Local Electronic Structure and Dynamics of Muon-Polaron Complexes in Fe$_2$O$_3$

We perform detailed muon spin rotation ($\mu$SR) measurements in the classic antiferromagnet Fe$_2$O$_3$ and explain the spectra by considering dynamic population and dissociation of charge-neutral muon-polaron complexes. We show that charge-neutral muon states in Fe$_2$O$_3$, despite lacking the signatures typical of charge-neutral muonium centers in nonmagnetic materials, have a significant impact on the measured $\mu$SR frequencies and relaxation rates. Our identification of such polaronic muon centers in Fe$_2$O$_3$ suggests that isolated hydrogen (H) impurities form analogous complexes, and that H interstitials may be a source of charge carrier density in Fe$_2$O$_3$.