A comprehensive report and analysis of our observations of numerous parity-allowed direct two-photon transitions within the
4f7 configuration of the
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+:La
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
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
4f65d 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+:La
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+ 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 .
Two-photon absorption spectroscopy is used to investigate the 8 S 7/2 → 6 P J , 6 I 7/2 transitions of Gd 3+ ions in the cubic elpasolite Cs 2 NaGdCl 6 . The Gd 3+ ions occupy a centro-symmetric site (O h ); so the odd terms of the crystal field vanish and the pure electric dipole transitions should not be observed in one-photon experiments. As a consequence the electric dipole allowed two-photon transitions involving the 6 I 7/2 and 6 P 3/2 excited states are well observed in contrast with their weakness in the one-photon spectrum. Furthermore the magnetic dipole character of the transitions to the 6 P 5/2 and 6 P 7/2 levels is confirmed. The occurrence of the one-photon transition to 6 P 3/2 is tentatively explained by the J mixing involving the 6 P 7/2 excited state. A qualitative analysis of the relative intensities of the transitions to the 6 P J and 6 I 7/2 levels is presented.
The high-resolution optical-absorption spectra of the magnetic insulators Gd
Cl3 and Gd
(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
6P27 and
6P25 manifolds of the
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.
The two-photon transitions between the Stark levels of the
7F0 and
5D2 multiplets of the
Sm2+ ion in BaClF are investigated both from an experimental and theoretical viewpoint. Direct two-photon excitation spectra of the
5D2 fluorescence resulting from an optical excitation with an infrared laser beam are presented and the polarization dependence of the observed transitions is analyzed. These new data are interpreted along the lines of a simple model which originates in the second-order theory developed by Axe [Phys. Rev. 136, A42 (1964)] for two-photon processes in complex atoms. The extension of this theory to the case of rare-earth ions embedded in crystalline fields is carried out by use of symmetry-adaptation techniques based on the use of an SU(2)\ensuremath{\supset}
G∗ chain of groups. It is shown that the resulting model (limited up to second-order terms) describes correctly the relative intensities of the two-photon transitions between the Stark levels of the
7F0 and
5D2 multiplets of
Sm2+ in BaClF.
Observation by fluorescence of direct two photon absorption within the 8S7/2→6P7/2 transition of the Gd3+ ion following excitation with a pulse dye laser is reported. The whole fluorescence spectra correlate well with the ones obtained from the one UV photon absorption. However excitation spectra exhibits a linenarrowing compare to the OPA and an observable shift when decreasing the temperature from 4.4 K down to the ferromagnetic order below Tc = 2.2 K. At these temperatures, exciton decay exhibits a non exponential behaviour which can be only treated as a sum of two expoentials in disagreament with the OPA measurements.