographic structure that is parent from the perovskite structure ${AB\text{O}}_{3}$ with an ordered sublattice of oxygen vacancies, forming a network of one-dimensional chiral chains of oxygen tetrahedra carrying electric dipoles. The distribution of left-and right-handed chains enables the formation of different, polar or nonpolar, crystallographic phases with close internal energies. We have performed first-principles calculations on the nonmagnetic ${\mathrm{Ca}}_{2}{\mathrm{Al}}_{2}{\mathrm{O}}_{5}$ oxide, chosen as a case study, in order to investigate the effect of an external electric field, applied in the direction parallel to the chains, on the stability of four different crystallographic phases. We found that reversing the direction of the electric polarization in the $Ima2$ phase necessitates going through different intermediate phases. However, we also showed that, even if the application of the electric field allows to change the relative stability of each phase, it cannot be sufficient to change one-chain handedness at low temperature, owing to the high barrier energies, of the order of $\ensuremath{\sim}$1 eV per chain of two tetrahedra, which has to be overpassed. Switching between different phases would thus require applying an electric field at high temperature or with the application of additional stress. Finally, we demonstrated that polar phases, such as $Ima2$ or $Pmc{2}_{1}$, display negative longitudinal piezoelectric coefficients due to the lattice response to the applied electric field.