PHYSICAL REVIEW B VOLUME 28, NUMBER 9 1 NOVEMBER 1983 Study of new 4f levels of Eu + in CaFz and SrF2 using two-photon absorption spectroscopy M. C. Downer* and C. D. Cordero-Montalvo~ Diuision of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 H. Crosswhite Chemistry Diuison, Argonne National Laboratory, Argonne, Illinois 60439 (Received 22 July 1983) Two-photon dye-laser excitation is used to observe numerous sharp 4f' levels of Eu + in CaF2 and SrF2 which are overlapped by the 4f Sd band, and thus inaccessible to single-photon spectros- copy. 4f excited states belonging to the I and D groups have been identified for the first time. Energy-level calculations are presented which confirm the f -level assignments and determine free- ion and crystal-field parameters for both host lattices. Measurements of the relative intensities and polarization dependence of the f + f tran— sitions confirm the existence of third- and fourth-order contributions to the two-photon intensities which have been postulated in recent analyses of the two-photon spectrum of the isoelectronic Gd + ion. In some cases { S7/2~ +7/25/2 D7/p), howev- er, these higher-order contributions are weaker than expected. It is shown that by relaxing the clo- sure approximation in summing over the intermediate states, the agreement with the data is im- provedd. I. INTRODUCTION We recently presented a comprehensive report and analysis' (subsequently referred to as I) of our observa- tions of numerous direct two-photon transitions be- tween levels of the 4f configuration of Gd + in LaF3 and in aqueous solution. The observations revealed widespread and severe discrepancies with the angular momentum selection rules (b, L, b, J&2), relative intensi- ties, and polarization dependence predicted by a standard second-order theory of two-photon absorption (TPA). Subsequent analysis, ' however, demonstrated that the discrepancies could be explained in quantitative detail by expanding the theory of TPA to include third- and fourth-order contributions which take into account spin- orbit and crystal-field interactions among levels of the excited 4f 5d configuration, which serve as intermediate states. In the present work we use two-photon spectroscopy to study the 4f levels of the isoelectronic Eu + ion in the cubic crystals CaF2 and SrF2. Experimental details of the Eu + samples are described in Sec. II. Because the excited 4f 5d configuration lies at much lower energy in the di- valent ion, it completely overlaps even the lowest sharp 4f excited states, which lie in the near ultraviolet. Con- sequently, only the intense broad bands arising from elec- tric dipole allowed 4f ~4f 5d transitions can be seen in the single-photon absorption spectrum of these crystals. With TPA, however, the broad bands are suppressed by the parity selection rule, allowing the sharp 4f levels to be observed. Fritzler and Schaak ' first demonstrated this possibility by observing the P7/z 5/2 levels of 4f in Eu +:CaF2,SrF2. These two levels had been observed ear- lier in the one-photon spectrum of Eu + in KMgF2, ' alkaline-earth sulfates, " and ternary alkaline-earth alumi- num fluorides, ' where they lie just below the onset of the 4f 5d absorption band edge. In the present study we have also observed the higher excited states in CaF2 and SrF2 belonging to the I and D groups for the first time. In Sec. III the evidence for identifying the new spectral lines as 4f levels is presented. Energy-level calculations which confirm these assignments are the subject of Sec. IV. Because the separation Edf of the single-photon energy from the average energy of the intermediate 4f 5d states is roughly a factor of 3 smaller in Eu + than in Gd +, an increase in the absolute two-photon line strengths is ex- pected and observed. Moreover, since the nth-order con- tribution to TPA scales as Edf" ", we expect transitions which owe their strength primarily to third- and fourth- order contributions to increase considerably more in inten- sity than those dominated by the second-order contribu- tion. Measurements of the relative intensities and polari- zation dependence of the S7/2~ I'J IJ and DJ two- photon transitions, described in Sec. III, bear out this ex- pectation in some cases ( S7/2~ IJ), but not in others ( S7/2 ~ P7/2 5/2 D 7/2 ). In the anal'ysis of the two- photon line strengths, presented in Sec. V, it is argued that this discrepancy may result in part from a much greater relative spread of the energy denominators for the various intermediate states. The closure approximation conven- tionally used to simplify the sum over intermediate states thus becomes questionable. When the closure approxima- tion is relaxed by introducing term-dependent energy denominators, the agreement between predicted and ob- served intensities improves for the P7/p 5/2 D7p lines, al- though a significant discrepancy remains for I'7/2 The Eu + results thus confirm the general expectations of the theory developed to explain the earlier Gd + data, ' al- though the quantitative agreement is less satisfactory. 4931 1983 The American Physical Society