Antiferroelectricity is a state of matter that has so far eluded a clear-cut definition. Even in the best-known material realization, ${\mathrm{PbZrO}}_3$, the physical nature of the driving force towards an antipolar order has not been settled yet. Here, by building a Landau-like continuum Hamiltonian from first principles via an exact long-wave approach, we reconcile the existing theories in terms of a single physical mechanism. In particular, we find that a formerly overlooked trilinear coupling between tilts, tilt gradients, and polarization provides a surprisingly accurate description of the energetics and structure of the antiferroelectric ground state of ${\mathrm{PbZrO}}_3$. We discuss the relevance of our findings to other ferrielectric and incommensurate polar structures that were recently observed in perovskites.

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• Antiferroelectricity
• Electric polarization
• Ferroelectricity
• Flexoelectricity
• Phase diagrams
• Structural order parameter
• Structural phase transition
• Perovskites
• Density functional theory
• First-principles calculations