Two-photon spectroscopy of europium (III) elpasolites

Article abstract of DOI:10.1088/0953-8984/11/40/311

We present polarized two-photon excitation (TPE) spectra, including Zeeman data, for europium(III) in the elpasolites Cs₂NaEuCl₆ and Cs₂NaYF₆:Eu³⁺. Approximately 80 and 60 levels of unambiguous symmetry have been assigned respectively in each compound up to 32000 cm^-1 with the aid of a one-electron crystal field Hamiltonian. This represents the most complete and extensive data set so far reported for Eu(III) at a cubic site. Comparisons are made between comparable data sets for Eu(III) f⁶ and Tb(III) f⁸. Deviations from the predictions of the one-electron crystal field model are discussed in terms of the spin correlation crystal field.

Full text of DOI:10.1088/0953-8984/11/40/311

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J. Phys.: Condens. Matter 11 (1999) 7851–7866. Printed in the UK
PII: S0953-8984(99)05482-X
Two-photon spectroscopy of europium(III) elpasolites
J R G Thorne†, M Jones†, C S McCaw†, K M Murdoch†, R G Denning† and
N M Khaidukov‡
† Department of Chemistry, University of Oxford, Inorganic Chemistry Laboratory,
South Parks Road, Oxford OX1 3QR, UK
‡ Russian Academy of Sciences, N S Kurnakov Institute of General and Inorganic Chemistry,
31 Leninskii Prospekt, 117907 Moscow, Russia
Received 24 June 1999, in final form 4 August 1999
Abstract. We present polarized two-photon excitation (TPE) spectra, including Zeeman data,
for europium(III) in the elpasolites Cs2NaEuCl6 and Cs2NaYF6:Eu3+
. Approximately 80 and
60 levels of unambiguous symmetry have been assigned respectively in each compound up to
32 000 cm−1 with the aid of a one-electron crystal field Hamiltonian. This represents the most
complete and extensive data set so far reported for Eu(III) at a cubic site. Comparisons are made
between comparable data sets for Eu(III) f6 and Tb(III) f8. Deviations from the predictions of the
one-electron crystal field model are discussed in terms of the spin correlation crystal field.
1. Introduction
A lanthanide ion in a crystal field can be described by a combination of a free ion Hamiltonian,
and a crystal field potential which acts as a perturbation on the free ion states [1]. The former
contains contributions from coulombic (Fk, k = 2, 4, 6), electrostatically correlated coulombic
(α, β, γ , T i, i = 2, 3, 4, 6, 7, 8), spin–orbit coupling (ζso), two-electron spin–other-orbit
(Mk, k = 0, 2, 4) and electrostatically correlated spin–orbit (Pk, k = 2, 4, 6) interactions.
When parameterized in this way the Hamiltonian provides a satisfactory model of the free ion
levels [2]. The crystal field is usually expressed as the sum of one-electron operators:
X
HCF
=
Bq(k)u(qk)(i)
(1)
i,q,k
where u(qk)(i) is a unitary tensor operator for the ith f electron, of rank k where k = 2, 4, 6, with
q restricted by symmetry. A rigorous test of the crystal field model requires a large energy
level data set and a small number of crystal field parameters.
The cubic elpasolites provide an octahedral lanthanide(III) site, that requires only two
one-electron crystal field parameters to model the f-electron–lattice interaction. However,
one-photon f–f transitions are electric-dipole forbidden, magnetic-dipole transitions are not
always observed and the absorption cross-section of vibronic transitions is low. Energy level
determinations have relied mainly on emission data; these locate multiplet components near the
ground state, but only a few upper levels. For this reason empirical Hamiltonians for lanthanide
haloelpasolites have been based on an average of only 30 observed levels for each ion [1, 3].
Although large data sets comprising over 100 levels are available for many lanthanides in low
symmetry hosts such as LaCl3 (C3h site) [4] and LaF3 (C2 site) [5], their analysis requires up
to nine one-electron crystal field parameters.
0953-8984/99/407851+16$30.00 © 1999 IOP Publishing Ltd
7851

7852
J R G Thorne et al
Figure 1. Energy level diagram for europium(III) and terbium(III) in zero field. The levels
were calculated using the free ion parameters for Cs2NaEuCl6 in table 2 and those of [13] for
Cs2NaTbCl6.
The 7FJ and 5DJ levels of europium(III) have been recently studied in Cs2NaEuCl6 [6]
and Cs2NaYF6:Eu3+ [7] by single-photon spectroscopy, including parametrization using the
same free ion and crystal field Hamiltonian as in this work, based on ∼20 levels belonging to
the 7FJ and 5D3,2,1,0 multiplets.
On the other hand, in two-photon spectroscopy, parity-conserving electronic transitions
are allowed and the spectra contain little significant phonon structure [8]. As a result, this
technique allows access to a large number of excited state energy levels in sites of octahedral
symmetry. In this paper, which is part of a series [8–14] covering the Cs2NaLnX6 elpasolites
with X = F, Cl and Br, we use two-photon excitation to identify the energies and symmetries
for Ln = Eu, of a very much larger sequence of levels than has previously been compiled.
Our analogous experimental results for Ln = Tb are to be found in [12] and [13], and for
Ln = Sm in reference [14]. Other previous two-photon studies of rare-earth elpasolites have
been limited to a small number of excited states in Cs2NaGdCl6 [15].

TPE spectra of Eu(III) elpasolites
7853
(a)
(b)
Figure 2. TPE spectra for (a) Cs2NaEuCl6 at 120 K and (b) Cs2NaYF6:Eu at 70 K for polarizations
with α = 0◦ and α = 45◦.
2. Experiment
Cs2NaY1−xEuxF6 was synthesized by the reaction of aqueous solutions of CsF and NaF with
mixtures of Eu2O3 and Y2O3 (99.995%) at a temperature of 750 K and pressures of 100–
150 MPa [7]. The crystal used in this work had nominal composition Cs2NaY0.8Eu0.2F6.
Henceforth, we refer to this mixed Y/Eu material as Cs2NaYF6:Eu3+.

7854
J R G Thorne et al
(a)
(b)
Figure 3. TPE spectra for (a) Cs2NaEuCl6 at 120 K and (b) Cs2NaYF6:Eu at 70 K for polarizations
with α = 0◦ and α = 45◦.
Cs2NaEuCl6 crystals were grown from the fused component binary chlorides by the
Bridgman method. NaCl (99.999%) and CsCl (99.9%)were purified by vacuum sublimation.
Anhydrous EuCl3 was prepared from Eu2O3 using the ammonium chloride route [16] by
vacuum decomposition of (NH4)2 [EuCl5]. Any oxychloride present was converted to chloride

TPE spectra of Eu(III) elpasolites
7855
(a)
(b)
Figure 4. TPE spectra for (a) Cs2NaEuCl6 at 120 K and (b) Cs2NaYF6:Eu at 70 K for polarizations
with α = 0◦ and α = 45◦.
by exposing the freshly made EuCl3 to a stream of dry HCl gas at 450 ◦C for 36 hours. NaCl,
CsCl and EuCl3 powders in the appropriate ratio were mixed and transferred into an HF etched
Bridgman tube. Cs2NaEuCl6 was prepared by growth at a temperature of 750–800 ◦C under
a pressure of 7 atm Cl2 which was employed to prevent the formation of divalent europium

7856
J R G Thorne et al
(a)
(b)
Figure 5. TPE spectra for (a) Cs2NaEuCl6 at 120 K and (b) Cs2NaYF6:Eu at 70 K for polarizations
with α = 0◦ and α = 45◦.
[17]. Transparent sections of the resulting boule were identified as Cs2NaEuCl6 by x-ray
diffraction.
Crystals were oriented by Laue back reflection, and cut and polished with faces
perpendicular to {100}. Low temperature emission spectra, for comparison with published
work, were recorded excited at 355 nm.

TPE spectra of Eu(III) elpasolites
7857
It has been observed at 80 K that Cs2NaEuCl6 adopts a lower symmetry phase [18] but
we observed no depolarization of the excitation beam by the crystal at 100 K. Experiments
were performed at temperatures of both 10 K and, to avoid deviations from cubic behaviour,
at 120 K. Doped in the Cs2NaYF6 lattice, the EuF36− moiety is not subject to this distortion;
spectra were recorded at 70 K.
The europium(III) ion is almost as good a candidate for a comprehensive two-photon
study as terbium(III), because it has a window of linear absorption transparency between 5000
and 17 000 cm−1 (allowing non-resonant two-photon excitation (TPE) to states up to nearly
34 000 cm−1), and its high yield visible luminescence can be used to detect the excitation.
TPE spectra were recorded by monitoring the emission intensity as a function of the excitation
energy from an Nd:YAG pumped Spectra Physics PDL3 dye laser. The polarization integrity of
the laser output was improved using a calcite polarizer, and the polarization angle varied using
a double Fresnel rhomb. The beam was focused on to a {100} face of the sample mounted
in an Oxford Instruments CF204 cryostat with wedged windows. The laser frequency was
determined to <1 cm−1 by simultaneously recording the opto-galvanic spectrum of an Ar
discharge tube. Emission was detected directly through a series of bandpass and cutoff filters
5
with a window centred near 550 nm corresponding to emission from D1. The emission
was corrected for variations in the laser intensity by referencing against the square of the
laser energy, using a Molectron LP141 photodiode. Zeeman spectra were recorded in a Thor
Cryogenics magneto-optic cryostat at fields up to 5.0 T, as described elsewhere [11].
3. Results
An energy level diagram in the absence of the crystal field perturbation for europium(III),
and terbium(III) for comparison, is shown in figure 1; it is intended to serve as a guide to the
excited state manifold in the subsequent discussion. The levels indicate the energies of the
free ion terms; groups of SLJ levels are labelled by their parent Russell–Saunders term which
is shown as a hypothetical barycentre.
In europium(III), one-photon and two-photon absorption are followed by non-radiative
decay to the 5D0 and 5D1 manifolds from which emission occurs to the 7FJ crystal field levels.
The observed 5D1 emission decays with a lifetime of ∼2 ms at low temperature.
The mechanism, selection rules and polarization dependence of two-photon absorption
have been previously described [8]. Since all the electronic states of interest have even parity,
the gerade subscript is omitted from the irreducible representations of Oh. The ground state
of Eu3+ in Cs2NaLnX6 has A1 symmetry, from which single-colour two-photon transitions are
allowed to A1, E and T2 excited states. Here we consider a beam propagating along [001],
and define its polarization by the angle α of the electric vector with respect to [100]. When
α = 0◦, A1 → T2 transitions are forbidden, while the intensity of A1 → E transitions is at
a maximum. When α = 45◦, the A1 → T2 intensity is at a maximum, while the intensity of
A1 → E transitions decreases by a factor of four. The intensity of A1 → A1 transitions is
independent of α.
States of A2 and T1 symmetry are not accessible from the A1 ground state, but transitions
to them become allowed at higher temperature due to thermal population of the T1 component
7
of the F1 multiplet. Transitions from level 2 give rise to hot bands in the TPE spectrum,
displaced to lower energy by ∼350 cm−1 relative to the cold transitions. Hot bands that have
no counterpart in the cold spectrum indicate the position of T1 or A2 excited states. T1 → A1
transitions are forbidden, and the intensity of T1 → A2 and T1 → E transitions has the same
angular dependence as an A1 → T2 transition. The angular dependence of the T1 → T1 and
T1 → T2 intensities, however, is not constrained by symmetry.

7858
J R G Thorne et al
Table 1. Observed and calculated energy levels of Eu(III) in Cs2NaLnX6 (uncertain values are
shown in parentheses: literature values [6, 7] are in italics).
Cs2NaEuCl6
Cs2NaYF6:Eu
Energy Calc. E
Energy
(cm−1
Calc. E
(cm−1
(cm−1
)
(cm−1
)
1E
)
)
1E
1
2
3
4
5
6
7
8
9
7F0
7F1
7F2
7F2
7F3
7F3
7F3
7F4
7F4
A1g
T1g
Eg
T2g
A2g
T2g
T1g
T2g
Eg
T1g
A1g
T1g
Eg
T2g
T1g
Eg
0
360
875
−7
359
864
1093
1804
1912
1966
2674
2971
3016
7
1
11
−2
0
−8
−3
−9
4
7F0
7F1
7F2
7F2
7F3
7F3
7F3
7F4
7F4
7F4
7F4
7F5
7F5
7F5
7F5
7F6
7F6
7F6
7F6
7F6
7F6
A1g
T1g
Eg
T2g
A2g
T2g
T1g
T2g
Eg
T1g
A1g
T2g
T1g
Eg
0
337
807
−7
7
347 −10
774 33
1075 −10
1768 21
1091
1804
1904
1963
2665
2975
3007
3034
3811
3851
3876
4149
4835
4869
4945
5242
5254
5283
1065
1789
1953
2014
2670
3041
3151
3205
1976 −23
2027 −13
2642
3033
28
8
10 7F4
11 7F4
12 7F5
13 7F5
14 7F5
15 7F5
16 7F6
17 7F6
18 7F6
19 7F6
20 7F6
21 7F6
−9
3170 −19
3238 −33
3781
3848 −27
3054 −20
3817
3850
3867
4119
−6
1
9
3821
(3911)
4335
3872
4296
4817
4864
4945
5451
5482
5513
39
39
1
30
T1g
Eg
4855 −20
4884 −15
(4818)
T2g
A2g
T2g
T1g
A1g
T2g
A2g
T2g
T1g
A1g
4948
5216
5250
5279
−3
26
4
4
22 5D0 A1g 17 208
17 205
3
5D0 A1g 17 255
17 257
19 004
−2
−4
23 5D1 T1g
24 5D2 T2g
25 5D2 Eg
26 5D3 T1g
27 5D3 T2g
18 961
21 385
21 495
24 261
24 292
18 972 −11
21 396 −11
5D1 T1g
5D2 T2g
5D2 Eg
5D3 T1g
19 000
21 389
21 568
24 274
21 406 −17
21 469
26
21 540
24 283
28
24 282 −21
−9
24 297
24 343
24 747
24 816
24 899
25 118
−5
27
14
15
6
5D3 T2g (24 281)
24 314 −33
28 5D3 A2g 24 370
5D3 A2g
24 392
29 5L6
30 5L6
31 5L6
32 5L6
33 5L6
34 5L6
35 5L7
36 5L7
37 5L7
38 5L7
A1g 24 761
5L6
5L6
5L6
5L6
5L6
5L6
5L7
5L7
5L7
A1g 24 557
T1g
24 554
24 658
24 787
25 085
25 446
3
15
7
T1g
T2g
24 831
24 905
T2g
A2g
T2g
Eg
24 802
A2g 25 121
3
T2g
Eg
25 302
25 345
25 893
25 926
25 987
25 322 −20
25 377 −28
25 453
25 500
25 518 −18
T1g
Eg
25 886
25 914
25 980
7
12
7
T1g
Eg
25 759
25 855
25 897
25 862
25 904
26 121
26 180
26 204
26 206
−7
−7
T2g
T2g
A2g 26 099
26 119 −20
5G3 T1g
5G2 Eg
39 5G2 Eg
40 5G2 T2g
41 5G3 T1g
26 162
26 175
26 216
26 240
26 338
26 339
26 345
26 152
26 183
26 208
26 231
10
−8
8
26 190
10
5L7
A2g
5G3 T2g
5G2 T2g
5G4 Eg
26 204
26 256
26 295
−2
42 5L7
T2g
9
26 273 −17
26 312 −17
43 5G3 T2g
44 5G4 Eg
26 352 −14
26 355 −16
5G4 A1g 26 344
5G4 T1g
26 338
26 344
6
45 5L7
T1g
26 344
26 410
1
46 5G4 A1g 26 424
14
5G6 T2g
26 356
26 382 −26

TPE spectra of Eu(III) elpasolites
7859
Table 1. (Continued)
Cs2NaEuCl6
Cs2NaYF6:Eu
Energy Calc. E
Energy Calc. E
(cm−1
)
(cm−1
)
1E
(cm−1
)
(cm−1
)
1E
47 5G6
48 5G3
49 5G5
50 5G6
51 5G6
52 5G6
53 5G6
54 5G4
55 5G6
56 5G5
57 5G4
58 5G5
59 5G5
60 5L8
61 5L8
62 5L8
63 5L8
64 5L8
65 5L8
66 5L8
67 5D4
68 5D4
69 5D4
70 5L9
71 5L9
72 5D4
73 5L9
74 5L9
75 5L9
76 5L9
T2g
A2g
T1g
T1g
Eg
26 410
26 419
26 420
26 470
5L7
5L7
5G6
5G6
5G3
5G6
5G6
5L8
5G5
5G6
5G5
5G4
5L8
5L8
5G5
5G5
5L9
5L9
5L9
5L9
5D4
5D4
5D4
5D4
5L8
5L8
5L8
T1g
T2g
T1g
Eg
26 408
26 424
26 478
26 527
26 538
26 429
26 518
26 579
5
26 470
26 503
26 527
0
−9
26 513 −10
A2g
T2g
T2g
A2g
T2g
26 532
26 573
26 616
26 629
26 665
26 689
26 701
26 719
26 861
−5
26 618 −38
A1g 26 723
26 688
26 713
26 745
26 752
26 760
26 823
26 832
35
26 616
0
T2g
Eg
A1g 26 645
16
Eg
A2g
T1g
T1g
T1g
T2g
T1g
Eg
26 856
33
T2g
T2g
Eg
26 762
26 854
26 869
42
−7
26 879
27 031
26 890 −11
26 879 −10
26 966
T2g
T1g
T2g
26 988
27 130
27 366
27 394
27 395
27 416
27 518
27 525
27 586
27 590
27 609
27 605
27 730
27 824
27 843
27 889
27 896
28 185
28 284
43
T1g
T2g
Eg
27 175
27 294
A1g 27 393
−1
T1g
27 306
27 299
27 306
27 507
27 508
27 513
27 515
27 525
27 568
27 614
27 692
27 894
27 897
27 964
28 008
28 050
28 062
28 146
28 338
28 438
28 493
28 697
28 715
28 722
7
6
A2g
T1g
A1g 27 312
T1g 27 501
A1g 27 502
−6
−6
−4
Eg
27 510
27 526
−8
T2g
T1g
A1g
Eg
1
Eg
27 509
A2g
T2g
T2g
T1g
A1g
T1g
Eg
27 535
27 574
10
6
27 604
27 618
−5
T2g
13
T1g
5L10 T2g
5L10 Eg
5L8
5L10 T1g
27 832
27 843
8
0
27 900
27 959
3
A1g
77 5L10 T2g
78 5L9
T1g
−5
5L9
5L9
5L9
5L9
5L10 A1g
5L10 T1g
5L10 T2g
5L10 A2g
5L10 T2g
5L10 Eg
T1g
Eg
79 5L10 Eg
28 044
−6
80 5L9
T2g
T2g
28 301
28 313 −12
28 416
81 5L10 T1g
T1g
82 5L10 A1g 28 356
83 5L10 T1g
18
28 541
28 731
84 5L10 T2g
85 5L10 A2g
86 5L10 T2g
87 5L10 Eg
28 811
29 047
28 706
28 713
−9
−9
29 082
29 094
88 5H3
89 5H7
90 5H7
91 5H3
92 5H7
93 5H7
T1g
T1g
T2g
T2g
A2g
T2g
30 556
30 629
30 664
30 692
30 804
30 970
5H3
5H7
5H7
5H3
5H7
5H4
T1g
T1g
T2g
T2g
A2g
30 517
30 600
30 676
30 690
12
30 654
30 724
30 641
30 722
30 809
13
2
−2
A1g 30 949
30 962 −13

7860
J R G Thorne et al
Table 1. (Continued)
Cs2NaEuCl6
Cs2NaYF6:Eu
Energy
(cm−1
Calc. E
(cm−1
Energy
(cm−1
Calc. E
(cm−1
)
)
1E
)
)
1E
94 5H3 A2g
95 5H4 A1g
96 5H7 Eg
97 5H4 Eg
98 5H4 T1g
30 977
30 996
5H4 Eg
5H4 T1g
5H6 T2g
5H5 T1g
5H6 Eg
5H5 T2g
5H3 A2g
5H7 Eg
5H7 T2g
5H6 A2g
5H7 T1g
5H4 T2g
5H5 T1g
30 994
31 081
30 985
31 039
31 086
31 096
31 106
9
31 004
8
(31 004) 31 017 −13
−5
31 041
31 045
31 110
31 160
4
99 5H7 T1g (31 066) 31 064
2
31 184 −24
31 260
100 5H6 T2g
101 5H6 Eg
102 5H5 T2g
103 5H5 T1g
104 5H6 A2g
105 5H4 T2g
106 5H6 T1g
107 5H5 Eg
108 5H6 T2g
109 5H6 A1g
110 5H5 T1g
31 148
31 215
31 257
31 172 −24
31 232 −17
31 439
31 447
31 456 −17
31 259
31 274
31 329
−2
31 441
31 499
31 561
31 569
31 724
6
31 327
31 338 −11
31 567
−2
31 514
31 541
31 543
31 581
31 533
31 531
31 541
31 552
8
12
40
5H6 A1g (31 748) 31 758 −10
5H6 T2g
5H5 Eg
5H6 T1g
31 784
31 795
31 774
31 775
31 786
10
20
111 5F2
Eg
33 520
5F2
Eg
32 771
TPE spectra from 21 000 to 32 000 cm−1 are shown in figures 2–5. Two polarizations with
α = 0◦ and 45◦ are shown for both the chloroelpasolite and fluoroelpasolite. Each peak is
labelled with the sequence number of the final states in table 1. Hot bands are designated with
the subscript H. Peaks having E symmetry are labelled on the upper (0◦) spectrum where they
are stronger. In most cases the symmetry of the final state is readily apparent. The intensity
ratio between the two polarizations was usually large, approaching the theoretical limit. Thus
in figure 2(b), we see immediately that level 24 has T2 symmetry and level 25 E symmetry.
There are, for example, unpolarized transitions to level 29 in both spectra, which must therefore
have A1 symmetry. Where necessary, ambiguities in the final state symmetry were resolved
by monitoring the signal intensity as a function of polarization angle at the wavelength of each
peak. The symmetry determined in this way is included in table 1.
The spectra have been corrected in the regions 25 000–27 000, 27 000–29 000 and
30 000–32 000 cm−1 to indicate approximate relative TPE intensities that are consistent within
each segment. We have not attempted to obtain accurate relative intensities across the whole
spectrum.
Location of excited states with T1 and A2 symmetry is possible in two ways. At elevated
temperature, thermal population of the 7F1 T1 level allows transitions to levels of A2 and T1
symmetry. The larger 360 cm−1 energy gap for Eu(III) renders this method less useful than in
Tb(III), for appreciable excited state population is attained only at temperatures where the line
broadeningandfluorescencequenchingobscurethespectra. Moreusefulistoutilizeamagnetic
field to mix intensity into forbidden transitions [10, 11]. We have performed these experiments
only for Cs2NaEuCl6 and the larger data set for the chloro- compared to the fluoroelpasolite
in table 1 reflects this fact, along with the more complete literature data available for the low
energy states. Figure 6 shows selected parts of the chloroelpasolite two-photon spectrum in a
magnetic field that we have utilized to locate particular ‘forbidden’ excited states, or to remove

TPE spectra of Eu(III) elpasolites
7861
Figure 6. Cs2NaEuCl6 TPE spectra in a magnetic field at 4 K.
accidental degeneracy. Thus, peaks 32 (A2) and 41, 45, 65, 67 (T2) acquire intensity only in
a magnetic field, whilst the degeneracy of peaks 95 and 96 (A1, E) is lifted by the presence of
the field.
The energy level assignments (expressed in vacuum wavenumbers) are collected in table 1;
those in parentheses are tentative. For consistency, we take published emission data, listed in
italics in table 1, for pure Cs2NaEuCl6 from [6] and Cs2NaEu0.2Y0.8F6 [7], the sample used for
the latter study coming from the same source, omitting the authors’ ‘uncertain’ assignments
from our fit. We reject only the uncertain assignment of the fluoride 7F5 T2 level at 3881 cm−1
which deviates 100 cm−1 from our final fit.
,

7862
J R G Thorne et al
Table 2. Energy level parameters (cm−1) for Eu3+ in Cs2NaLnX6. M2 = 0.560M0, M4
=
0.310M0; P 4 = 0.750P2, P6 = 0.10P2.
Parameter Cs2NaEuCl6
Cs2NaYF6:Eu3+
Eav
F2
F4
F6
α
66 407
94 613
87 348
51 081
62 304
86 460
62 286
29 844
16.5
62.5
β
−882
−4368
1342
−256
−1388
−725
−1064
−1844
65
−3785
γ
4450
ζso
T 2
T 3
T 4
T 6
T 7
T 8
M0
P2
1347
−2987
−731
52
1001
−3225
−2187
−1.35
−947
2.87
333
2206
−305
B0(4)
B0(6)
σ
3776
−553
21.7
57
15.9
77
N
The observed levels are listed in sequence, and can be compared with the energies
calculated using a Hamiltonian in which the crystal field is represented as a sum over
one-electron operators. The parameter values for this Hamiltonian are given in table 2 in
wavenumber units; the number of levels fitted is N; the standard deviation is σ. The free ion
parameters, used to produce figure 1, indicate considerable configuration mixing, particularly
for the ‘twinned’ levels of 5G and 5H, in europium(III) relative to terbium(III).
7
5
5
The low energy states (1–34, F0−6, D0−3, L6) are all isolated and the SLJ labels
provide a good description. The identity of their components is unambiguous and their
energies therefore stringently test the success of the parametrization. To higher energy,
5
5
5
the states (35–87, L7−10, G2−6, D4) are heavily mixed, so that in some cases the SLJ
labels are a serious over-simplification, and we avoid a discussion of systematic deviations
between calculated and experimental splittings in those states where the underlying multiplet
5
character is poorly defined. At still higher energy, the H manifold is well isolated, but the
component states (88–110) are considerably mixed by the crystal field operator (particularly
in the fluoroelpasolite) so that the J label alone is poorly defined.
5
Tables 3 and 4 compare the crystal field parameters obtained in this work (up to H at
32 000 cm−1) with a previous parametrization using the levels obtained from single-photon
studies (up to ∼25 000 cm−1 including only 7FJ and 5D0,1,2,3). We have also performed fits to
the level subsets of quintet and septet (plus 5D0,1, which are unperturbed by the crystal field),
allowing F, B and ζSO parameters alone to vary.
4. Discussion
4.1. The correlation crystal field
The inadequacies of a one-electron crystal field model have been realized for some time
[19–22]. If the Bq(k) parameters are chosen to match the splitting of one sub-set of states,

TPE spectra of Eu(III) elpasolites
7863
Table 3. Crystal field parameters for Eu3+ in Cs2NaEuCl6.
This work
This work This work
[3]
No of levels N
Fitting range
B0(4)
B0(6)
77
56
23
27
0–32 000 cm−1
Quintets
2232
Septets+ 5D0,1
0–25 000 cm−1
2206
2282
2318
−305
−292
−346
−393
(Note B0(4) = 1.128B04 and B0(6) = −1.277B06, for parameters B0k quoted in references [3] and [7].)
Table 4. Crystal field parameters for Eu3+ in Cs2NaYF6.
This work
This work This work
[7]
No of levels
Fitting range
B0(4)
B0(6)
57
44
15
19
0–32 000 cm−1
Quintets
3896
Septets+ 5D0,1
0–25 000 cm−1
3776
3471
3540
−553
−515
−613
−488
they often give a poor description of other multiplets. For terbium(III) the maximum spin
multiplicity components of the ground state are well modelled in isolation, but the quality of
the fit deteriorates with the inclusion of states associated with higher energy terms [3, 23–26].
Each multiplet then experiences a different effective crystal field strength and the combined
fit of all energy levels yields a weighted average value, about which systematic variations may
be anticipated.
It is clear from tables 3 a nd 4 that crystal field parameter differences between our full
data set parametrizations and those performed with smaller data sets are reasonably small. In
the chloroelpasolite, however, the average crystal field experienced by the septet manifold is
larger than that experienced by the quintet manifolds. Preliminary investigation shows that
there is a small decrease in the crystal field parameters for the chloroelpasolite, both fourth
and sixth order, in the quintet compared to the septet manifold.
This result is in contrast to those we obtain for Tb(III) [9] and Sm(III) [14] in
chloroelpasolites, which show an average increase in effective crystal field parameters with
lower spin multiplicity; that is, the one-electron crystal field under-estimates the average
splitting in the states of next-to-maximum multiplicity in these two ions.
Early suggestions [19, 20] for a suitable physical origin for a correlated crystal field
included a spin dependent effect (‘the SCCF’):
X
HSCCF
=
bq(k)S · siuq(k)(i)
(2)
i,q,k
SCCFparametersbq(k) takeintoaccountchangesintheradialwavefunctionoftheith4felectron,
according to its spin orientation si and the total spin S, in response to the difference in exchange
energy. The importance of SCCF is measured by the parameters cq(k) = bq(k)/Bq(k) such that:
X
HT OT AL = HCF + HSCCF
=
Bq(k)uq(k)(i)(1 + S · sicq(k)).
(3)
i,q,k
∼
These parameters have been observed experimentally [1] to take values cq(k) ±0.1, yet the
=
expectation that the radial extent of the highest multiplicity wavefunction is the smallest should
clearly lead to negative values of cq(k) [19, 22]. Experimentally, we observe (table 3) that the
fractional changes in effective B0(4) and B0(6) on going from the septet (S = SMAX) to the quintet
(S = SMAX − 1) manifold in the europium chloroelpasolite are −2% and −16% respectively.

7864
J R G Thorne et al
In terms of effective crystal field parameters, we obtain from equation (3):
(k)
0
B0(k) eff ective(S = SMAX − 1)/B(k) eff ective(S = SMAX
)
(1 − 0.5c
)
(4)
∼
=
0
from which we estimate positive effective SCCF parameters for Cs2NaEuCl6:
c0(4) = +0.04
c0(6) = +0.3.
An alternative spin dependent ‘covalency’ effect has been suggested [22], whereby certain
spin states of some lanthanides would be particularly susceptible to mixing of charge transfer
transitions. Charge transfer mixing (ligand-to-metal) would be particularly favourable in the
ground septet state of europium, reflecting the tendency of Eu3+ to become Eu2+ in its octet
state. Intuitively, the radial extent of the f orbitals should be much larger in Eu(II) where the
effective nuclear charge seen by an f electron is considerably reduced. Greater mixing of CT
states in the septet compared to the quintet manifold would lead to the crystal field shrinking
at higher energy. A contraction of the crystal field at lower spin multiplicity is evidenced
by positive values of c0(4) and c0(6) for europium(III). The charge transfer (CT) or covalency
mechanism has been shown [22] to act in a sense opposite to that of the SCCF mechanism.
It has been shown [20] that this mechanism can be treated within the same parametrization
scheme as the SCCF, and that all the effective parameters cq(k) indeed have opposite sign. The
possibilities of ligand-to-metal CT effects in excited states of the lanthanides in the second half
of the series, and of metal-to-ligand CT in Tb(III) have also been suggested [20, 22]; all these
in principle contribute to the sign of effective SCCF parameters.
Our results from the fluoroelpasolite are ambiguous and reflect the uncertainty in the fit
of the septet manifold alone for which only 13 states have been located. The apparent 12%
increase in the fourth order CF parameter and 16% decrease in the sixth order parameter in
the quintet state in table 4: (c0(4) = −0.2, c0(6) = +0.3) may reflect a balance in the opposing
SCCF and CT contributions. The latter would be expected to be less dominant for the case of
the fluoride where ligand-to-metal charge transfer is less extensive than in the chloroelpasolite.
Because of its dependence upon the total spin, the SCCF Hamiltonian contains both one-
electron and two-electron contributions [21]. In principle, an apparent discontinuity [1] in
the magnitude of the sixth-rank one-electron crystal field parameters at the half-filled shell
can be reconciled on the basis of an interference between the one-electron operators, whose
matrix elements change sign on going from fN to f14−N , and two-electron operators whose sign
remains unchanged [21]. In practice, a spin-dependent correlation crystal field (SCCF) which
merely increases with lower spin multiplicity would not physically explain the discontinuity
in the crystal field parameters at the halfway point of the lanthanide series. An anomalously
increased (CT mixed) crystal field in the septet state of europium would, however, account
for large differences in the effective one-electron parameters between Eu(III) and Tb(III),
particularly when applied to limited data sets [1].
4.2. Rogue multiplets
In a number of lanthanides ‘rogue multiplets’ are found, for which the crystal field splitting
is either far too large or small relative to that predicted by calculations that use one-electron
operators. Some of these effects may be explicable in terms of spin dependent theories,
but others far exceed the ±20% changes that are typical for SCCF parametrization [27].
The anomalous spread (percentage deviation) of a multiplet is commonly quantified [28] by
100(σexp − σcalc)/σcalc, where σ is the standard deviation of the experimental or calculated
levels about their respective barycentres.
In terbium(III) we have observed that 5D is one such deviant manifold, showing greatly
reduced CF splitting compared to a one-body model [9]. It is apparent, however, that in

TPE spectra of Eu(III) elpasolites
7865
europium(III) the 5D splittings exceed those predicted by the averaged CF parameters. In 5D2
5
and D3 of the chloroelpasolite, the spread of the levels exceeds that predicted by 51% and
5
5
79% respectively; D2 of the fluoroelpasolite is larger by 34%, D3 is incompletely defined.
Interestingly, the expansion of 5D in Eu(III) and contraction in Tb(III) are multiplet specific
effects that oppose the general trend occurring in the quintet states for these two ions.
The data together may thus be taken as evidence that the deviations in these multiplets
have opposing directions in terbium(III) and europium(III). Such would be the predicted effect
when two electron crystal field operators (the matrix elements of which remain the same sign
in Tb and Eu) should have been included with the one-electron crystal field Hamiltonian (the
matrix elements of which have opposite sign in Tb and Eu). The data indicate the importance
of large correlation effects in the crystal field that are certainly not explicable by a simple spin
dependent effect. This observation may also account in part for the apparent discontinuity in
the magnitude of the sixth-rank one-electron crystal field parameters. The much reduced value
in Tb(III) compared to Eu(III), would be the result of the observed 5D deviancy in the limited
data sets previously used in the analysis of these two ions.
5. Conclusions
We have obtained extensive data for Eu(III) in cubic crystal fields in both chloro- and
fluoroelpasolite lattices. The effect of the ligand on the crystal field splitting of a large number
of multiplets, in an isostructural series, can now be directly compared with complementary data
for Tb(III). Our data provide an opportunity to understand the influence of ligand properties and
f electron number on correlation effects, and to determine the physical origin of various CCF
operators. Charge transfer in the septet ground state of europium appears to be the dominant
mechanism for the effective spin-dependent crystal field. Multiplet specific two-body effects
of unidentified physical origin are also observed to occur in higher lying states.
Experimental data over a similar energy range in samarium(III) d5 are presented in this
journal [14], and a full discussion of the spin (SCCF) and orbital (LCCF) dependence of the
effective crystal field in the Sm, Eu and Tb (III) ions will be presented shortly [29].
Acknowledgments
We thank the EPSRC for financial support, and the Rutherford Appleton Laboratory for the
use of a dye laser through the laser loan scheme. We also thank M F Reid for allowing us to
use his F-Shell program.
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