$\beta$-detected NMR of ${}^8\mathrm{Li}{}^{+}$ in Bi, Sb, and the topological insulator ${\mathrm{Bi}}_{0.9}{\mathrm{Sb}}_{0.1}$

We report the NMR Knight shift and spin-lattice relaxation of ${}^8\mathrm{Li}{}^{+}$ implanted $\sim 100$ nm into single crystals of semimetallic Sb, Bi, and topologically insulating ${\mathrm{Bi}}_{0.9}{\mathrm{Sb}}_{0.1}$. We find small negative shifts (of order 100 ppm) in all three. In the insulator, the shift is nearly temperature independent, while in Bi and Sb it becomes more negative at low temperature without following the bulk susceptibility, suggesting two distinct temperature dependent contributions, possibly from the orbital and spin response. However, a simple model is unable to account for the observed shift. The spin-lattice relaxation differs in both scale and temperature dependence in all three. It is Korringa-like in Bi and remarkably is fastest in the insulating alloy and slowest in Sb with the highest bulk carrier density. These surprising results call for detailed calculations, but phenomenologically demonstrate that $\beta$-detected NMR of implanted ${}^8\mathrm{Li}{}^{+}$ is sensitive to the magnetic response of low-density carriers. The prospects for depth-resolved studies of conventional and topological surface states at lower implantation energies are good.

Figure 1

Calculated implantation profiles for ${}^8\mathrm{Li}{}^{+}$ in Bi, Sb, and ${\mathrm{Bi}}_{0.9}{\mathrm{Sb}}_{0.1}$ from srim2013 [22] at the energies used in the experiment. The mean range is about 100 nm and a negligible fraction of the ${}^8\mathrm{Li}{}^{+}$ stop in the top 10 nm, where one may expect the properties to be modified by surface states.

Figure 2

The resonance spectrum of ${}^8\mathrm{Li}{}^{+}$ in bismuth, exhibiting four broader quadrupolar satellites and three sharper multiquantum resonances. (a) The combined asymmetry spectrum (combining the two helicities) together with a fit described in the text. The vertical dashed line marks the position of the resonance of ${}^8\mathrm{Li}{}^{+}$ in MgO at 300 K in this field, chosen as the reference of zero shift. (b) The spectra for the two laser helicities, the asymmetry of the spectrum about its center confirms the quadrupolar nature of the splitting.

Figure 3

(a) The helicity-combined and (b) helicity-resolved spectra in antimony at 300 K. The curve in (a) is the fit described in the text. The slight asymmetry in (b) may reflect unresolved quadrupolar splittings.

Figure 4

The resonance of ${}^8\mathrm{Li}{}^{+}$ in the ${\mathrm{Bi}}_{0.9}{\mathrm{Sb}}_{0.1}$ crystal, showing no evidence of resolved quadrupolar splitting. (a) The combined asymmetry together with the fit described in the text. (b) The helicity-resolved spectra show only a slight asymmetry.

Figure 5

As a function of temperature, from fits to the resonance spectra for ${}^8\mathrm{Li}{}^{+}$ in Bi (red triangles), Sb (black circles), and ${\mathrm{Bi}}_{0.9}{\mathrm{Sb}}_{0.1}$ (blue squares): (a) the raw shift from MgO; (b) the demagnetization corrected Knight shift; (c) the demagnetization correction defined by Eq. (2), using literature values of the volume susceptibility ${\chi }_{\parallel }$ (right scale); and (d) the linewidths (HWHM). For bismuth this is the single quantum satellite width. The open green circles are measurements made on a second Sb sample. The field is 6.55 T, except Sb and the open triangles (Bi) where it is 2.2 T.

Figure 6

The time dependence of the asymmetry during and after a 4 s beam pulse at 6.55 T for each sample near room temperature. Single exponential fits excluding the first second are also shown as the solid curves.

Figure 7

The spin-lattice-relaxation rates $\left(1/T_1\right)$ for ${}^8\mathrm{Li}{}^{+}$ in (a) ${\mathrm{Bi}}_{0.9}{\mathrm{Sb}}_{0.1}$, (b) Bi, and (c) Sb in 6.55 T field as a function of temperature. The data for Bi and Sb are replotted in grayscale in panel (a) to show the rates on the same scale. The curves are guides to the eye.

Figure 8

The hexagonal unit cell of the A7 crystal structure. The spheres represent Bi/Sb and the heavy lines represent the layered bonding network with each Bi/Sb bonded to its three nearest neighbors. Two high-symmetry interstitial sites are identified by the stars. They are at the center of a quasicube of surrounding atoms, but the cube is distorted by stretching (P) or compressing (O) along the trigonal axis (red line), along which the magnetic field is applied in the experiment.

Figure 9

The spectra at room temperature (from Figs. 2, 3, 4) shown on the same horizontal scale as shift from MgO in kHz. The vertical scales differ for each. The curves are the fits described in the text.

Figure 10

(a) The calculated Pauli susceptibility for bismuth matched to the Sommerfeld estimate at low temperature [21]. (b) A fit (solid curve) of the corrected shift in Bi to Eq. (13) with $K_{\text{spin}}\left(T\right)$ constrained to $-60$ ppm $(A$ is negative) at low temperature and to follow the temperature dependence in (a). This $K_{\text{spin}}\left(T\right)$ is shown as the dashed curve.