Local electronic and magnetic properties of the doped topological insulators Bi\(_{2}\)Se\(_{3}\):Ca and Bi\(_{2}\)Te\(_{3}\):Mn investigated using ion-implanted \(^{8}\)Li \(\beta\)-NMR

We report \(\beta\)-detected nuclear magnetic resonance (\(\beta\)-NMR) measurements in Bi\(_{2}\)Se\(_{3}\):Ca (BSC) and Bi\(_{2}\)Te\(_{3}\):Mn (BTM) single crystals using \(^{8}\)Li\(^{+}\) implanted to depths on the order of 100 nm. Above \(\sim 200\) K, spin-lattice relaxation (SLR) reveals diffusion of \(^{8}\)Li\(^{+}\), with activation energies of \(\sim 0.4\) eV (\(\sim 0.2\) eV) in BSC (BTM). At lower temperatures, the nuclear magnetic resonance (NMR) properties are those of a heavily doped semiconductor in the metallic limit, with Korringa relaxation and a small, negative, temperature-dependent Knight shift in BSC. From this, we make a detailed comparison with the isostructural tetradymite Bi\(_{2}\)Te\(_{2}\)Se (BTS) [McFadden et al., Phys Rev. B 99, 125201 (2019)]. In the magnetic BTM, the effects of the dilute Mn moments predominate, but remarkably the \(^{8}\)Li signal is not wiped out through the magnetic transition at 13 K, with a prominent critical peak in the SLR that is suppressed in a high applied field. This detailed characterization of the \(^{8}\)Li NMR response is an important step towards using depth-resolved \(\beta\)-NMR to study the low-energy properties of the chiral topological surface state (TSS). With the bulk NMR response now established in several Bi\(_{2}\)Ch\(_{3}\) tetradymite topological insulators (TIs), the prospect of directly probing their chiral TSS using the depth resolution afforded by \(\beta\)-NMR remains strong.