Superconducting properties of thin film $\mathrm{N}{\mathrm{b}}_{1-\mathrm{x}}\mathrm{T}{\mathrm{i}}_{\mathrm{x}}\mathrm{N}$ studied via the NMR of implanted ${}^8$Li

We report measurements of the normal-state and superconducting properties of thin-film $\mathrm{N}{\mathrm{b}}_{1-\mathrm{x}}\mathrm{T}{\mathrm{i}}_{\mathrm{x}}\mathrm{N}$ using ${}^8$Li $\beta$-detected nuclear magnetic resonance ($\beta$-NMR). In these experiments, radioactive ${}^8$Li${}^{+}$ probes were implanted $\sim 21$ nm below the surface of a $\mathrm{N}{\mathrm{b}}_{1-\mathrm{x}}\mathrm{T}{\mathrm{i}}_{\mathrm{x}}\mathrm{N}$(91 nm) film in $\mathrm{N}{\mathrm{b}}_{0.75}\mathrm{T}{\mathrm{i}}_{0.25}\mathrm{N}$(91 nm)/AlN(4 nm)/Nb and its NMR response recorded (via ${}^8$Li’s $\beta$-emissions) between 4.6 K and 270 K in a 4.1 T field applied normal to its surface. Resonance measurements reveal wide, symmetric lineshapes at all temperatures, with significant additional broadening below the film’s superconducting transition temperature $T_{\mathrm{c}}(0\mathrm{T})=15.4\pm 0.7$ K due to vortex lattice formation. Fits to a broadening model find a magnetic penetration depth $\lambda (0\mathrm{K})=180.57\pm 0.30$ nm and upper critical field $B_{\mathrm{c}2}(0\mathrm{K})=18\pm 4$ T, consistent with literature estimates. Spin-lattice relaxation (SLR) measurements find a Korringa response at low temperatures, with dynamic (i.e., thermally activated) contributions dominating above $\sim 100$ K. Below $T_{\mathrm{c}}$, we observe a small Hebel-Slichter coherence peak characterized by a superconducting energy gap $\mathrm{\Delta }(0\mathrm{K})=2.60\pm 0.12$ meV and modest Dynes-like broadening. Our measurements suggest a gap ratio $2\mathrm{\Delta }(0\mathrm{K})\mathrm{/}{k}_{\mathrm{B}}{T}_{\mathrm{c}}(0\mathrm{T})=3.92\pm 0.25$, consistent with strong-coupling behavior. Sources for the dynamic high-$T$ relaxation are suggested.