Electronic structure of shallow donor state associated with muonium in rutile TiO$_2$

The hyperfine structure of the interstitial muonium (Mu) center in rutile (TiO2, weakly n-type) has been identified by means of muon spin rotation technique. The angle-resolved hyperfine parameter has a tetragonal anisotropy within the ab plane and axial anisotropy along the c axis, strongly suggesting that Mu simulates the known local structure of interstitial hydrogen (H) located at an off-center position within a channel along c axis, and the electron wave function bound to Mu is highly delocalized (∼1.5 nm along c axis, ∼0.8 nm for a axis). The ionization energy of Mu (→ µ + +e − ) due to thermal activation is deduced to be 1.2(4) meV, as is directly inferred from the disappearance of Mu signal above ∼8 K. These observations suggest that electronic level associated with Mu (as well as H) is situated near the bottom of the conduction band, serving as a shallow donor state in rutile.