Direct Spectroscopic Observation of a Shallow Hydrogenlike Donor State in Insulating ${\mathrm{SrTiO}}_3$

We present a direct spectroscopic observation of a shallow hydrogenlike muonium state in ${\mathrm{SrTiO}}_3$ which confirms the theoretical prediction that interstitial hydrogen may act as a shallow donor in this material. The formation of this muonium state is temperature dependent and appears below $\sim 70\mathrm{K}$. From the temperature dependence we estimate an activation energy of $\sim 50\mathrm{meV}$ in the bulk and $\sim 23\mathrm{meV}$ near the free surface. The field and directional dependence of the muonium precession frequencies further supports the shallow impurity state with a rare example of a fully anisotropic hyperfine tensor. From these measurements we determine the strength of the hyperfine interaction and propose that the muon occupies an interstitial site near the face of the oxygen octahedron in ${\mathrm{SrTiO}}_3$. The observed shallow donor state provides new insight for tailoring the electronic and optical properties of ${\mathrm{SrTiO}}_3$-based oxide interface systems.

Figure 1

The normalized diamagnetic fraction of the ${\mu }^{+}$ precession signal at $B=10\mathrm{mT}$ as a function of temperature. Circles, squares, and triangles are measurements at 4.1 MeV ($B\perp ⟨100⟩$), 14.1 keV, and 1.6 keV ($B\parallel ⟨100⟩$), respectively. The drop in asymmetry below $\sim 70\mathrm{K}$ is due to formation of muonium. The dashed lines are fits to Eq. (1).

Figure 2

(a) The asymmetries at $T=25\mathrm{K}$ as a function of time for applied fields 1 and 10 mT ($B\perp ⟨100⟩$) and (b) the corresponding real Fourier transform showing at least four muonium precession frequencies in both cases. The solid lines are fits to a sum of precessing and damping signals.

Figure 3

The asymmetries measured (a) parallel and (b) perpendicular to $⟨100⟩$ at $T=25\mathrm{K}$ and in ZF. (c) and (d) are the corresponding Fourier transform showing clear ZF muonium precession frequencies in both cases. The solid lines are fits to a sum of precessing and damping signals

Figure 4

The observed muonium precession frequencies as a function of applied field (with an angle of $\sim 14°$ between $B$ and $⟨010⟩$) at $T=25\mathrm{K}$. The lines are calculated values with $A_X=1.37$, $A_Y=6.67$, and $A_Z=11.52\mathrm{MHz}$ with $(\alpha ,\beta ,\gamma )=(0°,57°,27°)$ (solid) and $(0°,17°,0°)$ (dashed).