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.