Uncompensated Polarization in Incommensurate Modulations of Perovskite Antiferroelectrics

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.