## 2 Materials and Methods  
**Synthesis of 10%Yb\({}^{3+}\):LiLuF4.** The reagents used in this synthesis are identical to those used in a similar synthesis in previous work [24].  
The following synthesis (Figure 1) is a slight modification of previous work [17]. In contrast to the referenced procedure, yttrium nitrate (Lu(NO\({}_{3}\))) and ytterbium nitrate (Yb(NO\({}_{3}\))) of 99.999% purity were used as purchased from Sigma-Aldrich. The nitrate powders were dissolved in Millipore deionized (DI) water to achieve a stock concentration of the respective nitrates. Additionally, nitric acid (HNO\({}_{3}\)) and ammonium bifluoride (NH\({}_{4}\)HF\({}_{2}\)) were not used in this synthesis. Lithium fluoride (LiF) and polyethylene glycol (PEG, \(M_{\text{n}}\) = 4000) were used directly without any purification. For this synthesis, 28.8 mL of 0.5 M Lu(NO\({}_{3}\))\({}_{3}\) and 3.2 mL of 0.5 M Yb(NO\({}_{3}\))\({}_{3}\) were mixed with 16 mmol of EDTA and 30 mmol of LiOH in 20 mL of Millipore DI water at 50 \({}^{\circ}\)C while stirring for 30 min to form solution A. Subsequently, 64 mmol of LiF were dissolved in 30 mL of 10 wt.% PEG Millipore DI water solution at room temperature while stirring for 1 h to form solution B. Solutions A and B were mixed together while stirring for 30 min to form a homogeneous white suspension, which was transferred to a 2-L Teflon-lined autoclave and heated to 180 \({}^{\circ}\)C for 24 h. After the autoclave cooled to room temperature, the Yb:LLF particles were recovered by centrifuging and washing with ethanol and Millipore DI water three times. The final white powder was obtained by calcining at 300 \({}^{\circ}\)C for 2 h in air, which was determined to be the ideal temperature for calcination via XRD and SEM (Figures S1 and S2). The theoretical yield was 4.120 g of Yb:LLF. The actual yield was 2.0 g, for a yield percentage of 48.5%  
Multiple variations of this base synthesis were performed to examine the effects of different variables on the crystals. In some experiments, the reagent amounts were reduced by a factor of 4. Other syntheses were performed at temperatures other than 180 \({}^{\circ}\)C, including 100, 120, 130, 200, and 220 \({}^{\circ}\)C for 24 h. The effect of time on the synthesis was also examined, with data from some syntheses collected at 3 h, 5 h, and 14 h, as well as the standard 24 h time point.  
**Characterization.** Scanning electron microscopy (SEM) images were taken on an FEI Sirion XL30 SEM at an accelerating voltage of 15 keV. Powder X-ray diffraction (XRD) patterns were obtained on the Bruker F8 Focus Powder XRD with Cu K-\(\alpha\) (40 kV, 40 mA) irradiation (\(\lambda\) = 0.154 nm). The 20 angle of the XRD data was 16\({}^{\circ}\) to 93\({}^{\circ}\), and the scanning rate was 0.36\({}^{\circ}\) s\({}^{-1}\). PL spectra were registered following a method outlined in previous work [24].  
When collecting photoluminescence spectra, Yb:LLF crystals were attached to optical fibers for the sake of thermal isolation. The crystals were then optically excited in air using a 1020 nm diode laser with irradiances ranging from 0.08 to 1 MW/cm\({}^{2}\). Temperatures were calibrated for individual Yb:LLF grains using an optical cryostat. Temperatures were scanned from 300 to 400 K with a low laser irradiance of 0.04 MW/cm\({}^{2}\) to minimize any photothermal effects caused by optical excitation. Cold Brownian motion data were collected using a home-built optical trapping setup and following a procedure from previous work [17].