The local electronic states of muon (Mu) as an isotope of hydrogen (H) in high-quality single-crystalline ceria (${\mathrm{CeO}}_2$) are investigated using muon spin rotation/relaxation and first-principles density functional theory (DFT) calculations. Upon positive muon implantation, both paramagnetic (${\mathrm{Mu}}^0$) and diamagnetic (${\mathrm{Mu}}^{*}$) states are observed below $\approx 10\mathrm{K}$. Magnetic field dependence of the ${\mathrm{Mu}}^0$ signals combined with DFT results provides evidence for the formation of a polaron state, consisting of Mu bonded to a ligand oxygen and a $4f$ electron localized on a nearby Ce site. The crystal-orientation dependence of the ${\mathrm{Mu}}^0$ signal suggests strong anisotropy of the $4f$ electron due to the spin-orbit coupling with lifted degeneracy. Furthermore, the ${\mathrm{Mu}}^0$ state exhibits transition to the ${\mathrm{Mu}}^{*}$ state that corresponds to another ${\mathrm{Mu}}^0$ state (exhibiting a diamagnetic response due to fast spin/charge fluctuations) at temperatures above $\approx 10\mathrm{K}$, before disappearing above $\approx 30\mathrm{K}$. These findings suggest rapid diffusive motion of the $4f$ electrons and/or Mu (as well as H) at higher temperatures.

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• Defects
• Ionic conductivity
• Polarons
• Solid oxide fuel cells
• Rare-earth ions
• DFT+U
• Muon spin relaxation & rotation