${\mathrm{NaYF}}_4$ nanoparticles (NPs) form in two crystal structures, cubic ($\alpha$-phase) and hexagonal ($\beta$-phase), each one presenting a different crystal electric field (CEF) Stark effect, that affects the upconversion (UC) light emission of the NPs when doped with rare-earth elements. Therefore, the knowledge of the CEF parameters, the wave functions, and energy levels of the rare earth (RE) $J$-multiplet is expected to be of great help for the understanding and improvement of the UC light emission. In this work, $\alpha$-phase ${\mathrm{NaYF}}_4$ NPs doped with ${\mathrm{Dy}}^{3+}, {\mathrm{Er}}^{3+}$, or ${\mathrm{Yb}}^{3+}$ were investigated by means of magnetization, electron spin resonance (ESR), and optical spectroscopy techniques. Fittings of the temperature- and magnetic-field-dependent magnetization were performed to determine the fourth- and sixth-order cubic CEF parameters, $B_4$ and $B_6$. The ground state of ${\mathrm{Er}}^{3+}, {\mathrm{Yb}}^{3+}$, and ${\mathrm{Dy}}^{3+}$ in these $\alpha \text{−}{\mathrm{NaYF}}_4$ NPs was confirmed by low-temperature ESR experiments. The obtained CEF parameters were used to write down a total Hamiltonian that allows to determine the CEF Stark splitting for all energy levels of the REs $4f$ unfilled shell. We give details of how the Stark effect affects the overall energy splitting of the various $J$-multiplets and may explain the fine structure of the UC light emission in these cubic ${\mathrm{NaY}}_{1-\delta }{\mathrm{RE}}_{\delta }{\mathrm{F}}_4$ NPs.

中文翻译：

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晶体场斯塔克效应对掺杂 Dy3+、Er3+ 或 Yb3+ 的 α-NaYF4 纳米粒子上转换发光光谱的影响

${\mathrm{氟化钠}}_4$纳米粒子 (NPs) 以两种晶体结构形式形成，立方 ($\alpha$-相）和六角形（$\beta$相），每个都呈现不同的晶体电场（CEF）斯塔克效应，当掺杂稀土元素时，该效应会影响纳米粒子的上转换（UC）光发射。因此，了解稀土（RE）的 CEF 参数、波函数和能级$Ĵ$-multiplet有望对UC发光的理解和改进有很大帮助。在这项工作中，$\alpha$-阶段${\mathrm{氟化钠}}_4$NPs 掺杂${镝}^{3+}, {呃}^{3+}$， 或者${镱}^{3+}$通过磁化，电子自旋共振（ESR）和光谱技术进行了研究。进行温度和磁场相关磁化的拟合以确定四阶和六阶立方 CEF 参数，${乙}_4$和${乙}_6$. 的基态${呃}^{3+}, {镱}^{3+}$， 和${镝}^{3+}$在这些$\alpha \text{-}{\mathrm{氟化钠}}_4$NPs 通过低温 ESR 实验得到证实。获得的 CEF 参数用于记下总哈密顿量，该量允许确定 RE 的所有能级的 CEF Stark 分裂$4F$未填充的外壳。我们详细说明了斯塔克效应如何影响各种能量的整体分裂$Ĵ$-multiplet 并且可以解释这些立方中 UC 光发射的精细结构${无}_{1-\delta }{\mathrm{回覆}}_{\delta }{\mathrm{F}}_4$NP。