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The Journal of Chemical Physics

A new contribution to spin-forbidden rare earth optical transition intensities: Gd3+ and Eu3+

M. C. Downer, Gary W. Burdick, Dhiraj Kumar Sardar

Published Aug 15, 1988• 83 citations
Publisher

Abstract

Quantitative calculations show that numerous spin-forbidden linear optical transitions observed in trivalent rare earth ions acquire a major fraction of their intensity from hitherto neglected contributions involving spin–orbit linkages within excited configurations. Motivated by the importance of analogous linkages previously demonstrated in two-photon absorption, we derive a general expression applicable for all lN→lN transitions which can be incorporated into a revised Judd–Ofelt analysis of observed intensities. Presenting this revised analysis of observed linear absorption intensities for Gd3+ and Eu3+, we show that the new contribution is often comparable to standard contributions. With substantial modification of previously fitted phenomenological parameters, an improved fit to observed intensities is achieved, suggesting that reanalysis of linear intensity data for all trivalent rare earths is warranted.

DOI
10.1063/1.455125

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Quantitative calculations show that numerous spin-forbidden linear optical transitions observed in trivalent rare earth ions acquire a major fraction of their intensity from hitherto neglected contributions involving spin–orbit linkages within excited configurations. Motivated by the importance of analogous linkages previously demonstrated in two-photon absorption, we derive a general expression applicable for all lN→lN transitions which can be incorporated into a revised Judd–Ofelt analysis of observed intensities. Presenting this revised analysis of observed linear absorption intensities for Gd3+ and Eu3+, we show that the new contribution is often comparable to standard contributions. With substantial modification of previously fitted phenomenological parameters, an improved fit to observed intensities is achieved, suggesting that reanalysis of linear intensity data for all trivalent rare earths is warranted.
A comprehensive report and analysis of our observations of numerous parity-allowed direct two-photon transitions within the 4f74{f}^{7}4f7 configuration of the Gd3+{\mathrm{Gd}}^{3+}Gd3+ ion is presented. The experimental technique is ultraviolet fluorescence detection following optical excitation with a dye-laser beam. Previous results and analyses are extended in three ways. (1) The intensities and polarization dependence of individual Stark components, in addition to integrated multiplet intensities, are reported and analyzed for Gd3+{\mathrm{Gd}}^{3+}Gd3+:LaF3{\mathrm{F}}_{3}F3​. In those cases ($^{8}S_{\frac{7}{2}}\ensuremath{\rightarrow}^{6}P_{\frac{5}{2}},^{6}D_{\frac{9}{2},\frac{3}{2},\frac{5}{2}}$) where a second-order theory of two-photon absorption adequately explains the integrated intensity, it also (with the exception of 6D92^{6}D_{\frac{9}{2}}6D29​​) explains the Stark-component intensities. The remaining transitions are anomalously strong, and in some cases violate the angular momentum selection rules $\ensuremath{\Delta}L,\ensuremath{\Delta}J\ensuremath{\le}2$ and exhibit strong anisotropies, in contradiction to the second-order theory. It is shown that introduction of third- and fourth-order contributions involving spin-orbit and/or crystal-field interactions among levels of the 4f65d4{f}^{6}5d4f65d configuration, which serve as intermediate states, can account for both the integrated and Stark-component intensities of these transitions. (2) The strong anisotropy observed for the transitions $^{8}S_{\frac{7}{2}}\ensuremath{\rightarrow}^{6}P_{\frac{3}{2}},^{6}I_{J},^{6}D_{\frac{1}{2}}$ in Gd3+{\mathrm{Gd}}^{3+}Gd3+:LaF3{\mathrm{F}}_{3}F3​ is explained quantitatively as a polarization-dependent interference between contributions to the intensity which are comparable in magnitude. Interference is destructive for $\stackrel{\ensuremath{\rightarrow}}{E}\ensuremath{\parallel}\stackrel{^}{z}$ and constructive for $\stackrel{\ensuremath{\rightarrow}}{E}\ensuremath{\perp}\stackrel{^}{z}$, creating an order-of-magnitude contrast in the line strength for the two polarizations. (3) A two-photon excitation spectrum of Gd3+{\mathrm{Gd}}^{3+}Gd3+ in aqueous solution is reported. Linewidths comparable to those of room-temperature solids and Stark splittings which suggest a low-symmetry quasistatic environment are observed.
Recent observations of two-photon absorption within the configuration 4f 7 of Gd 3+ in LaF 3 have indicated an anomalously high line strength for the transition 8 S 7/2 to 6 P 7/2 compared with 8 S 7/2 to 6 P 5/2 and 8 S 7/2 to 6 P 3/2 . It is shown that the standard expression for the two-photon intensity is unusually small for all three transitions and that a higher-order correction, involving matrix elements of the spin-orbit interaction within the intermediate configuration 4f 6 5d, predominates. The principal term is scalar, implying (in the absence of J mixing by the crystal field) isotropic contributions to the various components of the Delta J=0 transition. The line strengths that have been observed can be accounted for reasonably well without having to invoke variations in the radial integral (4f mod r mod 5d) or inadequacies in the closure approximation. Expressions for the transition matrix elements are given for the general configuration l N .
The absorption of a single photon by the simultaneous excitation of two rare-earth ions was first reported by Varsanyi and Dieke in 1961.1 D. L. Dexter explained this unusual observation by including the electron-electron interactions (that also give rise to energy transfer) between the rare earth ions with perturbation theory.2 In the 70's Dexter became interested in electronic-vibrational coupling. A theory of two-center optical transitions was developed for a rare-earth ion weakly coupled to a high energy, internal vibrational mode of a near-lying ion.3 Using theoretical techniques that had been developed for rare-earth ion pairs, intensities and selection rules could be determined.
The change of intensities of optical transitions of atoms, molecules, and their ions in the near field of nanoobjects is of interest for researchers from both basic and applied points of view. The concept of a near field was used as early as the 1960s to study the mechanisms of hypersensitive transitions of rare-earth (RE) ions. In this work, it is once more emphasized that, precisely for these transitions, changes in characteristics under the action of local properties of the medium are especially strong and, correspondingly, these transitions are especially promising for use. The Judd method for the calculation of the intensities of hypersensitive transitions of RE ions taking into account the inhomogeneous ligand field is extended to RE ions in the near field of nanoobjects. A simple analytical expression for the Judd-Ofelt intensity parameter Ω 2 for RE ions in the field of spherical nanoparticles of a subwavelength size is derived.