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Physical Review Letters

Excited-State Exchange Broadening of Optical Transitions in Pr Cl3

K. R. German, Alvin E. Kiel

Published Oct 21, 1974• 11 citations
Publisher

Abstract

We have observed an anomalous broadening of two fluorescence lines in Pr${\mathrm{Cl}}_{3}$. The new effect is observed only when the terminal state is a magnetic doublet and only at low temperatures ($T<100$ K). However, the effect is seen far above any transition or ordering temperature. The broadening can be, at least partially, suppressed by application of a large magnetic field. The effect is almost certainly a cooperative phenomenon arising from an interaction between ground- and excited-state ions.

DOI
10.1103/physrevlett.33.1039

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Fluorine Spin Diffusion Barrier in Pr3+;LaF3 Observed by Cross Relaxation

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Photon echo measurements made at 2 °K on the 3H4 - 1D2 transition in Pr3+:LaF3 show that magnetic dipolar couplings between the Pr and F nuclei account for the 56 kHz homogeneous linewidth of this transition.1 The homogeneous broadening arises from the enhanced 141Pr nuclear moment (I=5/2) interacting with the local field fluctuations of the 19F nuclear moments undergoing mutual spin flip transitions. Such resonant fluctuations should, in the absence of a fluorine spin diffusion barrier, produce a homogeneous linewidth of about 200 kHz which is, in fact, roughly what is observed for the inhomogeneous broadening of the Pr3+ hyperfine levels and is considerably broader than that obtained by the photon echo measurements. Shelby et al2 proposed a simple model analogous to the spin diffusion barriers responsible for narrowing the homogeneous lines in certain electron paramagnetic resonance transitions3. In such systems, the field produced by the electron magnetic dipole moment (2-3 orders of magnitude larger than the enhanced nuclear moment associated with the ground state of Pr3+ in LaF3) de-tunes the nearest neighbors from each other, prohibiting mutual spin flips among them. Thus, the fields produced by the neighboring spins are static and their interaction with the paramagnetic ion contributes to the inhomogeneous linewidth and not to homogeneous broadening. The de-tuned neighbors are referred to as the "frozen core." Application of this picture to the case of Pr3+:LaF3 is supported by the calculation of Devoe et al.4 Their Monte Carlo calculation of the Pr3+ optical dephasing times shows that the observed homogeneous linewidth could be explained by deleting the nearest neighbor F spins from the lattice of rapidly fluctuating fluorine moments, in effect, treating them as part of a frozen core.

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The high-resolution optical-absorption spectra of the magnetic insulators Gd${\mathrm{Cl}}_{3}$ and Gd${(\mathrm{OH})}_{3}$ in a 35-kG magnetic field are used to demonstrate, for the first time, the influence of the magnon dispersion on the line shapes of single-ion-induced optical transitions. The absorption line shapes for transitions from the first thermally populated spin state to several single-ion states of the $^{6}P_{\frac{7}{2}}$ and $^{6}P_{\frac{5}{2}}$ manifolds of the ${\mathrm{Gd}}^{+3}$ ion are calculated. The initial and final states are properly treated as a magnon and exciton, respectively, including the dispersion of both states. The single-ion transition-moment operator is transformed to a basis in the crystal eigenstates and the resulting absorption line shape is shown to depend on a $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$-dependent transition-moment operator weighted by a combined exciton-magnon density of states and the magnon occupation number. The magnon dispersion is calculated from the known ground-state exchange interactions while the exciton dispersion is varied to give a best fit to the observed line shapes. The resulting excited-state exchange parameters are shown to be reasonable. The exciton dispersion is found to be quite significant (up to 2 ${\mathrm{cm}}^{\ensuremath{-}1}$) for one of the excited states. These two materials thus represent the first examples for which the exciton dispersion of the electronically excited states of a rare-earth salt have been directly observed.

Physical review. B, Solid state•Jul 1, 1972•40 citations
We have observed an anomalous broadening of two fluorescence lines in PrCl3{\mathrm{Cl}}_{3}Cl3​. The new effect is observed only when the terminal state is a magnetic doublet and only at low temperatures (T<100T<100T<100 K). However, the effect is seen far above any transition or ordering temperature. The broadening can be, at least partially, suppressed by application of a large magnetic field. The effect is almost certainly a cooperative phenomenon arising from an interaction between ground- and excited-state ions.
Data are reported which show that the temperature dependence of fluorescence linewidths in PrF3{\mathrm{F}}_{3}F3​ are qualitatively like those in LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+. This result is interpreted as supporting the explanation of German and Kiel for the anomalous temperature dependence of fluorescence linewidths in PrCl3{\mathrm{Cl}}_{3}Cl3​.
A large number of small but sharp changes (increases and decreases) of the R 1 fluorescence in ruby are observed as a function of applied magnetic field between 2 K and 77 K. At liquid helium temperatures, these signals have linewidths much narrower than the inhomogeneous linewidth (∼0.1 cm -1 ) of the R 1 line. All of these signals appear at the fields where the Zeeman splittings in the excited state \bar E ( 2 E ) and the ground state 4 A 2 satisfy an energy-matching condition for simultaneous transitions of two or more ions. Two distinct mechanisms are found to be responsible for the signals: spin-spin cross-relaxation between \bar E ( 2 E ) and 4 A 2 , and resonant self-trapping of the R 1 line. From the temperature dependence of the linewidths of the signals, thermal broadening of \bar E ( 2 E ) is measured below 77 K. Similar signals are observed in the N lines due to energy transfer from isolated ions to pairs.
The absorption of single photons by coupled pairs of ions in rare-earth solids was first observed by Varsanyi and Dieke.1 They noticed that weak absorption of light occurred in PrCl3 at frequencies close to the sum of transition frequencies of individual Pr ions, giving rise to rare-earth fluorescence. This effect was explained by the perturbation theory of Dexter.2 He showed that weak multipole or exchange interactions between rare-earth ions permitted the simultaneous promotion of two ions to excited states by the action of one absorbed photon in an electric dipole allowed transition. Similarly, two ions initially in excited states could emit one sum frequency photon in a cooperative manner.
Photon echo measurements made at 2 °K on the 3H4 - 1D2 transition in Pr3+:LaF3 show that magnetic dipolar couplings between the Pr and F nuclei account for the 56 kHz homogeneous linewidth of this transition.1 The homogeneous broadening arises from the enhanced 141Pr nuclear moment (I=5/2) interacting with the local field fluctuations of the 19F nuclear moments undergoing mutual spin flip transitions. Such resonant fluctuations should, in the absence of a fluorine spin diffusion barrier, produce a homogeneous linewidth of about 200 kHz which is, in fact, roughly what is observed for the inhomogeneous broadening of the Pr3+ hyperfine levels and is considerably broader than that obtained by the photon echo measurements. Shelby et al2 proposed a simple model analogous to the spin diffusion barriers responsible for narrowing the homogeneous lines in certain electron paramagnetic resonance transitions3. In such systems, the field produced by the electron magnetic dipole moment (2-3 orders of magnitude larger than the enhanced nuclear moment associated with the ground state of Pr3+ in LaF3) de-tunes the nearest neighbors from each other, prohibiting mutual spin flips among them. Thus, the fields produced by the neighboring spins are static and their interaction with the paramagnetic ion contributes to the inhomogeneous linewidth and not to homogeneous broadening. The de-tuned neighbors are referred to as the "frozen core." Application of this picture to the case of Pr3+:LaF3 is supported by the calculation of Devoe et al.4 Their Monte Carlo calculation of the Pr3+ optical dephasing times shows that the observed homogeneous linewidth could be explained by deleting the nearest neighbor F spins from the lattice of rapidly fluctuating fluorine moments, in effect, treating them as part of a frozen core.
The high-resolution optical-absorption spectra of the magnetic insulators GdCl3{\mathrm{Cl}}_{3}Cl3​ and Gd(OH)3{(\mathrm{OH})}_{3}(OH)3​ in a 35-kG magnetic field are used to demonstrate, for the first time, the influence of the magnon dispersion on the line shapes of single-ion-induced optical transitions. The absorption line shapes for transitions from the first thermally populated spin state to several single-ion states of the 6P72^{6}P_{\frac{7}{2}}6P27​​ and 6P52^{6}P_{\frac{5}{2}}6P25​​ manifolds of the Gd+3{\mathrm{Gd}}^{+3}Gd+3 ion are calculated. The initial and final states are properly treated as a magnon and exciton, respectively, including the dispersion of both states. The single-ion transition-moment operator is transformed to a basis in the crystal eigenstates and the resulting absorption line shape is shown to depend on a $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$-dependent transition-moment operator weighted by a combined exciton-magnon density of states and the magnon occupation number. The magnon dispersion is calculated from the known ground-state exchange interactions while the exciton dispersion is varied to give a best fit to the observed line shapes. The resulting excited-state exchange parameters are shown to be reasonable. The exciton dispersion is found to be quite significant (up to 2 ${\mathrm{cm}}^{\ensuremath{-}1}$) for one of the excited states. These two materials thus represent the first examples for which the exciton dispersion of the electronically excited states of a rare-earth salt have been directly observed.