Fig. 4: Confirmation of hydrogen bond formation and resulting crystal-field-perturbation upon interstitial H⁺-doping.

a Schematic illustration of interstitial H⁺-doping of the NaMgF₃:Yb/Er lattice to form stable hydrogen bonds (F–H⋯F) that result in crystal-field perturbation. b High-resolution X-ray photoelectron spectroscopy (XPS) (F 1 s) profiles of NaMgF₃:Yb/Er (NMF-H-X) nanocrystals (NCs) with different nominal acetic acid (HAc) additions (X = 0–14.7 mmol). The shift in peak position with increasing HAc addition demonstrates the formation of hydrogen bonds. c, d Crystal-field perturbations lead to limited changes in the bond lengths and bond angles within [ErF₆]³⁻ or [YbF₆]³⁻ (c) as well as significant changes in the differential charge density distribution (d). e Comparison of the ⁴F_9/2 lifetime (τ) of the Er³⁺ emitters in the NMF-H-0 and NMF-H-3.1 NCs at 10 K. f Comparison of the typical absorption spectra of NMF-H-0, NMF-H-3.1, and NMF-H-14.7 NCs at 972 nm (²F_7/2 → ²F_5/2 transition of Yb³⁺). g Experimental (dots) and Fourier-transform fitting results (solid lines) of Yb L_III-edge EXAFS spectra of NMF-H-0, NMF-H-3.1, and NMF-H-14.7 NCs, confirming that the structure of the NaMgF₃:Yb/Er NCs was essentially unchanged after H⁺-doping. R_Yb–F is the average Yb–F interatomic distance. Source data are provided as a Source Data file.