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We report $\beta$-detected nuclear magnetic resonance ($\beta$-NMR)measurements in Bi$_{2}$Se$_{3}$:Ca (BSC) and Bi$_{2}$Te$_{3}$:Mn (BTM) singlecrystals 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) inBSC (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 Knightshift in BSC. From this, we make a detailed comparison with the isostructuraltetradymite 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 magnetictransition at 13 K, with a prominent critical peak in the SLR that issuppressed 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 topologicalsurface state (TSS). With the bulk NMR response now established in severalBi$_{2}$Ch$_{3}$ tetradymite topological insulators (TIs), the prospect ofdirectly probing their chiral TSS using the depth resolution afforded by$\beta$-NMR remains strong.

physical review. b./physical review. b

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