  The hyperfine structure of the interstitial muonium (Mu) center in rutile
(TiO$_2$, 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 ($\rightarrow \mu^+ +
e^-$) 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.

Materials Science