Ferroelectric to incommensurate fluctuations crossover in PbHfO3-PbSnO3

Abstract

A. Models of antiferroelectricsComplexity of antiferroelectrics resulted in a rather large number of different approaches and perspectives in their modeling. To help the reader navigate that, a brief systematization follows.First model of antiferroelectrics is due to Kittel [1], who reduced an (at that time -abstract) antiferroelectric to two inter-penetrating lattices with anti-parallel polarizations. The most studied real antiferroelectric, PbZrO 3 , is much more complex than that, in part -due to the more complex dipole ordering ↑↑↓↓ [24], due to the possibility of alternative incommensurate orderings [9] and due to the presence of anti-phase octahedral tilts as a second type of distortion [24], usually coexisting with the anti-polar ordering of cations.Modern models fall, roughly, into three categories. First -ab-initio analysis [25][26][27] of energy landscape at zero Kelvin, sometimes extended to modeling of finite temperature behavior via molecular dynamics [22,28,29]. Usually this extension needs a parametrization of energy in terms of local ionic displacements around

Tilt-driven antiferroelectricity in PbZrO$_3$

“…Such a critical behavior suggests that the antiferroelectric state of PZO may, in fact, originate from a triggered IC transition [governed, at leading order in φ y , by E tr = Kφ 2 y (∂P y /∂x) 2 ], thus questioning the necessity of the rotopolar mechanism that we propose here. (Note that this same coupling term, E tr , was proposed recently as a driving force towards incommensuration in closely related materials [29].) To rule out this possibility, we have performed constrained-DFT relaxations where the secondary tilt φ x (and hence the rotopolar coupling) is suppressed by hand.…”