## 3 Results  
Scanning electron microscopy (SEM) of two different Yb:LLF crystals are shown in Figure 2a. In the first case (Figure 2a), the Yb:LLF crystals have been synthesized through an NH\({}_{4}\)HF\({}_{2}\)-assisted hydrothermal method [17; 24]. They have a tetragonal bipyramidal morphology with a dominating (101) surface. The Yb:LLF crystals synthesized through the PEG-assisted hydrothermal method (Figure 2b) have two dominating surfaces: (101) and (112), respectively, which was predicted in [PERSON]'s works [29; 30] for a yttrium lithium fluoride (YLF) crystal. Figure S3 also shows the room-temperature FTIR spectra of the Yb:LLF crystals obtained at different conditions. The weak peaks in the FTIR spectra can be attributed to atmospheric water and carbon dioxide adsorbed on the optical elements of the spectrometer and on the samples, and the absence of strong bands in the range of 1000-4000 cm\({}^{-1}\) implies that there is no residual PEG and minimal oxyfluorides on the surface of the crystals regardless of synthesis method. X-ray diffraction analysis confirms that crystals from both syntheses adopt a tetragonal scheelite structure (ICDD number 04-002-3255) with space group \(I4_{1}/a\) (Figure 2c). Comparison of the two X-ray diffraction spectra of Yb:LLF (Figure 2c) corresponding to NH\({}_{4}\)HF\({}_{2}\)- (blue) and PEG-assisted (red) syntheses gives different ratios of \(I\)(101):\(I\)(112), which correlates with the morphology of the Yb:LLF crystals. Stereographic projections of crystal facets related to the most intensive XRD peaks are shown in Figure 2d (inset) as red circles. Crystals grown using the base PEG-assisted synthesis described previously were subjected to photoluminescence (PL) measurements to examine the cooling abilities of the crystals grown via this new method. Crystals grown via the base synthesis method were used due to the method's ability to consistently produce pure single crystals with only one phase. This avoids issues caused by parasitic energy transfer or luminescence quenching due to impurities, maximizing the laser cooling power of the crystals. The PL spectra obtained at different 1020 nm laser powers are shown in Figure 3a. Changes in the ratio of the integrated emission bands \(R_{1}\) and \(R_{2}\) (and their respective intensities in a.u., \(I_{1}\), and \(I_{2}\)), which stem from transitions between energy states E\({}_{6}\)-E\({}_{1}\) and E\({}_{5}\)-E\({}_{2,3}\), respectively, are directly correlated to a change in the crystal temperature through a Boltzmann distribution  
Figure 1: Schematic of the base PEG-assisted hydrothermal synthesis of Yb:LLF microcrystals. (Figure 3b). Ratiometric spectral measurements were used to calibrate temperature in which ln(I\({}_{1}\)/I\({}_{2}\)) varies linearly with 1/T (calibration shown in Figure S4). The decrease in the logarithmic ratio of \(I_{1}\) to \(I_{2}\) with increasing irradiance reflects a decrease in the internal lattice temperature of approximately 15 K below room temperature (Figure 3b). Analogous laser cooling trends (approximately 5 K below room temperature) were observed for individual Yb:LLF grains optically trapped in water (Figure 3c). These values are comparable to cooling temperatures Yb:LLF crystals obtained via the NH4 HF2-assisted synthesis. [24] Additionally, these crystals exhibit much greater cooling capability than 5%-Yb doped LLF crystals grown via the Czochralski process but do not cool to the cryogenic temperatures reached by Czochralski-grown Yb:YLF crystals [15; 31]. Reducing the concentration of reagents by a factor of four leads to the synthesis of significantly smaller crystals. The low concentration synthesis produced crystals around 5 \(\upmu\)m in size, whereas the standard synthesis could produce crystals as large as 20 \(\upmu\)m. Although their size is greatly changed, the morphology of the crystals remains the same regardless of the reagent concentration. The (112) plane remains clearly visible on both sets of crystals (Figure S5).