High-precision luminescence cryothermometry strategy by using hyperfine structure
A novel, to the best of our knowledge, ultralow-temperature luminescence thermometry strategy is proposed, based on a measurement of relative intensities of hyperfine components in the spectra of Ho$^{3+}$ ions doped into a crystal. A $^{7}$LiYF$_4$:Ho$^{3+}$ crystal is chosen as an example. First, we show that temperatures in the range 10-35 K can be measured using the Boltzmann behavior of the populations of crystal-field levels separated by an energy interval of 23 cm$^{-1}$. Then we select the 6089 cm$^{-1}$ line of the holmium $^5I_5 \rightarrow ^5I_7$ transition, which has a well-resolved hyperfine structure and falls within the transparency window of optical fibers (telecommunication S band), to demonstrate the possibility of measuring temperatures below 3 K. The temperature $T$ is determined by a least-squares fit to the measured intensities of all eight hyperfine components using the dependence $I(\nu) = I_1 \exp(-b\nu)$, where $I_1$ and $b = a\nu + \frac{\nu}{kT}$ are fitting parameters and a accounts for intensity variations due to mixing of wave functions of different crystal-field levels by the hyperfine interaction. In this method, the absolute and relative thermal sensitivities grow at $T$ approaching zero as $\frac{1}{T^2}$.and $\frac{1}{T}$, respectively. We theoretically considered the intensity distributions within hyperfine manifolds and compared the results with experimental data. Application of the method to experimentally measured relative intensities of hyperfine components of the 6089 cm$^{-1}$ PL line yielded $T = 3.7 \pm 0.2$ K. For a temperature of 1 K, an order of magnitude better accuracy is expected.