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One- and two-photon spectroscopy of Eu3+ in LuPO4
Journal of Luminescence 79 (1998) 55—64
One- and two-photon spectroscopy of Eu3` in LuPO 4 Keith M. Murdoch*, An-Dien Nguyen, Norman M. Edelstein Chemical Sciences Division, MS 70A-1150, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Received 4 August 1997; received in revised form 22 December 1997; accepted 29 January 1998
Abstract One-photon laser excitation and fluorescence spectra have been recorded for the Eu3` ion diluted in single crystals of LuPO . Analysis of these spectra resulted in the assignment of 23 energy levels of the 7F and 5D multiplets, which were 4 J J fitted to the parameters of an empirical Hamiltonian with an rms deviation of 8.7 cm~1. The intensities of the two-photon absorption transitions to the 5D0 and 5D2 multiplets have been investigated. The polarization dependences of transitions to all five of the crystal-field levels were measured and are compared with theoretical predictions. The intensity model included the third-order spin—orbit interaction. Good agreement was found for three of the five transitions observed. However, the polarization dependences of the other two did not agree with the predicted behavior, as they exhibited an additional isotropic component. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Two-photon absorption; Polarization analysis; Crystal-field analysis
1. Introduction The lanthanide orthophosphate LuPO forms 4 the tetragonal zircon-type structure at high temperatures [1,2] and has excellent chemical stability and resistance to damage by ionizing radiation. Other trivalent lanthanide [2,3] and actinide [4] ions enter this lattice substitutionally at sites of D point symmetry. Crystals of LuPO doped 2$ 4 with optically active rare-earth ions have potential applications as thermophosphors for remote temperature measurement, as X- and c-ray scintillators for medical imaging, and as laser materials [5]. Previous studies have reported on the one-photon spectroscopy of Eu3` ions diluted into the related phosphate YPO [6] and the vanadate YVO [7]. 4 4 * Corresponding author. Tel.: (608) 263 1082; fax: (608) 262 0381; e-mail: [email protected].
Crystal-field parameters were obtained for the Eu3` site in each of these crystals and used in a qualitative analysis of their structural differences [6]. Analyses of intra-configurational 4fN—4fN twophoton absorption (TPA) transitions of rare-earth ions in various host crystals have generated much theoretical interest since the standard second-order theory of Axe [8] has proven inadequate to explain many of the observed relative transition intensities [9—11]. Judd and Pooler [12] introduced a thirdorder correction by including the spin—orbit interaction between intermediate states of the 4fN~15d lowest lying excited configuration. The predominant term arising from this mechanism is a scalar and contributes an isotropic component to the intensities of *J "0 TPA transitions. They note that this is the only term which contributes to the 7F P 5D TPA transition of the Eu3` ion. 0 0 Downer et al. [11,13,14] subsequently included other higher-order corrections to account for the
0022-2313/98/$ — see front matter ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 9 8 ) 0 0 0 1 4 - 3
56
K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
observed discrepancies, particularly the crystalfield interaction between intermediate states. Recently, Gaˆcon et al. [15—18] presented measurements of Sm2` and Eu3` TPA intensities. They found several TPA transitions in Sm2` : BaClF, Sm2`:SrClF, Eu(OH) , and Eu3`:LuPO with po3 4 larization behavior which is inconsistent with the polarization dependencies calculated by Bader and Gold [19] using symmetry considerations. These transitions have an additional isotropic intensity component over all polarization angles h, where h is the angle between the crystallographic c-axis and the polarization unit vector of the excitation beam. This component could be parameterized by introducing complex variables into the expression of the TPA amplitude. However, it could not be explained by any of the aforementioned mechanisms which are known to contribute to TPA intensities. Similar anomalous behavior was observed for some TPA transitions of Cm3` in LuPO [20]. 4 In the present work, laser absorption and fluorescence spectroscopy has been used to determine many of the crystal-field levels belonging to the 7F and 5D multiplets for Eu3` in LuPO . These J J 4 have been analyzed in terms of an empirical Hamiltonian. The fitted parameters were then used to calculate wave functions for those levels involved in the measured TPA transitions. Prompted by the observations of Gaˆcon et al., we have recorded the polarization behavior of five TPA transitions for Eu3` in LuPO . These results are analyzed in 4 terms of a new formalism for calculating twophoton transition intensities [21], which includes second- and third-order contributions. Explicit functions for the polarization dependencies were calculated from the crystal-field wave functions. The alternative expressions of Bader and Gold [19] include only second-order perturbations and contain arbitrary phenomenological parameters.
2. Experimental A single crystal of LuPO doped with Eu3` ions 4 was grown using the high-temperature solution technique described previously [22,23]. The concentration of Eu3` in the melt was approximately 6 mole % of that of the Lu3` ion. Due to the
difference in their ionic radii, the concentration of Eu3` in the resulting single crystals is probably much less. All the spectra were recorded with the sample cooled to about 4 K using an Oxford Instruments CF1204 optical cryostat. Initially, high-resolution one-photon absorption spectra were recorded to determine the crystal-field levels of the 5D and 5D multiplets. A Spex 1403 1 2 double monochromator was used to analyze the transmitted light, which was detected by a Hamamatsu R375 PMT, and measured using a Stanford Research SR400 photon counter. The 7F crystal-field levels were then obtained by J single-photon fluorescence spectroscopy with the same monochromator and were assigned from their polarization behavior. A 75 W Xe lamp in an Oriel Photomax housing was used as the light source in both these single-photon experiments. The monochromator was calibrated against a number of atomic discharge lamps. TPA spectra were obtained using a Lambda Physik Scanmate optical parametric oscillator (OPO) pumped by the third-harmonic output of a Spectra Physics GCR-3 Nd:YAG laser. This is a hybrid OPO, which uses a dye oscillator as a seed laser. Coumarin 503 and Coumarin 540A laser dyes were used when exciting the 5D and 5D mul0 2 tiplets, respectively. The output beam was filtered by a Corning 2-64 color filter. A Spectra Physics 310-21 polarization rotator was used to vary the excitation polarization. A 25 cm quartz lens directed the beam onto the crystal. The sample was displaced slightly from the focal point, in the direction of the lens, so that the incident energy density was approximately 1 J cm~2 for each pulse. The excitation energy was between 0.2 and 0.3 mJ, with a pulse duration of 5 ns. A Hamumatsu IP28 PMT was placed against a window of the cryostat to detect the broadband fluorescence. This was filtered with Corning 4-94 and 3-68 color filters, placed between the PMT and the window. The signal was preamplified by a Stanford Research SR445 fast preamplifier and then measured using the SR400 gated photon counter, with a gate delay of 100 ls and width of 5 ms. Transition intensities were measured from the TPA spectra using the line fitting routines of the GRAMS 386 program from Galactic Industries.
K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
3. Theory The observed energy levels were fitted to a phenomenological Hamiltonian H"HFI#HCF by a simultaneous diagonalization of the free-ion Hamiltonian HFI and the crystal-field Hamiltonian HCF. The free-ion Hamiltonian is given by the expression [24,25] HFI" + Fk(4f, 4f )f #f a #a¸(¸#1) k 4f S.O. k/0,2,4,6 #bG(G )#cG(R )# + ¹kt 2 7 k k/2,8 kE5 # + Mkm # + Pkp (1) k k, k/0,2,4 k/2,4,6 where the Fk(4f,4f ) and f parameters represent the 4& radial parts of the electrostatic and spin-orbit interactions, respectively, and f and a the angular k S.O. parts of these interactions between the 4f electrons. The parameters a, b, and c are associated with the two-body effective operators of the configuration interaction and ¹k are the corresponding parameters for the three-body-configuration interaction. The Mk parameters arise from spin—spin and spin-other-orbit interactions and the Pk parameters represent the electrostatic-spin-orbit interaction with higher configurations. The ¹k, Mk, and Pk are the radial parts of these interactions, whereas t , m , k k and p are the corresponding angular parts. For the k different interaction mechanisms present the angular parts can be evaluated exactly, while the radial portions are treated as parameters. For D symmetry, the crystal-field Hamiltonian 2$ can be expressed in terms of five phenomenological parameters Bk and the angular tensor operators Ck. q q For this particular symmetry, the values of DqD are limited to 0 and 4 and the Hamiltonian is given by [24] HCF"B2C2#B4C4#B4[C4 #C4] 4 4 ~4 0 0 0 0 (2) #B6C6#B6[C6 #C6]. 4 4 ~4 0 0 The polarization of incident photons is described in polar coordinates with respect to the Eu3` site axes. The z-axis is parallel to the crystallographic c-axis, h is the angle between the polarization unit
57
vector and the z-axis, and u is the angle between the polarization unit vector and the x-axis in the x—y plane. In LuPO the Eu3` site axes are rotated 4 by 45° about the z-axis from the crystallographic axes [23]. Therefore, the angle u is 45° for a beam entering the crystal normal to one of the cleavage faces. The intensity analysis of the Eu3` TPA transitions in LuPO follows the general formalism for 4 calculating two-photon intensities developed in Ref. [21]. This was applied previously to analyze the polarization behavior of electronic Raman transitions in PrVO and NdVO [26] and TPA 4 4 transitions of Cm3` in LuPO [20]. In this case, 4 there is one incident laser beam and therefore just one excitation frequency. The one-color twophoton transition intensity between the initial and final crystal-field states D 4f 6 2Si`1¸ C T and D4f 6 2Sf`1¸ C T iJi i fJf f is proportional to S "DS4f 6 2Si`1¸ C DaTPAD4f 6 2Sf`1¸ C TD2, if iJi i fJf f
(3)
where C is the irreducible representation of a partij cular crystal-field state in the multiplet 2Sj`1¸ . jJj The two-photon tensor operator aTPA has the form !1 (0) 3cos2h!1 (2) e~*usin2h (2) a0 # a0 ! a1 aTPA" 2 J3 J6 #
e*usin2h (2) e~2*usin2h (2) e2*usin2h (2) a21# a2 # a22 . 2 2 2 (4)
The wave functions for these states can be expressed in terms of Russell—Saunders coupled wave functions: D4f6 2Si`1L CT" + a(4f6 2Si`1L C ;4f6kSLJJ ) z iJi i iJi i kSLJJz ]D4f6kSLJJ T z ]D4f6 2Sf`1L C T fJf f " + a@(4f6 2Sf`1L C ;4f6kSLJJ )D z fJf f kSLJJz ]4f6kSLJJ T. (5) z
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K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
Particular multiplets are identified by the 2S`1L quantum numbers of their dominant RusJ sell—Saunders component. Second- and third-order matrix elements of the form
4. Results
ak"S4f 6 2Si`1L C DaTPAD4f 6 2Sf`1L C T q iJi i fJf f
Table 2 Calculated and experimental energy levels for Eu3` diluted in LuPO . All the experimental levels are for vacuum and have an 4 uncertainty of $1 cm~1
(6)
were calculated as described in Ref. [20]. In the case of Eu3`, 4f 55d is the lowest-lying excited configuration. Symmetry selection rules for a given TPA transition between two crystal-field levels, of C and i C symmetry, lead to specific expressions for the f (t) aTPA operator. In D symmetry the a q tensors can 2$ be expressed as sums of irreducible tensors which transform as irreducible representations of the D symmetry group [15,20]: 2$ a(0t)"a(Ct1) (t"0, 2), $1 (2) a (2) (a C5c1$a (2) G1" C5c2), J2
In total 23 Eu3` crystal-field levels were measured by single-photon spectroscopy and assigned
Multiplet Symmetry Calculated label energy (cm~1) 7F 0 7F 1 7F 2
7F 3
7F 4
1 (2) a (2) (a (2) $2" C3$a C4 ). J2
(7)
Considering the group selection rules for TPA from the 7F (C ) ground state, it follows that the non0 1 vanishing contributions of transitions to C sym1 metry levels involve only at matrix elements, 0 transitions to C or C levels involve only a2 , and 3 4 B2 transitions to C levels involve only a2 . TPA 5 B1 C PC transitions are forbidden in D sym1 2 2$ metry. Polarization dependence functions for the TPA transitions of non-Kramers ions calculated using Eqs. (4) and (7) are listed in Table 1.
7F 5
7F 6
Table 1 Polarization dependence functions for the TPA transitions of Eu3` ions in D symmetry 2$ Transition
Polarization dependence function
C PC 1 1
C
C PC 1 2 C PC 1 3 C PC 1 4 C PC 1 5
A
BD
1 3cos2 h!1 2 ! a0# a2 0 0 J3 J6
0 (1/4)(a2#a2 )2sin4 h cos2 2u 2 ~2 (1/4)(a2!a2 )2sin4 h sin2 2u 2 ~2 (1/4)(a2)2sin22h#(1/4)(a2 )2sin2 2h 1 ~1
5D 0 5D 1 5D 2
C 1 C 5 C 2 C 4 C 1 C 5 C 3 C 4 C 2 C 5 C 3 C 5 C 3 C 5 C 4 C 1 C 2 C 5 C 1 C 1@2 C 1@2 C 5 C 1@2 C 4 C 5 C 5 C 3@4 C 4 C 5 C 1@2 C 3@4 C 3@4 C 1@2 C 5 C 3@4 C 1@2 C 5 C 1 C 5 C 2 C 3 C 5 C 1 C 4
0 356 414 915 1039 1051 1106 1819 1843 1882 1917 1952 2623 2815 2842 2843 2866 2990 3013 3755 3801 3847 3854 3912 3982 4011 4046 4856 4872 4886 4991 5008 5031 5032 5052 5088 5092 17 191 18 931 18 953 21 383 21 406 21 417 21 428
Experimental Difference energy E !E %91 #!-# (cm~1) 0 349 412 907
0 !7 !2 !8
1059 1103 1827 1859 1880
8 !3 8 16 !2
1950
!2
2804 2846
!11 4
2994
4
3977 4012
!5 1
4863 4882
7 10
17 186 18 937 18 951 21 368 21 409 21 419 21 454
!5 6 !2 !15 3 3 26
K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64 Table 3 Parameter values for Eu3` ions in LuPO . Those values in 4 square brackets were fixed during this fitting procedure. A total of 18 experimental levels had been fitted initially [27], using free-ion parameters from Ref. [28]. The 23 levels listed in Table 1 were included in the final fit, which had an RMS deviation of 8.7 cmv1 Parameter
Final fit (cm~1)
Error (cm~1)
F2 F4 F6 f a b c T2 T3 T4 T6 T7 T8 M0 M2 M4 P2 P4 P6 B2 0 B4 0 B4 4 B6 0 B6 4
89,537 [61,194] [41,350] 1,324 [16.8] [!640] [1750] [370] [40] [40] [!330] [380] [370] [2.38] [1.33] [0.90] [245] [184] [123] 174 255 !804 !1251 39
103
1.0
21 82 29 77 98
59
definitively from their polarization behavior (Table 2). There was no evidence for a lowering of the symmetry at the Eu3` site in the nominally 6 mol% Eu3` crystal studied. In particular, the symmetry degenerate ! states did not exhibit any 5 low symmetry splittings. The measured levels were fitted to the Hamiltonian defined in Eqs. (1) and (2), starting from the best fit parameters of an earlier study [27]. A number of free-ion parameters were fixed at the values given for Eu3` in LaCl [28]. 3 The final values of the fitted parameters are listed in Table 3. The crystal-field parameters were not changed significantly by fitting the additional levels obtained in the present study. Wave functions for the crystal-field states of the 7F and 5D multiplets were obtained from the final 0 J fit and are listed in Table 4. These were then used to calculate at matrix elements for the measured TPA q transitions. The non-zero values calculated in second order and the corresponding polarization dependence functions for the 7F P5D TPA 0 J transitions are listed in Table 5. The combined second-order and third-order spin—orbit functions are given in Table 6. The calculations included only the 4f55d excited configuration, with values of 100 000 cm~1 for its average energy (E ) and 5$ 1300 cm~1 for its spin-orbit coupling parameter (f ). 5$ TPA was observed to the 5D state and to all 0 four levels of the 5D multiplet. Polarized excita2 tion spectra showing the 7F P 5D TPA 0 2 transitions for different h angles are presented in
Table 4 Calculated wave functions for the 7F and 5D crystal-field states of Eu3` in LuPO . These are expressed in terms of the pure 2S`1L (J ) 0 J 4 J z states Multiplet
Symmetry label
7F 0
C 1
0
5D 0 5D 1
C 1 C 5 C 2 C 3
17 191 18 931 18 953 21 383
C 5 C 1 C 4
21 406 21 417 21 428
5D 2
Calculated energy (cm~1)
Wave function !0.963 7F (0)#0.188 5D1 (0)!0.167 5D3 (0) 0 0 0 #0.039 7F (0)!0.006 5D1 (0) #0.005 5D3 (0) 2 2 2 0.244 7F (0)#0.550 5D1 (0)!0.672 5D3 (0) 0 0 0 0.216 7F (1)#0.576 5D1 (1)!0.710 5D3 (1) 1 1 1 0.216 7F (0)#0.577 5D1 (0) ! 0.710 5D3 (0) 1 1 1 0.119 7F (!2)#0.422 5D1 (!2)!0.518 5D3 (!2) 2 2 2 #0.119 7F (2) #0.422 5D1 (2)!0.518 5D3 (2) 2 2 2 0.168 7F (1)#0.597 5D1 (1)!0.734 5D3 (1) 2 2 2 !0.168 7F (0)!0.597 5D1 (0)#0.734 5D3 (0) 2 2 2 !0.119 7F (!2)!0.422 5D1 (!2)#0.518 5D3 (!2) 2 2 2 #0.119 7F (2) #0.422 5D1 (2)! 0.518 5D3 (2) 2 2 2
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K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
Table 5 Polarization dependence functions calculated for the 7F P5D 0 J TPA transitions of Eu3` in LuPO . These are the non-zero 4 second-order contributions Transition
at matrix q elements (10~7)
Polarization dependence (10~14)
7F (C )P5D (C ) 0 1 0 1 7F (C )P5D (C ) 0 1 1 5 7F (C )P5D (C ) 0 1 1 2 7F (C )P5D (C ) 0 1 2 3 7F (C )P5D (C ) 0 1 2 5 7F (C )P5D (C ) 0 1 2 1 7F (C )P5D (C ) 0 1 2 4
a2"!0.115 0 None None a2 "!1.35 B2 a2 "!1.91 B1 a2"!1.91 0 a2 "1.35 B2
0.0022 (3 cos2 h! 1)2 0 0 1.80 sin4 h cos2 2u 1.81 sin2 2h 0.61(3 cos2 h!1)2 1.80 sin4 h sin2 2u
Figs. 1 and 2. While recording the spectra in Fig. 1 the laser beam was perpendicular to the crystallographic ac-plane, so u"45°. For Fig. 2 the crystal had been rotated about the c-axis by approximately 23°. Allowing for refraction of the laser beam in the crystal, calculated from a refractive index of 1.70 for phosphates [29], the angle u was approximately 32° for half the centers and 58° for the other half. All the spectra have been plotted on the same scale for comparison, although there must be higher reflection losses in Fig. 2. They have not been corrected for the small changes in laser intensity as the OPO was scanned towards the peak of the oscillator dye curve. With u"45°, TPA was observed to the 5D (C ) 0 1 level at 17 186 cm~1 and to the 5D levels at 2 21 409, 21 419, and 21 454 cm~1. The latter were assigned as the C , C , and C states of the 5 1 4 5D multiplet, respectively. The 7F (C ) 2 0 1
Fig. 1. h"0°, 45°, and 90° polarized spectra of the TPA transitions to the 5D multiplet for u"45° at 4.2 K. The 2 transitions are labelled i, according to the C symmetry of the * 5D levels. 2
P 5D (C ) transition could be identified unam2 5 biguously as it had zero intensity when h"0 or 90°, and was most intense when h"45° or 135°. The TPA transition to the 5D level at 2 21 368 cm~1, which was absent when u"45°, was observed as predicted when the crystal was rotated. It was assigned to the 5D (C ) state. Fig. 3 shows 2 3 the experimental polarization dependencies of the
Table 6 Polarization dependence functions calculated for the 7F P 5D TPA transitions of Eu3` in LuPO . These are the total second- and 0 J 4 third-order contributions Transition
at matrix elements (10~7) q
Polarization dependence (10~14)
7F (C )P5D (C ) 0 1 0 1 7F (C )P5D (C ) 0 1 1 5 7F (C )P5D (C ) 0 1 1 2 7F (C )P5D (C ) 0 1 2 3 7F (C )P5D (C ) 0 1 2 5 7F (C )P5D (C ) 0 1 2 1 7F (C )P5D (C ) 0 1 2 4
a0"6.0, a2 "!0.11 0 0 None None a2 "1.3 B2 a2 "!1.9 B1 a0"0.2, a2 "!1.9 0 0 a2 "1.3 B2
0.02 cos4 h#0.92 cos2 h#11.69 0 0 1.80 sin4 h cos2 2u 1.81 sin2 2h 5.42 cos4 h#3.07 cos2 h#0.44 1.80 sin4 h sin2 2u
K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
61
Gaˆcon et al. [16—18] observed that in such cases the experimental polarization behavior could be fitted if the two-photon tensor operator aTPA contained complex rather than purely real elements. This is demonstrated in Fig. 4, where the experimental intensities have been fitted to a parameterized polarization function Dj! k(3 cos2 h!1)D2, where j is a complex and k is a real parameter. In the earlier analyses the ratio j/k was complex [16—18]. That the imaginary part of j accounts for the additional isotropic component of the TPA transitions to the C levels is obvi1 ous when this function is expressed as: DRe(j)#i Im(j)!k(3 cos2h!1)D2 "[Re(j)!k(3 cos2h!1)]2#Im(j)2.
Fig. 2. h"0°, 45°, and 90° polarized spectra of the TPA transitions to the 5D multiplet for u"32°/58° at 4.2 K. The 2 transitions are labelled i, according to the C symmetry of the * 5D levels. 2
7F P 5D TPA transitions, which are compared 0 J to the predicted polarization functions calculated in the second and third order and listed in Table 6. The observed polarization behavior of the 7F P 5D transition was identical to that re0 0 ported previously [17].
5. Discussion The TPA polarization behavior predicted using the second-order theory agrees well with that observed experimentally for the transitions to the C , 3 C , and C levels of the 5D multiplet. For these 5 4 2 transitions the third-order spin—orbit contribution was found to be at least two orders of magnitude smaller than the second-order contribution. However, there is very poor agreement for TPA transitions to the C states of both the 5D and 1 0 5D multiplets, even after the inclusion of the sub2 stantial third-order contributions represented by their non-zero a0 matrix elements. 0
(8)
The fitted value of j for the 7F (C )P5D (C ) 0 1 0 1 polarization dependence in Fig. 4a, after scaling !k to the value of (1/J6)a2 from Table 6, is 0 (0.00$ i0.07)]10~7. This is numerically equivalent to adding a (3.47$ i0.07)]10~7 complex term to the combined second and third-order amplitude of the calculated function given in Table 6. The value of Dj/kD is 1.56, compared to 1.21 found by Gaˆcon et al. [17] for the same transition. It is interesting to note that if Re(j) is taken as the value of (!1/J3)a0, the first term 0 in the definition of aTPA in Eq. (4), then the a0 para0 meter becomes zero. Similarly, the fitted value of k for the 7F (C )P5D (C ) transition in Fig. 4b is 0 1 2 1 (0.43$ i0.95)]10~7. In this case a (0.55$ i0.95)]10~7 complex term is required and it is equivalent to a Dj/kD value of 1.35. The fitted value of Re(j) corresponds to a value for a0 of 0 !0.75]10~7.
6. Conclusions Polarized one-photon absorption and fluorescence spectroscopy has been used to measure and identify 23 crystal-field levels for the Eu3` ion located at the D symmetry site of LuPO . These 2$ 4 levels have been fitted to a parameterized Hamiltonian using a least-squares fitting procedure. Two-photon excitation was observed to all five levels of the 5D and 5D multiplets and the 0 2
62
K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
Fig. 3. Experimental polarization behavior (dots) of the (a) 7F (C ) P 5D (C ), (b) 7F P 5D (C ), (c) 7F P 5D (C ), (d) 0 1 0 1 0 2 3 0 2 5 7F P 5D (C ), and (e) 7F P 5D (C ) TPA transitions. The combined second- and third-order calculated polarization dependencies 0 2 1 0 2 4 from Table 6 are represented by the solid lines.
intensities of these transitions were investigated. The results presented here are consistent with those reported previously by Gaˆcon et al. [16—18]. TPA transitions with calculated intensities dominated by second-order contributions exhibited good agree-
ment between their calculated and observed polarization behavior. Inclusion of the third-order spin— orbit interaction was not sufficient to account for the polarization behavior of other TPA transitions and alternative mechanisms must be considered.
K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
63
Fig. 4. Experimental polarization behavior (dots) of the (a) 7F (C ) P 5D (C ) and (b) 7F P 5D (C ) TPA transitions. The 0 1 0 1 0 2 1 polarization dependencies obtained by fitting this data to the intensity function defined in Eq. (8) are represented by the solid line.
Acknowledgements Drs. M.M. Abraham and L.A. Boatner of Oak Ridge National Laboratory are gratefully acknowledged for growing and providing the crystal used for this work. This research was sponsored in part by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the US. Department of Energy under Contract No. DE-AC03-76SF00098 with the University of California.
References [1] D.F. Mullica, W.O. Milligan, D.A. Grossie, G.W. Beall, L.A. Boatner, Inorg. Chem. Acta 95 (1984) 231. [2] D.F. Mullica, D.A. Grossie, L.A. Boatner, J. Solid State Chem. 58 (1985) 71. [3] P.C. Becker, T. Hayhurst, G. Shalimoff, J.G. Conway, N.M. Edelstein, L.A. Boatner, M.M. Abraham, J. Chem. Phys. 81 (1984) 2872 and references therein.. [4] K.M. Murdoch, N.M. Edelstein, L.A. Boatner, M.M. Abraham, J. Chem. Phys. 105 (1996) 2539 and references therein. [5] A. Lempicki, E. Berman, A.J. Wojtowicz, M. Balcerzyk, L.A. Boatner, IEEE Trans. Nucl. Sci. 40 (1993) 384. [6] C. Brecher, H. Samelson, R. Riley, A. Lempicki, J. Chem. Phys. 49 (1968) 3303. [7] C. Brecher, H. Samelson, A. Lempicki, R. Riley, T. Peters, Phys. Rev. 155 (1967) 178. [8] J.D. Axe, Phys. Rev. 136 (1964) A42.
[9] M. Degenais, M.C. Downer, R. Neumann, N. Bloembergen, Phys. Rev. Lett. 46 (1981) 561. [10] M.C. Downer, A. Bivas, N. Bloembergen, Opt. Commun. 41 (1982) 335. [11] M.C. Downer, in: W.M. Yen (Ed.), Laser Spectroscopy of Solids, Topics Appl. Phys., vol. 65, Springer, Berlin, 1989, p. 29. [12] B.R. Judd, D.R. Pooler, J. Phys. C 15 (1982) 591. [13] M.C. Downer, A. Bivas, Phys. Rev. B 28 (1983) 3677. [14] M.C. Downer, C.D. Cordero-Montalvo, H. Crosswhite, Phys. Rev. B 28 (1983) 4931. [15] J.C. Gaˆcon, J.F. Marcerou, M. Bouazaoui, B. Jacquier, M. Kibler, Phys. Rev. B 40 (1989) 2070. [16] J.C. Gaˆcon, B. Jacquier, J.F. Marcerou, M. Bouazaoui, M. Kibler, J. Lumin. 45 (1990) 162. [17] J.C. Gaˆcon, M. Bouazaoui, B. Jacquier, M. Kibler, L.A. Boatner, M.M. Abraham, Eur. J. Solid State Inorg. Chem. 28 (1991) 113. [18] R. Mahiou, J.C. Gaˆcon, B. Jacquier, R.L. Cone, J. Lumin. 60&61 (1994) 664. [19] T.R. Bader, A. Gold, Phys. Rev. 171 (1968) 997. [20] K.M. Murdoch, A.D. Nguyen, N.M. Edelstein, S. Hubert, J.C. Gaˆcon, Phys. Rev. B 56 (1997) 3038. [21] A.D. Nguyen, Phys. Rev. B 55 (1997) 5786. [22] L.A. Boatner, G.W. Beall, M.M. Abraham, C.B. Finch, R.J. Floran, P.G. Huray, M. Rappaz, Management of AlphaContaminated Wastes, IAEA-SM-245/73, International Atomic Energy Agency, Vienna, 1981 p. 114. [23] M. Rappaz, L.A. Boatner, M.M. Abraham, J. Chem. Phys. 73 (1980) 1095. [24] B.G. Wybourne, Spectroscopic Properties of Rare Earths, Wiley, New York, 1965. [25] W.T. Carnall, H. Crosswhite, H.M. Crosswhite, J.P. Hessler, N.M. Edelstein, J.G. Conway, G.V. Shalimoff, R. Sarup, J. Chem. Phys. 72 (1980) 5089.
64
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[26] A.D. Nguyen, K.M. Murdoch, N.M. Edelstein, L.A. Boatner, M.M. Abraham, Phys. Rev. B 56 (1997) 7974. [27] D. Piehler, D.S. Kim, unpublished work. [28] W.T. Carnall, H. Crosswhite, H.M. Crosswhite, Energy level structure and transition probabilities of the trivalent
lanthanides in LaF , Table 1 in Appendix 1, Special 3 Report 1977, Chemistry Division, Argonne National Laboratory, Argonne, IL. [29] A. Armbruster, R. Thoma, H. Wehrle, Stat. Sol. A 24 (1974) K71.
One- and two-photon spectroscopy of Eu3` in LuPO 4 Keith M. Murdoch*, An-Dien Nguyen, Norman M. Edelstein Chemical Sciences Division, MS 70A-1150, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Received 4 August 1997; received in revised form 22 December 1997; accepted 29 January 1998
Abstract One-photon laser excitation and fluorescence spectra have been recorded for the Eu3` ion diluted in single crystals of LuPO . Analysis of these spectra resulted in the assignment of 23 energy levels of the 7F and 5D multiplets, which were 4 J J fitted to the parameters of an empirical Hamiltonian with an rms deviation of 8.7 cm~1. The intensities of the two-photon absorption transitions to the 5D0 and 5D2 multiplets have been investigated. The polarization dependences of transitions to all five of the crystal-field levels were measured and are compared with theoretical predictions. The intensity model included the third-order spin—orbit interaction. Good agreement was found for three of the five transitions observed. However, the polarization dependences of the other two did not agree with the predicted behavior, as they exhibited an additional isotropic component. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Two-photon absorption; Polarization analysis; Crystal-field analysis
1. Introduction The lanthanide orthophosphate LuPO forms 4 the tetragonal zircon-type structure at high temperatures [1,2] and has excellent chemical stability and resistance to damage by ionizing radiation. Other trivalent lanthanide [2,3] and actinide [4] ions enter this lattice substitutionally at sites of D point symmetry. Crystals of LuPO doped 2$ 4 with optically active rare-earth ions have potential applications as thermophosphors for remote temperature measurement, as X- and c-ray scintillators for medical imaging, and as laser materials [5]. Previous studies have reported on the one-photon spectroscopy of Eu3` ions diluted into the related phosphate YPO [6] and the vanadate YVO [7]. 4 4 * Corresponding author. Tel.: (608) 263 1082; fax: (608) 262 0381; e-mail: [email protected].
Crystal-field parameters were obtained for the Eu3` site in each of these crystals and used in a qualitative analysis of their structural differences [6]. Analyses of intra-configurational 4fN—4fN twophoton absorption (TPA) transitions of rare-earth ions in various host crystals have generated much theoretical interest since the standard second-order theory of Axe [8] has proven inadequate to explain many of the observed relative transition intensities [9—11]. Judd and Pooler [12] introduced a thirdorder correction by including the spin—orbit interaction between intermediate states of the 4fN~15d lowest lying excited configuration. The predominant term arising from this mechanism is a scalar and contributes an isotropic component to the intensities of *J "0 TPA transitions. They note that this is the only term which contributes to the 7F P 5D TPA transition of the Eu3` ion. 0 0 Downer et al. [11,13,14] subsequently included other higher-order corrections to account for the
0022-2313/98/$ — see front matter ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 9 8 ) 0 0 0 1 4 - 3
56
K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
observed discrepancies, particularly the crystalfield interaction between intermediate states. Recently, Gaˆcon et al. [15—18] presented measurements of Sm2` and Eu3` TPA intensities. They found several TPA transitions in Sm2` : BaClF, Sm2`:SrClF, Eu(OH) , and Eu3`:LuPO with po3 4 larization behavior which is inconsistent with the polarization dependencies calculated by Bader and Gold [19] using symmetry considerations. These transitions have an additional isotropic intensity component over all polarization angles h, where h is the angle between the crystallographic c-axis and the polarization unit vector of the excitation beam. This component could be parameterized by introducing complex variables into the expression of the TPA amplitude. However, it could not be explained by any of the aforementioned mechanisms which are known to contribute to TPA intensities. Similar anomalous behavior was observed for some TPA transitions of Cm3` in LuPO [20]. 4 In the present work, laser absorption and fluorescence spectroscopy has been used to determine many of the crystal-field levels belonging to the 7F and 5D multiplets for Eu3` in LuPO . These J J 4 have been analyzed in terms of an empirical Hamiltonian. The fitted parameters were then used to calculate wave functions for those levels involved in the measured TPA transitions. Prompted by the observations of Gaˆcon et al., we have recorded the polarization behavior of five TPA transitions for Eu3` in LuPO . These results are analyzed in 4 terms of a new formalism for calculating twophoton transition intensities [21], which includes second- and third-order contributions. Explicit functions for the polarization dependencies were calculated from the crystal-field wave functions. The alternative expressions of Bader and Gold [19] include only second-order perturbations and contain arbitrary phenomenological parameters.
2. Experimental A single crystal of LuPO doped with Eu3` ions 4 was grown using the high-temperature solution technique described previously [22,23]. The concentration of Eu3` in the melt was approximately 6 mole % of that of the Lu3` ion. Due to the
difference in their ionic radii, the concentration of Eu3` in the resulting single crystals is probably much less. All the spectra were recorded with the sample cooled to about 4 K using an Oxford Instruments CF1204 optical cryostat. Initially, high-resolution one-photon absorption spectra were recorded to determine the crystal-field levels of the 5D and 5D multiplets. A Spex 1403 1 2 double monochromator was used to analyze the transmitted light, which was detected by a Hamamatsu R375 PMT, and measured using a Stanford Research SR400 photon counter. The 7F crystal-field levels were then obtained by J single-photon fluorescence spectroscopy with the same monochromator and were assigned from their polarization behavior. A 75 W Xe lamp in an Oriel Photomax housing was used as the light source in both these single-photon experiments. The monochromator was calibrated against a number of atomic discharge lamps. TPA spectra were obtained using a Lambda Physik Scanmate optical parametric oscillator (OPO) pumped by the third-harmonic output of a Spectra Physics GCR-3 Nd:YAG laser. This is a hybrid OPO, which uses a dye oscillator as a seed laser. Coumarin 503 and Coumarin 540A laser dyes were used when exciting the 5D and 5D mul0 2 tiplets, respectively. The output beam was filtered by a Corning 2-64 color filter. A Spectra Physics 310-21 polarization rotator was used to vary the excitation polarization. A 25 cm quartz lens directed the beam onto the crystal. The sample was displaced slightly from the focal point, in the direction of the lens, so that the incident energy density was approximately 1 J cm~2 for each pulse. The excitation energy was between 0.2 and 0.3 mJ, with a pulse duration of 5 ns. A Hamumatsu IP28 PMT was placed against a window of the cryostat to detect the broadband fluorescence. This was filtered with Corning 4-94 and 3-68 color filters, placed between the PMT and the window. The signal was preamplified by a Stanford Research SR445 fast preamplifier and then measured using the SR400 gated photon counter, with a gate delay of 100 ls and width of 5 ms. Transition intensities were measured from the TPA spectra using the line fitting routines of the GRAMS 386 program from Galactic Industries.
K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
3. Theory The observed energy levels were fitted to a phenomenological Hamiltonian H"HFI#HCF by a simultaneous diagonalization of the free-ion Hamiltonian HFI and the crystal-field Hamiltonian HCF. The free-ion Hamiltonian is given by the expression [24,25] HFI" + Fk(4f, 4f )f #f a #a¸(¸#1) k 4f S.O. k/0,2,4,6 #bG(G )#cG(R )# + ¹kt 2 7 k k/2,8 kE5 # + Mkm # + Pkp (1) k k, k/0,2,4 k/2,4,6 where the Fk(4f,4f ) and f parameters represent the 4& radial parts of the electrostatic and spin-orbit interactions, respectively, and f and a the angular k S.O. parts of these interactions between the 4f electrons. The parameters a, b, and c are associated with the two-body effective operators of the configuration interaction and ¹k are the corresponding parameters for the three-body-configuration interaction. The Mk parameters arise from spin—spin and spin-other-orbit interactions and the Pk parameters represent the electrostatic-spin-orbit interaction with higher configurations. The ¹k, Mk, and Pk are the radial parts of these interactions, whereas t , m , k k and p are the corresponding angular parts. For the k different interaction mechanisms present the angular parts can be evaluated exactly, while the radial portions are treated as parameters. For D symmetry, the crystal-field Hamiltonian 2$ can be expressed in terms of five phenomenological parameters Bk and the angular tensor operators Ck. q q For this particular symmetry, the values of DqD are limited to 0 and 4 and the Hamiltonian is given by [24] HCF"B2C2#B4C4#B4[C4 #C4] 4 4 ~4 0 0 0 0 (2) #B6C6#B6[C6 #C6]. 4 4 ~4 0 0 The polarization of incident photons is described in polar coordinates with respect to the Eu3` site axes. The z-axis is parallel to the crystallographic c-axis, h is the angle between the polarization unit
57
vector and the z-axis, and u is the angle between the polarization unit vector and the x-axis in the x—y plane. In LuPO the Eu3` site axes are rotated 4 by 45° about the z-axis from the crystallographic axes [23]. Therefore, the angle u is 45° for a beam entering the crystal normal to one of the cleavage faces. The intensity analysis of the Eu3` TPA transitions in LuPO follows the general formalism for 4 calculating two-photon intensities developed in Ref. [21]. This was applied previously to analyze the polarization behavior of electronic Raman transitions in PrVO and NdVO [26] and TPA 4 4 transitions of Cm3` in LuPO [20]. In this case, 4 there is one incident laser beam and therefore just one excitation frequency. The one-color twophoton transition intensity between the initial and final crystal-field states D 4f 6 2Si`1¸ C T and D4f 6 2Sf`1¸ C T iJi i fJf f is proportional to S "DS4f 6 2Si`1¸ C DaTPAD4f 6 2Sf`1¸ C TD2, if iJi i fJf f
(3)
where C is the irreducible representation of a partij cular crystal-field state in the multiplet 2Sj`1¸ . jJj The two-photon tensor operator aTPA has the form !1 (0) 3cos2h!1 (2) e~*usin2h (2) a0 # a0 ! a1 aTPA" 2 J3 J6 #
e*usin2h (2) e~2*usin2h (2) e2*usin2h (2) a21# a2 # a22 . 2 2 2 (4)
The wave functions for these states can be expressed in terms of Russell—Saunders coupled wave functions: D4f6 2Si`1L CT" + a(4f6 2Si`1L C ;4f6kSLJJ ) z iJi i iJi i kSLJJz ]D4f6kSLJJ T z ]D4f6 2Sf`1L C T fJf f " + a@(4f6 2Sf`1L C ;4f6kSLJJ )D z fJf f kSLJJz ]4f6kSLJJ T. (5) z
58
K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
Particular multiplets are identified by the 2S`1L quantum numbers of their dominant RusJ sell—Saunders component. Second- and third-order matrix elements of the form
4. Results
ak"S4f 6 2Si`1L C DaTPAD4f 6 2Sf`1L C T q iJi i fJf f
Table 2 Calculated and experimental energy levels for Eu3` diluted in LuPO . All the experimental levels are for vacuum and have an 4 uncertainty of $1 cm~1
(6)
were calculated as described in Ref. [20]. In the case of Eu3`, 4f 55d is the lowest-lying excited configuration. Symmetry selection rules for a given TPA transition between two crystal-field levels, of C and i C symmetry, lead to specific expressions for the f (t) aTPA operator. In D symmetry the a q tensors can 2$ be expressed as sums of irreducible tensors which transform as irreducible representations of the D symmetry group [15,20]: 2$ a(0t)"a(Ct1) (t"0, 2), $1 (2) a (2) (a C5c1$a (2) G1" C5c2), J2
In total 23 Eu3` crystal-field levels were measured by single-photon spectroscopy and assigned
Multiplet Symmetry Calculated label energy (cm~1) 7F 0 7F 1 7F 2
7F 3
7F 4
1 (2) a (2) (a (2) $2" C3$a C4 ). J2
(7)
Considering the group selection rules for TPA from the 7F (C ) ground state, it follows that the non0 1 vanishing contributions of transitions to C sym1 metry levels involve only at matrix elements, 0 transitions to C or C levels involve only a2 , and 3 4 B2 transitions to C levels involve only a2 . TPA 5 B1 C PC transitions are forbidden in D sym1 2 2$ metry. Polarization dependence functions for the TPA transitions of non-Kramers ions calculated using Eqs. (4) and (7) are listed in Table 1.
7F 5
7F 6
Table 1 Polarization dependence functions for the TPA transitions of Eu3` ions in D symmetry 2$ Transition
Polarization dependence function
C PC 1 1
C
C PC 1 2 C PC 1 3 C PC 1 4 C PC 1 5
A
BD
1 3cos2 h!1 2 ! a0# a2 0 0 J3 J6
0 (1/4)(a2#a2 )2sin4 h cos2 2u 2 ~2 (1/4)(a2!a2 )2sin4 h sin2 2u 2 ~2 (1/4)(a2)2sin22h#(1/4)(a2 )2sin2 2h 1 ~1
5D 0 5D 1 5D 2
C 1 C 5 C 2 C 4 C 1 C 5 C 3 C 4 C 2 C 5 C 3 C 5 C 3 C 5 C 4 C 1 C 2 C 5 C 1 C 1@2 C 1@2 C 5 C 1@2 C 4 C 5 C 5 C 3@4 C 4 C 5 C 1@2 C 3@4 C 3@4 C 1@2 C 5 C 3@4 C 1@2 C 5 C 1 C 5 C 2 C 3 C 5 C 1 C 4
0 356 414 915 1039 1051 1106 1819 1843 1882 1917 1952 2623 2815 2842 2843 2866 2990 3013 3755 3801 3847 3854 3912 3982 4011 4046 4856 4872 4886 4991 5008 5031 5032 5052 5088 5092 17 191 18 931 18 953 21 383 21 406 21 417 21 428
Experimental Difference energy E !E %91 #!-# (cm~1) 0 349 412 907
0 !7 !2 !8
1059 1103 1827 1859 1880
8 !3 8 16 !2
1950
!2
2804 2846
!11 4
2994
4
3977 4012
!5 1
4863 4882
7 10
17 186 18 937 18 951 21 368 21 409 21 419 21 454
!5 6 !2 !15 3 3 26
K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64 Table 3 Parameter values for Eu3` ions in LuPO . Those values in 4 square brackets were fixed during this fitting procedure. A total of 18 experimental levels had been fitted initially [27], using free-ion parameters from Ref. [28]. The 23 levels listed in Table 1 were included in the final fit, which had an RMS deviation of 8.7 cmv1 Parameter
Final fit (cm~1)
Error (cm~1)
F2 F4 F6 f a b c T2 T3 T4 T6 T7 T8 M0 M2 M4 P2 P4 P6 B2 0 B4 0 B4 4 B6 0 B6 4
89,537 [61,194] [41,350] 1,324 [16.8] [!640] [1750] [370] [40] [40] [!330] [380] [370] [2.38] [1.33] [0.90] [245] [184] [123] 174 255 !804 !1251 39
103
1.0
21 82 29 77 98
59
definitively from their polarization behavior (Table 2). There was no evidence for a lowering of the symmetry at the Eu3` site in the nominally 6 mol% Eu3` crystal studied. In particular, the symmetry degenerate ! states did not exhibit any 5 low symmetry splittings. The measured levels were fitted to the Hamiltonian defined in Eqs. (1) and (2), starting from the best fit parameters of an earlier study [27]. A number of free-ion parameters were fixed at the values given for Eu3` in LaCl [28]. 3 The final values of the fitted parameters are listed in Table 3. The crystal-field parameters were not changed significantly by fitting the additional levels obtained in the present study. Wave functions for the crystal-field states of the 7F and 5D multiplets were obtained from the final 0 J fit and are listed in Table 4. These were then used to calculate at matrix elements for the measured TPA q transitions. The non-zero values calculated in second order and the corresponding polarization dependence functions for the 7F P5D TPA 0 J transitions are listed in Table 5. The combined second-order and third-order spin—orbit functions are given in Table 6. The calculations included only the 4f55d excited configuration, with values of 100 000 cm~1 for its average energy (E ) and 5$ 1300 cm~1 for its spin-orbit coupling parameter (f ). 5$ TPA was observed to the 5D state and to all 0 four levels of the 5D multiplet. Polarized excita2 tion spectra showing the 7F P 5D TPA 0 2 transitions for different h angles are presented in
Table 4 Calculated wave functions for the 7F and 5D crystal-field states of Eu3` in LuPO . These are expressed in terms of the pure 2S`1L (J ) 0 J 4 J z states Multiplet
Symmetry label
7F 0
C 1
0
5D 0 5D 1
C 1 C 5 C 2 C 3
17 191 18 931 18 953 21 383
C 5 C 1 C 4
21 406 21 417 21 428
5D 2
Calculated energy (cm~1)
Wave function !0.963 7F (0)#0.188 5D1 (0)!0.167 5D3 (0) 0 0 0 #0.039 7F (0)!0.006 5D1 (0) #0.005 5D3 (0) 2 2 2 0.244 7F (0)#0.550 5D1 (0)!0.672 5D3 (0) 0 0 0 0.216 7F (1)#0.576 5D1 (1)!0.710 5D3 (1) 1 1 1 0.216 7F (0)#0.577 5D1 (0) ! 0.710 5D3 (0) 1 1 1 0.119 7F (!2)#0.422 5D1 (!2)!0.518 5D3 (!2) 2 2 2 #0.119 7F (2) #0.422 5D1 (2)!0.518 5D3 (2) 2 2 2 0.168 7F (1)#0.597 5D1 (1)!0.734 5D3 (1) 2 2 2 !0.168 7F (0)!0.597 5D1 (0)#0.734 5D3 (0) 2 2 2 !0.119 7F (!2)!0.422 5D1 (!2)#0.518 5D3 (!2) 2 2 2 #0.119 7F (2) #0.422 5D1 (2)! 0.518 5D3 (2) 2 2 2
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K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
Table 5 Polarization dependence functions calculated for the 7F P5D 0 J TPA transitions of Eu3` in LuPO . These are the non-zero 4 second-order contributions Transition
at matrix q elements (10~7)
Polarization dependence (10~14)
7F (C )P5D (C ) 0 1 0 1 7F (C )P5D (C ) 0 1 1 5 7F (C )P5D (C ) 0 1 1 2 7F (C )P5D (C ) 0 1 2 3 7F (C )P5D (C ) 0 1 2 5 7F (C )P5D (C ) 0 1 2 1 7F (C )P5D (C ) 0 1 2 4
a2"!0.115 0 None None a2 "!1.35 B2 a2 "!1.91 B1 a2"!1.91 0 a2 "1.35 B2
0.0022 (3 cos2 h! 1)2 0 0 1.80 sin4 h cos2 2u 1.81 sin2 2h 0.61(3 cos2 h!1)2 1.80 sin4 h sin2 2u
Figs. 1 and 2. While recording the spectra in Fig. 1 the laser beam was perpendicular to the crystallographic ac-plane, so u"45°. For Fig. 2 the crystal had been rotated about the c-axis by approximately 23°. Allowing for refraction of the laser beam in the crystal, calculated from a refractive index of 1.70 for phosphates [29], the angle u was approximately 32° for half the centers and 58° for the other half. All the spectra have been plotted on the same scale for comparison, although there must be higher reflection losses in Fig. 2. They have not been corrected for the small changes in laser intensity as the OPO was scanned towards the peak of the oscillator dye curve. With u"45°, TPA was observed to the 5D (C ) 0 1 level at 17 186 cm~1 and to the 5D levels at 2 21 409, 21 419, and 21 454 cm~1. The latter were assigned as the C , C , and C states of the 5 1 4 5D multiplet, respectively. The 7F (C ) 2 0 1
Fig. 1. h"0°, 45°, and 90° polarized spectra of the TPA transitions to the 5D multiplet for u"45° at 4.2 K. The 2 transitions are labelled i, according to the C symmetry of the * 5D levels. 2
P 5D (C ) transition could be identified unam2 5 biguously as it had zero intensity when h"0 or 90°, and was most intense when h"45° or 135°. The TPA transition to the 5D level at 2 21 368 cm~1, which was absent when u"45°, was observed as predicted when the crystal was rotated. It was assigned to the 5D (C ) state. Fig. 3 shows 2 3 the experimental polarization dependencies of the
Table 6 Polarization dependence functions calculated for the 7F P 5D TPA transitions of Eu3` in LuPO . These are the total second- and 0 J 4 third-order contributions Transition
at matrix elements (10~7) q
Polarization dependence (10~14)
7F (C )P5D (C ) 0 1 0 1 7F (C )P5D (C ) 0 1 1 5 7F (C )P5D (C ) 0 1 1 2 7F (C )P5D (C ) 0 1 2 3 7F (C )P5D (C ) 0 1 2 5 7F (C )P5D (C ) 0 1 2 1 7F (C )P5D (C ) 0 1 2 4
a0"6.0, a2 "!0.11 0 0 None None a2 "1.3 B2 a2 "!1.9 B1 a0"0.2, a2 "!1.9 0 0 a2 "1.3 B2
0.02 cos4 h#0.92 cos2 h#11.69 0 0 1.80 sin4 h cos2 2u 1.81 sin2 2h 5.42 cos4 h#3.07 cos2 h#0.44 1.80 sin4 h sin2 2u
K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
61
Gaˆcon et al. [16—18] observed that in such cases the experimental polarization behavior could be fitted if the two-photon tensor operator aTPA contained complex rather than purely real elements. This is demonstrated in Fig. 4, where the experimental intensities have been fitted to a parameterized polarization function Dj! k(3 cos2 h!1)D2, where j is a complex and k is a real parameter. In the earlier analyses the ratio j/k was complex [16—18]. That the imaginary part of j accounts for the additional isotropic component of the TPA transitions to the C levels is obvi1 ous when this function is expressed as: DRe(j)#i Im(j)!k(3 cos2h!1)D2 "[Re(j)!k(3 cos2h!1)]2#Im(j)2.
Fig. 2. h"0°, 45°, and 90° polarized spectra of the TPA transitions to the 5D multiplet for u"32°/58° at 4.2 K. The 2 transitions are labelled i, according to the C symmetry of the * 5D levels. 2
7F P 5D TPA transitions, which are compared 0 J to the predicted polarization functions calculated in the second and third order and listed in Table 6. The observed polarization behavior of the 7F P 5D transition was identical to that re0 0 ported previously [17].
5. Discussion The TPA polarization behavior predicted using the second-order theory agrees well with that observed experimentally for the transitions to the C , 3 C , and C levels of the 5D multiplet. For these 5 4 2 transitions the third-order spin—orbit contribution was found to be at least two orders of magnitude smaller than the second-order contribution. However, there is very poor agreement for TPA transitions to the C states of both the 5D and 1 0 5D multiplets, even after the inclusion of the sub2 stantial third-order contributions represented by their non-zero a0 matrix elements. 0
(8)
The fitted value of j for the 7F (C )P5D (C ) 0 1 0 1 polarization dependence in Fig. 4a, after scaling !k to the value of (1/J6)a2 from Table 6, is 0 (0.00$ i0.07)]10~7. This is numerically equivalent to adding a (3.47$ i0.07)]10~7 complex term to the combined second and third-order amplitude of the calculated function given in Table 6. The value of Dj/kD is 1.56, compared to 1.21 found by Gaˆcon et al. [17] for the same transition. It is interesting to note that if Re(j) is taken as the value of (!1/J3)a0, the first term 0 in the definition of aTPA in Eq. (4), then the a0 para0 meter becomes zero. Similarly, the fitted value of k for the 7F (C )P5D (C ) transition in Fig. 4b is 0 1 2 1 (0.43$ i0.95)]10~7. In this case a (0.55$ i0.95)]10~7 complex term is required and it is equivalent to a Dj/kD value of 1.35. The fitted value of Re(j) corresponds to a value for a0 of 0 !0.75]10~7.
6. Conclusions Polarized one-photon absorption and fluorescence spectroscopy has been used to measure and identify 23 crystal-field levels for the Eu3` ion located at the D symmetry site of LuPO . These 2$ 4 levels have been fitted to a parameterized Hamiltonian using a least-squares fitting procedure. Two-photon excitation was observed to all five levels of the 5D and 5D multiplets and the 0 2
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K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
Fig. 3. Experimental polarization behavior (dots) of the (a) 7F (C ) P 5D (C ), (b) 7F P 5D (C ), (c) 7F P 5D (C ), (d) 0 1 0 1 0 2 3 0 2 5 7F P 5D (C ), and (e) 7F P 5D (C ) TPA transitions. The combined second- and third-order calculated polarization dependencies 0 2 1 0 2 4 from Table 6 are represented by the solid lines.
intensities of these transitions were investigated. The results presented here are consistent with those reported previously by Gaˆcon et al. [16—18]. TPA transitions with calculated intensities dominated by second-order contributions exhibited good agree-
ment between their calculated and observed polarization behavior. Inclusion of the third-order spin— orbit interaction was not sufficient to account for the polarization behavior of other TPA transitions and alternative mechanisms must be considered.
K.M. Murdoch et al. / Journal of Luminescence 79 (1998) 55—64
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Fig. 4. Experimental polarization behavior (dots) of the (a) 7F (C ) P 5D (C ) and (b) 7F P 5D (C ) TPA transitions. The 0 1 0 1 0 2 1 polarization dependencies obtained by fitting this data to the intensity function defined in Eq. (8) are represented by the solid line.
Acknowledgements Drs. M.M. Abraham and L.A. Boatner of Oak Ridge National Laboratory are gratefully acknowledged for growing and providing the crystal used for this work. This research was sponsored in part by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the US. Department of Energy under Contract No. DE-AC03-76SF00098 with the University of California.
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