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Physical Review

Phonon-Induced Relaxation in Excited Optical States of Trivalent Praseodymium in La F3

William M. Yen, W. C. Scott, ARTHUR L. SCHAWLOW

Published Oct 5, 1964• 270 citations
Publisher

Abstract

Phonon-ion interactions have recently been shown to satisfactorily explain the temperature dependence of widths and positions of the $R$ lines of some $3d$ ions in crystals. These interactions give rise to phonon relaxation processes and are investigated here as the mechanisms responsible for the widths and positions of sharp optical transitions in ($4f$) ions, in particular La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$. The widths of transitions originating or terminating in the metastable $^{3}P_{0}$ state and involving the $^{3}H_{4}$, $^{3}H_{6}$, $^{3}F_{2}$, and $^{3}F_{4}$ states of ${\mathrm{Pr}}^{3+}$ in La${\mathrm{F}}_{3}$ have been investigated as a function of temperature and are found to be both qualitatively and quantitatively explainable in terms of lifetime broadening of the interacting states via nonradiative processes. Temperature-dependent shifts have also been measured for the above four groups of transitions and are shown to be in qualitative agreement with theoretical predictions. Additional features of the La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$ spectrum, including several unreported weak transitions and vibrational sidebands, are also reported.

DOI
10.1103/physrev.136.a271

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Physical review. B, Condensed matter•May 1, 1984•9 citations
Phonon-ion interactions have recently been shown to satisfactorily explain the temperature dependence of widths and positions of the RRR lines of some 3d3d3d ions in crystals. These interactions give rise to phonon relaxation processes and are investigated here as the mechanisms responsible for the widths and positions of sharp optical transitions in (4f4f4f) ions, in particular LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+. The widths of transitions originating or terminating in the metastable 3P0^{3}P_{0}3P0​ state and involving the 3H4^{3}H_{4}3H4​, 3H6^{3}H_{6}3H6​, 3F2^{3}F_{2}3F2​, and 3F4^{3}F_{4}3F4​ states of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in LaF3{\mathrm{F}}_{3}F3​ have been investigated as a function of temperature and are found to be both qualitatively and quantitatively explainable in terms of lifetime broadening of the interacting states via nonradiative processes. Temperature-dependent shifts have also been measured for the above four groups of transitions and are shown to be in qualitative agreement with theoretical predictions. Additional features of the LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+ spectrum, including several unreported weak transitions and vibrational sidebands, are also reported.
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We have investigated the process of quenching of fluorescence from the 3P0^{3}P_{0}3P0​ excited state of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in LaF3{\mathrm{F}}_{3}F3​ due to cross relaxation among the Pr ions. The fluorescence decay of the ensemble of Pr ions after pulsed excitation is measured as a function of temperature for Pr concentration of 20 mol%. About 12% of the ions are in nonquenching sites and contribute an exponential component to the decay. The remainder of the decay originates from the bulk of the ions in quenching sites. Cross relaxation occurs directly in steps after transfer within the inhomogeneous line. Knowledge of the dynamics occurring within the inhomogeneous line derived from fluorescence line-narrowing experiments is used to analyze the cross-relaxation process from a microscopic viewpoint based on a recent model for fluorescence in the presence of traps. At 2 K the decay is consistent with an electric dipole-dipole transfer mechanism with a nearest-neighbor quenching rate of 8.9 \ifmmode\times\else\texttimes\fi{} 104{10}^{4}104 ${\mathrm{s}}^{\ensuremath{-}1}$ which is independent of temperature for T<32T<32T<32 K and which successfully predicts the observed decay rate in PrF3{\mathrm{F}}_{3}F3​. The temperature dependence of the decay for $8\ensuremath{\le}T\ensuremath{\le}32$ K is well described by a hopping model for excitation trapping. For T>35T>35T>35 K an activation process becomes dominant consistent with the onset of cross relaxation involving the 1D2(5)^{1}D_{2}(5)1D2​(5) and 3H6(1)^{3}H_{6}(1)3H6​(1) states in which a 190-${\mathrm{cm}}^{\ensuremath{-}1}$ phonon is created.
The temporal dependence of the fluorescence line shape of Pr ion diluted in LaF3{\mathrm{F}}_{3}F3​ has been studied in detail. The line-shape study is based on the assumption that the cross relaxation between Pr ions dominates the nonradiative process. The ion-ion interaction has been directly probed by the two-ion cooperative absorption process under which a 3P0^{3}P_{0}3P0​ level lifetime dilation has been observed. The dilation effect can be suppressed when the spectral energy transfer is switched on by raising the temperature of the host crystal. The temporal behavior of the fluorescence line shape of the 1D2^{1}D_{2}1D2​ level has been systematically investigated. The "inhomogeneous" linewidth is found to be composed of a main central peak and a series of ion-pair satellites. The shorter decay lifetime of the ion-pair states results in the narrowing of the emission line shape at later times. The energy positions of the ion-pair states have been measured from the 1D2^{1}D_{2}1D2​ ion pairs up-conversion fluorescence process. The lifetime of the ion-pair states is determined by the coupling strength of the cross relaxation from an excited ion to its partner ion and hence varies according to the ion-pair separation. The decay under the inhomogeneous width is nonexponential in general. Based on the number of the distinguished ion pair levels, a concept of the sphere of influence is introduced. Following this model, an approach has been developed which allows us to study the decay characteristics. Systematical trends emerge from such analysis. The cross-relaxation coupling constants for ion pairs have been extracted from the decay curves and profiles of the ion-pairs line shape have been mapped out. Their peak positions agree with those obtained from 1D2^{1}D_{2}1D2​ ion-pair up-conversion fluorescence measurements.
We present optical linewidth and line-shape studies of transitions of 4f4f4f impurity ions in doubly doped systems and show that interactions which involve excitation transfer between the impurity systems produce homogeneous broadening and line-shape changes in the optical transitions. In particular, we have studied the behavior of the 5985-\AA{} line of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in doubly doped LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+, Nd3+{\mathrm{Nd}}^{3+}Nd3+ as a function of Nd3+{\mathrm{Nd}}^{3+}Nd3+ concentration. The 5985-\AA{} Pr3+{\mathrm{Pr}}^{3+}Pr3+ transition at 4.2\ifmmode^\circ\else\textdegree\fi{}K involves two long-lived electronic states of the Pr3+{\mathrm{Pr}}^{3+}Pr3+ ion; it follows that in the singly doped LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+ the transition shows a Gaussian shape which is characteristic of inhomogeneous strain and imperfection broadening. As Nd3+{\mathrm{Nd}}^{3+}Nd3+ is added to the system, a broader Lorentzian component begins to appear in the 5985-\AA{} Pr3+{\mathrm{Pr}}^{3+}Pr3+ transition and eventually (at Nd3+{\mathrm{Nd}}^{3+}Nd3+ concentrations of \ensuremath{\sim}1% or above) completely dominates the width and shape of the transition. The Lorentzian component of the transition line shape was successfully separated using a Fourier-transform technique and the width of this component was studied as a function of the Nd3+{\mathrm{Nd}}^{3+}Nd3+ concentration. The width is found to increase linearly with increasing Nd3+{\mathrm{Nd}}^{3+}Nd3+ concentration up to concentrations of 2%; at higher concentrations, the linewidth saturates and approaches an asymptotic value of \ensuremath{\sim}2 ${\mathrm{cm}}^{\ensuremath{-}1}$. We construe this homogeneous component to be evidence of a rapid short-range energy transfer mechanism between the Pr3+{\mathrm{Pr}}^{3+}Pr3+ and Nd3+{\mathrm{Nd}}^{3+}Nd3+ systems at the terminating (3H6)1{(^{3}H_{6})}_{1}(3H6​)1​ level of the 5985-\AA{} Pr3+{\mathrm{Pr}}^{3+}Pr3+ transition. Various mechanisms are investigated as causes of the energy transfer process; it is concluded that the spin-exchange interaction is the most probable cause for the transfer. Results of other spectroscopic measurements on the doubly doped LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+, Nd3+{\mathrm{Nd}}^{3+}Nd3+ system are also presented.
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We have investigated the process of quenching of fluorescence from the 3P0^{3}P_{0}3P0​ state of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in La0.72{\mathrm{La}}_{0.72}La0.72​Pr0.25{\mathrm{Pr}}_{0.25}Pr0.25​Nd0.03{\mathrm{Nd}}_{0.03}Nd0.03​F3{\mathrm{F}}_{3}F3​ due to cross relaxation to Pr and Nd ions. The fluorescence decay of the ensemble of Pr ions after pulsed excitation is measured as a function of temperature in the (2-70)-K region. Cross relaxation occurs either directly or through a donor-donor transfer within the inhom-geneous line. Knowledge of the dynamics occurring within the inhomogeneous line derived from previous fluorescence line-narrowing experiments is used to analyze the cross-relaxation process from a microscopic viewpoint according to models for fluorescence decay in the presence of traps. In general the decay is consistent with an electric dipole-dipole transfer mechanism. At 2 K the decay can be well described by a direct transfer to Pr and Nd traps without donor-donor transfer. The temperature dependence of the decay at long times can be described for 35<T<7035<T<7035<T<70 K by the hopping model. The agreement with theory is much better if the cross relaxation to Nd ions is assumed to occur mainly via the lowest Stark level of the 4I92^{4}I_{\frac{9}{2}}4I29​​ manifold.