Energy level structure of4f5dstates and the Stokes shift inLaPO4:Pr3+: A theoretical study

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The energy levels and the Stokes shift of the excited $4{f}^{1}5{d}^{1}$ states of ${\text{Pr}}^{3+}$ ions doped into ${\text{LaPO}}_{4}$ are calculated using a combined theoretical approach. The local structure of the rare-earth site in ${\text{LaPO}}_{4}$ is obtained from first-principles calculations, while the $4{f}^{1}5{d}^{1}$ states of ${\text{Pr}}^{3+}$ are treated parametrically in terms of a model Hamiltonian. The crystal-field energies of the $5d$ electron of a low-symmetry rare-earth site in ${\text{LaPO}}_{4}$ are obtained from angular-overlap model calculations. First-principles calculations are performed for ${\text{LaPO}}_{4}:{\text{Ce}}^{3+}$ used as a reference compound for ${\text{LaPO}}_{4}:{\text{Pr}}^{3+}$; the geometry parameters of the rare-earth site are determined for the ground state $(4f)$ and for the excited $(5d)$ state of the central ${\text{Ce}}^{3+}$ ion. It is shown that the $4f\text{\ensuremath{-}}5d$ excitation in ${\text{LaPO}}_{4}:{\text{Ce}}^{3+}$ is accompanied by a strong relaxation of the local structure of the rare-earth site due to rotations of one of the neighboring tetrahedral ${\text{PO}}_{4}$ phosphate groups: the coordination number of ${\text{Ce}}^{3+}$ reduces from nine to eight and the average Ce-O distance shortens by about $0.1\text{ }\text{\AA{}}$. This leads to a considerably larger crystal-field splitting energy of the $5d$ states for the excited-state geometry of the cerium site ($\ensuremath{\sim}17\text{ }700\text{ }{\text{cm}}^{\ensuremath{-}1}$ vs $\ensuremath{\sim}12\text{ }000\text{ }{\text{cm}}^{\ensuremath{-}1}$ in the ground state) and to a large $5d\text{\ensuremath{-}}4f$ Stokes shift in ${\text{LaPO}}_{4}:{\text{Ce}}^{3+}$ ($3980\text{ }{\text{cm}}^{\ensuremath{-}1}$ calculated and $4880\text{ }{\text{cm}}^{\ensuremath{-}1}$ experimental). The $5d$ crystal-field splitting energies obtained for ${\text{Ce}}^{3+}$ are then employed for calculations of the $4{f}^{1}5{d}^{1}$ energy levels in ${\text{LaPO}}_{4}:{\text{Pr}}^{3+}$. The calculated Stokes shift in ${\text{LaPO}}_{4}:{\text{Pr}}^{3+}$ is $3610\text{ }{\text{cm}}^{\ensuremath{-}1}$. Due to such a large Stokes shift, in an excited ${\text{Pr}}^{3+}$ ion the lowest $4{f}^{1}5{d}^{1}$ energy level lies below the upper ${^{1}\text{S}}_{0}(4{f}^{2})$ level, while in an unexcited ion (in the ground $4{f}^{2}$ state) the order of these states is reverse. This fact is responsible for the absence of $4f\text{\ensuremath{-}}4f$ emission from the ${^{1}\text{S}}_{0}$ state in ${\text{LaPO}}_{4}:{\text{Pr}}^{3+}$.