  Complex polar structures of incommensurate modulations (ICMs) are revealed in
chemically modified PbZrO$_3$ perovskite antiferroelectrics using advanced
transmission electron microscopy techniques. The Pb-cation displacements,
previously assumed to arrange in a fully-compensated antiparallel fashion, are
found to be either antiparallel but with different magnitudes, or in a nearly
orthogonal arrangement in adjacent stripes in the ICMs. Ab initio calculations
corroborate the low-energy state of these arrangements. Our discovery corrects
the atomic understanding of ICMs in PbZrO$_3$-based perovskite
antiferroelectrics.
