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Incommensurate charge order in hole-doped oxides is intertwined with exoticphenomena such as colossal magnetoresistance, high-temperaturesuperconductivity, and electronic nematicity. Here, we map at atomic resolutionthe nature of incommensurate order in a manganite using scanning transmissionelectron microscopy at room temperature and cryogenic temperature ($\sim$ 93K).In diffraction, the ordering wavevector changes upon cooling, a behaviortypically associated with incommensurate order. However, using real spacemeasurements, we discover that the underlying ordered state islattice-commensurate at both temperatures. The cations undergo picometer-scale($\sim $6-11 pm) transverse displacements, which suggests that charge-latticecoupling is strong and hence favors lattice-locked modulations. We furtherunearth phase inhomogeneity in the periodic lattice displacements at roomtemperature, and emergent phase coherence at 93K. Such local phase variationsnot only govern the long range correlations of the charge-ordered state, butalso results in apparent shifts in the ordering wavevector. Theseatomically-resolved observations underscore the importance of lattice couplingand provide a microscopic explanation for putative "incommensurate" order inhole-doped oxides.

Commensurate Stripes and Phase Coherence in Manganites Revealed with Cryogenic Scanning Transmission Electron Microscopy