First-principles and experimental analysis offn−fn−1d1absorption spectra and multiplet energy levels ofPr3+,Nd3+, andU3+inLiYF4

Abstract

We performed experimental and theoretical investigation of the ${f}^{n}\text{\ensuremath{-}}{f}^{n\text{\ensuremath{-}}1}{d}^{1}$ transitions of ${\text{Pr}}^{3+}$, ${\text{Nd}}^{3+}$, and ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$. The $4{f}^{2}\text{\ensuremath{-}}4{f}^{1}5{d}^{1}$ absorption spectra for ${\text{Pr}}^{3+}$ in ${\text{LiYF}}_{4}$ and the $4{f}^{3}\text{\ensuremath{-}}4{f}^{2}5{d}^{1}$ absorption spectra for ${\text{Nd}}^{3+}$ in ${\text{LiYF}}_{4}$ were measured using a synchrotron radiation light source at several different temperatures while the $5{f}^{3}\text{\ensuremath{-}}5{f}^{2}6{d}^{1}$ absorption spectra for ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$ referred to report of Hubert et al. The multiplet energy levels and ${f}^{n}\text{\ensuremath{-}}{f}^{n\text{\ensuremath{-}}1}{d}^{1}$ absorption spectra were calculated by a first-principles four-component relativistic configuration-interaction method. For all calculations of ${\text{Nd}}^{3+}$ and ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$, we used the Dirac-Coulomb-Breit Hamiltonian and the molecular spinors obtained from the relativistic Vosko-Wilk-Nusair potential. The overall features of the theoretical absorption spectra of both ${\text{Nd}}^{3+}$ and ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$ reproduced the experimental features well. The origins of the experimental absorption spectra were clarified by performing a configuration analysis based on the many-electron wave functions. The splitting between peaks were affected by both spin-orbit interaction of $f$ orbitals and crystal-field splitting of $d$ orbitals. We found that the oscillator strengths of the $4{f}^{3}\text{\ensuremath{-}}4{f}^{2}5{d}^{1}$ transition for ${\text{Nd}}^{3+}$ in ${\text{LiYF}}_{4}$ are slightly larger than those of the $5{f}^{3}\text{\ensuremath{-}}5{f}^{2}6{d}^{1}$ transition for ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$. The experimental absorption spectra for ${\text{Nd}}^{3+}$ in ${\text{LiYF}}_{4}$ measured at nine different temperatures indicated that the $4{f}^{3}\text{\ensuremath{-}}4{f}^{2}5{d}^{1}$ absorption spectra for ${\text{Nd}}^{3+}$ in ${\text{LiYF}}_{4}$ have no significant temperature dependence. For ${\text{Pr}}^{3+}$ in ${\text{LiYF}}_{4}$, we performed more detailed investigations. The lattice relaxation effects due to the substitution of ${\text{Y}}^{3+}$ by ${\text{Pr}}^{3+}$ were estimated using a first-principles density-functional calculation. Structural optimization calculations indicated that the local structure of the ${\text{Pr}}^{3+}$ site was slightly distorted. Overall, the theoretical $4{f}^{2}\text{\ensuremath{-}}4{f}^{1}5{d}^{1}$ absorption spectra reproduced the experimental spectra. The experimental absorption spectra were investigated by configuration analysis based on the many-electron wave functions. The theoretical calculations indicated that the temperature dependence of the experimental spectra was due to both thermal excitation and phonon effects. In addition, we also investigated the effects of the exchange-correlation interaction and the Breit term by comparing the results from six different Hamiltonians.