Breakdown of ion-polarization-correspondence and born effective charges: Algebraic formulas of accurate polarization under field

Polarization, especially of ferroelectrics FEs, is conventionally described by ion positions, e.g., by Born effective charges, where the complete entanglement of electron polarization with that of ions is implicitly assumed. We find that such descriptions or Born effective charge polarization-type approaches break down partially in the presence of high field, owing to the partial disentanglement of electrons with ions. To overcome this, we propose a correction (non-Born effective charge polarization) that calculates both macroscopic and unit-cell-by-unit-cell total polarization accurately. The accuracy of this method is demonstrated in prototypical situations of depolarization field Ed that exists in finite-size or inhomogeneous insulating FEs: paraelectric/FE, FE capacitors, and FE/vacuum. Here, FE/vacuum are shown to be electrically identical to encountering domains. This method provides simple algebraic formulas to calculate total polarization PS and Ed using conventionally estimated polarizations that are obtained from local ion positions. Therefore, it can be easily used in experimental estimations of PS and Ed, including 3D cases. For example, this method reveals that PS varies across ferroelectric/insulator far less than the conventional estimate, which explains substantially reduced Ed and the absence of metallicity. In addition, vortexlike domains are discussed in view of Ed. The partial disentanglement of ion and electron polarization would imply limitation of Ginzburg-Landau framework of ferroelectrics under high field.