Crystal-field Stark effect on the upconversion light emission spectrum of α−NaYF4 nanoparticles doped with Dy3+,

${\mathrm{NaYF}}_{4}$ nanoparticles (NPs) form in two crystal structures, cubic ($\ensuremath{\alpha}$-phase) and hexagonal ($\ensuremath{\beta}$-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, $\ensuremath{\alpha}$-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 $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{NaYF}}_{4}$ 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 ${\mathrm{NaY}}_{1\ensuremath{-}\ensuremath{\delta}}{\mathrm{RE}}_{\ensuremath{\delta}}{\mathrm{F}}_{4}$ NPs.