dipolar vortices and octahedral super-tilting versus quantum suppression*

PbZrO₃ and PbHfO₃ are still considered the antiferroelectric (AFE) archetypes despite their shared complex crystal structure and plethora unresolved questions regarding the paraelectric to AFE phase transition. In this work, we question the the nature of the ground state AFE phase of both materials. That is, first principles density functional theory (DFT) simulations of AFE PbZrO₃ and PbHfO₃ reveal a dynamical instability in the phonon spectra of their purported low temperature Pbam ground states. This instability doubles the c-axis of Pbam and condenses five new small amplitude phonon modes giving rise to an 80-atom Pnam structure. Compared with Pbam, the stability of this new structure is slightly enhanced and highly reproducible as demonstrated through using different DFT codes and different treatments of electronic exchange & correlation interactions. Remarkably, one unstable mode condenses dipolar vortex-antivortex pairs reminiscent of those observed in PbTiO₃/SrTiO₃ superlattices and ultrathin PbTiO₃ films. Our findings suggest one of three things: (i) Pnam is the correct space-group below the AFE phase transition temperature and previous assignments were incomplete, missing small amplitude symmetry-breaking components (ii) Pnam is the result of a new transition at super-cryogenic temperatures or, most likely, (iii) these new phonon modes are suppressed by quantum fluctuations making PZO and PHO members of a class of quantum suppressed crystals. We rationalize each of these possibilities through pairing experimental and theoretical arguments. With this Pnam phase, we bring parity between the supposed AFE archetypes and recent observations of a very similar phase in doped or electrostatically engineered BiFeO₃.