Measurements of the first-flux-penetration field in surface-treated and coated Nb: Distinguishing between surface pinning and an interface energy barrier

We report measurements of the first-flux-penetration field in surface-treated and coated Nb samples using muon spin rotation ($\mu$SR). Using thin Ag foils as energy moderators for the implanted muon spin-probes, we "profile" the vortex penetration field $\mu_{0} H_{\mathrm{vp}}$ at sub-surface depths on the order of $\sim 10$ $\mathrm{\mu}$m to $\sim 100$ $\mathrm{\mu}$m. In a coated sample [Nb$_3$Sn(2 $\mathrm{\mu}$m)/Nb], we find that $\mu_{0} H_{\mathrm{vp}}$ is depth-independent with a value of 234.5(35) mT, consistent with Nb's metastable superheating field and suggestive of surface energy barrier for flux penetration. Conversely, in a surface-treated sample [Nb baked in vacuum at 120 $^{\circ}$C for 48 h], vortex penetration onsets close to pure Nb's lower critical field $\mu_{0}H_\mathrm{c1} \approx 170$ mT, but increases with increasing implantation depth, consistent with flux-pinning localized at the surface. The implication of these results for technical applications of superconducting Nb, such as superconducting radio frequency (SRF) cavities, is discussed.