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\subsubsection{\texorpdfstring{LCO}{LCO}}
\label{sec:lco}


The nature of magnetic ordering in LaCoO\textsubscript{3} epitaxial thin
films has been the subject of considerable debate. We present direct
observations of the spin-state modulation of Co ions in
LaCoO\textsubscript{3} epitaxial thin films on an atomic scale using
aberration-corrected scanning transmission electron microscopy (STEM),
electron energy loss spectroscopy (EELS), and ab initio calculations
based on density functional theory (DFT) calculations. The results of
an atomic-resolution STEM/EELS study indicate that the superstructure
is not associated with oxygen vacancies; rather, it is associated with
a higher spin state of Co\textsubscript{3}\textsuperscript{+} ions and their
ordering. DFT calculations successfully reproduced the modulation of
lattice spacing with the introduction of spin ordering. This result
identifies the origins of intrinsic phenomena in strained
LaCoO\textsubscript{3} and provides fundamental clues for understanding
ferromagnetism in Co-base oxides.

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