Polaronic nature of a muonium-related paramagnetic center in SrTiO$_3$

The hyperfine features and thermal stability of a muonium (Mu)-related paramagnetic center were investigated in the SrTiO$_3$ perovskite titanate via muon spin rotation spectroscopy. The hyperfine coupling tensor of the paramagnetic center was found to have prominent dipolar characteristics, indicating that the electron spin density is dominantly distributed on a Ti site to form a small polaron near an ionized Mu$^+$ donor. Based on a hydrogen-Mu analogy, interstitial hydrogen is also expected to form such a polaronic center in the dilute doping limit. The small activation energy of 30(3) meV found for the thermal dissociation of the Mu$^+$-polaron complex suggests that the strain energy required to distort the lattice is comparable to the electronic energy gained by localizing the electron.