Depth-resolved measurement of the Meissner screening profile in a niobium thin film from spin-lattice relaxation of the implanted $\beta$-emitter ${}^8$Li

We report measurements of the Meissner screening profile in a Nb(300 nm)/Al${}_2$O${}_3$ thin film using ${}^8$Li $\beta$-detected nuclear magnetic resonance ($\beta$-NMR). The NMR probe ${}^8$Li was ion-implanted into the Nb film at energies $\le$ 20 keV, corresponding to mean stopping depths comparable to Nb’s magnetic penetration depth $\lambda$. ${}^8$Li’s strong dipole-dipole coupling with the host ${}^{93}$Nb nuclei provided a “cross-relaxation” channel that dominated in low magnetic fields, which conferred indirect sensitivity to the local magnetic field via the spin-lattice relaxation (SLR) rate $1\mathrm{/}{T}_1$. From a fit of the $1\mathrm{/}{T}_1$ data to a model accounting for its dependence on temperature, magnetic field, and ${}^8$Li${}^{+}$ implantation energy, we obtained a magnetic penetration depth ${\lambda }_0$ = 51.5(22) nm, consistent with a relatively short carrier mean-free-path $\mathrm{\ell }$ = 18.7(29) nm typical of similarly prepared Nb films. The results presented here constitute an important step towards using ${}^8$Li $\beta$-NMR to characterize bulk Nb samples with engineered surfaces, which are often used in the fabrication of particle accelerators.