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Complex polar structures of incommensurate modulations (ICMs) are revealed inchemically modified PbZrO$_3$ perovskite antiferroelectrics using advancedtransmission electron microscopy techniques. The Pb-cation displacements,previously assumed to arrange in a fully-compensated antiparallel fashion, arefound to be either antiparallel but with different magnitudes, or in a nearlyorthogonal arrangement in adjacent stripes in the ICMs. Ab initio calculationscorroborate the low-energy state of these arrangements. Our discovery correctsthe atomic understanding of ICMs in PbZrO$_3$-based perovskiteantiferroelectrics.

Uncompensated Polarization in Incommensurate Modulations of Perovskite Antiferroelectrics