Fig. 1: Theory of crystal-field-perturbation and upconversion luminescence (UCL) enhancement through interstitial H⁺-doping of orthorhombic NaMgF₃:Yb/Er nanocrystals (NCs).

a Schematic illustrations of interstitial H⁺-doping (left), crystal-field perturbation (middle), and UCL enhancement (right). When H⁺ ions are doped into interstitial lattice sites, they form hydrogen bonds with the neighboring F⁻ ions, perturbing the crystal field around the Ln³⁺ ions and relaxing the Ln–F bonds, and thereby mitigating the parity-selection rule of the Ln³⁺ emitter. Thus, under near-infrared (NIR) irradiation, the f_ed and A_ed are greatly enhanced. This means that during the upconversion transition process, the probability of the electrons of Ln³⁺ to undergo the intra-4f transition from the ground state (E₁) to the intermediate level (E₂) and then to the excited state (E₃), as well as the radiation transition probability of electrons falling back from E₃ to E₁, will be increased, thus greatly amplifying the luminescence. b Crystal structure and doping sites of orthorhombic NaMgF₃:Yb/Er NCs. In this system, Ln³⁺ ions substitute Mg²⁺ ions at the octahedral symmetry centers (S₆), and H⁺ ions are doped in interstitial lattice sites. c Formation energy (ΔE_form) per atom for NaMgF₃:Yb³⁺_Mg-V_Na-xH_i NCs as a function of the number of H⁺ interstitial defects (x), as calculated by first-principles density functional theory (DFT). Yb³⁺_Mg represents Yb³⁺ in a Mg²⁺ site, V_Na is a Na⁺ vacancy, and H_i is interstitial H⁺. ΔE_form is the energetic difference between the NaMgF₃:Yb³⁺_Mg-V_Na-xH_i NCs and the isolated constituent atoms. Source data are provided as a Source Data file.