We report a comprehensive muon spin rotation ($mu$SR) study of the prototypical magnetoelectric antiferromagnet Cr$_2$O$_3$. We find the positively charged muon ($mu^+$) occupies several distinct interstitial sites, and displays a rich dynamic behavior involving local hopping, thermally activated site transitions and the formation of a charge-neutral complex composed of a muon and an electron polaron. The discovery of such a complex has implications for the interpretation of $mu$SR spectra in a wide range of magnetic oxides, and opens a route to study the dopant characteristics of interstitial hydrogen impurities in such materials. We address implications arising from implanting a $mu^+$ into a linear magnetoelectric, and discuss the challenges of observing a local magnetoelectric effect generated by the charge of the muon.
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