Towards a quantum theory of polarization in ferroelectrics: The case ofKNbO3

Abstract

The spontaneous macroscopic polarization of perovskite ${\mathrm{KNbO}}_3$ is calculated as a Berry’s phase using the Bloch functions of the tetragonal crystal. The result P=0.35 C/${\mathrm{m}}^2$ supports the measured value 0.37 C/${\mathrm{m}}^2$ and implies that earlier data from hysteresis loops are too low. The polarization is linear in the ferroelectric distortion; the Born effective charges show strong variations from nominal ionic values and a large inequivalence of the O ions. Linearity posteriori demonstrates that the polarization of perovskites at finite temperature can be safely predicted assuming the ions frozen in their time-averaged positions.