  At variance with structural ferroic phase transitions which give rise to
macroscopic tensors coupled to macroscopic fields, criteria defining
antiferroelectric (AFE) phase transitions are still under discussion due to the
absence of specific symmetry properties characterizing their existence. They
are recognized by the proximity of a ferroelectric (FE) phase induced under
applied electric field, with a double hysteresis loop relating the induced
polarization to the electric field and a typical anomaly of the dielectric
permittivity. Here, we show that there exist indeed symmetry criteria defining
AFE transitions. They relate the local symmetry of the polar crystallographic
sites emerging at an AFE phase transition with the macroscopic symmetry of the
AFE phase. The dielectric properties of AFE transitions are deduced from a
Landau theoretical model in which ferroelectric and ferrielectric phases are
shown to stabilize as the result of specific symmetry-allowed couplings of the
AFE order- parameter with the field-induced polarization.
