Towards an understanding of antiferroelectricity in PbZrO$_3$ from first principles

For decades, PbZrO$_3$ has been referred to as the prototypical antiferroelectric. According to a recent analysis, an essential requirement for antiferroelectricity is that there is a polar phase almost degenerate with the nonpolar ground state. Indeed, as previously reported, first-principles calculations show that the polar $R3c$ structure of PbZrO$_3$ is only 1 meV per formula unit higher in energy than the nonpolar ground state $Pbam$ structure. Here, we explore the question of how these two structures, which seem to be only distantly related, can be so close in energy. Using first-principles methods we investigate the energy landscape of PbZrO$_3$. We introduce a simple structural model that both describes the relevant, low-energy, structural motifs and captures the gross energy landscape relating to both structures. We use this model (and test with direct first-principles calculations) to explore a possible switching path between the non-polar ground state and the metastable polar structure. Our results provide insight into why PbZrO$_3$ is antiferroelectric, which may prove useful in identifying new antiferroelectric materials.