Local electronic structure and dynamics of hydrogen in CeO 2

The local electronic states of muon (Mu) as an isotope of hydrogen (H) in high-quality single-crystalline ceria (CeO₂) are investigated using muon spin rotation/relaxation (μSR) and first-principles density functional theory (DFT) calculations. Upon positive muon implantation, both paramagnetic (Mu⁰) and diamagnetic (Mu^*) states are observed below ≈10 K. Magnetic field dependence of the Mu⁰ 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 Mu⁰ signal suggests strong anisotropy of the $4f$ electron due to the spin-orbit coupling with lifted degeneracy. Furthermore, the Mu⁰ state exhibits transition to the Mu^* state that corresponds to another Mu⁰ state (exhibiting a diamagnetic response due to fast spin/charge fluctuations) at temperatures above ≈10 K, before disappearing above ≈30 K. These findings suggest rapid diffusive motion of the $4f$ electrons and/or Mu (as well as H) at higher temperatures.