Determination of the nature of fluctuations using ${}^8\mathrm{Li}$ and ${}^9\mathrm{Li}\beta$-NMR and spin-lattice relaxation

We report a comparison of the $1/T_1$ spin-lattice relaxation rates for ${}^9\mathrm{Li}$ and ${}^8\mathrm{Li}$ in Pt and ${\mathrm{SrTiO}}_3$, in order to differentiate between magnetic and electric quadrupolar relaxation mechanisms. In Pt, the ratio of the $1/T_1$ spin relaxation rates $R_{\text{Pt}}$ was found to be 6.82(29), which is close to but less than the theoretical limit of $\sim 7.68$ for pure magnetic relaxation. In ${\mathrm{SrTiO}}_3$ this ratio was found to be 2.7(3), which is close to but larger than the theoretical limit of $\sim 2.14$ expected for pure electric quadrupolar relaxation. These results bring insight into the nature of the fluctuations in the local environment of implanted ${}^8\mathrm{Li}$ observed by $\beta$-NMR.

Figure 1

Properties of the principle $\beta$-decay modes of ${}^8\mathrm{Li}$ and ${}^9\mathrm{Li}$ [11]. The asymmetry ($a$) of each decay mode of ${}^9\mathrm{Li}$ is documented in Table 1. The total asymmetry for ${}^9\mathrm{Li}$ is the sum of the asymmetry weighted by the relevant probability of each decay mode.

Figure 2

SLR spectra for ${}^8\mathrm{Li}^{+}$ (left) and ${}^9\mathrm{Li}^{+}$ (right) implanted in Pt foil with an energy of 18 keV at 300 K under 6.55 T. The solid lines are fits to Eq. (10). Note the different time scales, which reflect the lifetime of each radionuclide. The absolute SLR rate for ${}^9\mathrm{Li}^{+}$ is 1.60(10) and 0.2368(26) for ${}^8\mathrm{Li}^{+}$.

Figure 3

Measured SLR rates for ${}^8\mathrm{Li}$ implanted in Pt. The relaxation rate increases linearly with temperature, appearing insensitive to both implantation energy and magnetic field strength, consistent with a Korringa mechanism [7]. Measurements from this work are highlighted in colored disks, while black diamond markers indicate data from earlier measurements on Pt foil [10]. The solid line is a Korringa fit to all the SLR rates in Pt and differs somewhat from the result of Ofer et al. [10] due to the additional data points from this work.

Figure 4

SLR spectra of ${}^8\mathrm{Li}$ (left) and ${}^9\mathrm{Li}$ (right) in single-crystal ${\mathrm{SrTiO}}_3$ at 300 K. The solid lines are a global fit to Eqs. (3) and (12) where a common parameter $f$ is shared between all spectra.

Figure 5

Field dependence of $1/T_1$ for ${}^8\mathrm{Li}$ and ${}^9\mathrm{Li}$ in ${\mathrm{SrTiO}}_3$ at 300 K. The (orange) triangle represents a linear interpolation at 3.6 mT from the 2.5 and 5 mT ${}^8\mathrm{Li}$ measurements.

Figure 6

Ratios of ${}^9\mathrm{Li}$ to ${}^8\mathrm{Li}1/T_1$ relaxation rates in Pt (weighted average of all measurements) and in the two ${\mathrm{SrTiO}}_3$ samples. The red line represents the weighted average of the measurements in both ${\mathrm{SrTiO}}_3$ samples.