Abstract
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. Abinitio calculations corroborate the low-energy state of these arrangements. Our discovery corrects the atomic understanding of ICMs in PbZrO_{3}-based perovskite antiferroelectrics.
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