Examination of permittivity for depolarization field of ferroelectric by ab initio calculation, suggesting hidden mechanisms

Electrostatics of depolarization field E(d) in relation to the polarization is studied. In particular, the value of permittivity for E(d) (ε(d)) in prototypical situations of ferroelectrics, including Mehta formula, is examined by ab initio calculations. By using spontaneous polarization P(S) corresponding to accurate experiment ones, we show ε(d) = 1, which suggests that the results of ε(d) ≫ 1 indicate hidden mechanisms; ε(d) = 1 suggests that the effect of E(d) is significant to induce intriguing important phenomena overlooked by ε(d) ≫ 1. A bridge between ε(d) = 1 and ε(d) ≫ 1, i.e. the consistency of ε(d) = 1 with conventional results is presented. The exact electrostatic equality of head-to-head–tail-to-tail domains to free-standing ferroelectrics is deduced. Hence, most stoichiometric clean freestanding monodomain ferroelectrics and head-to-head–tail-to-tail domains are shown unstable regardless of size, unless partially metallic. This verifies the previous results in a transparent manner. This conclusion is shown consistent with a recent hyperferroelectric LiBeSb and “freestanding” monolayer ferroelectrics, of which origin is suggested to be adsorbates. In addition, this restriction is suggested to break in externally strained ultrathin ferroelectrics. The macroscopic formulas of E(d) are found valid down to a several unit-cells, when electronic and atomic-scale surface effects are unimportant and accurate P(S) is used.