Electron $g$-value comparison of paramagnetic muonium and hydrogen centers in rutile TiO$_2$

Abstract

Muonium (Mu) is widely used as a model for isolated hydrogen in condensed matter, but whether its electronic state is truly equivalent to that of hydrogen remains to be tested with an orbital-sensitive probe. Here we use double electron-muon resonance to determine the electron $g$ values of the paramagnetic Mu center in rutile TiO$_2$ for magnetic fields along [100], [110], and [001] directions. The obtained $g$ values closely follow those of the H-related Ti$^{3+}$ paramagnetic center in both magnitude and anisotropy. This agreement tests the Mu--H correspondence at the level of the Ti $3d$ electronic state and supports a common localized Ti$^{3+}$ electronic core for the two centers.