Fig. 6. Raman spectra of EuCu2Si 2 at different temperatures under 5309 A laser excitation. Verti- cal dashed lines mark the intraconfigurational exci- tations (EL,i...) of the free Eu 3+ ion having the 4f6(TFj_0...6) configuration. Solid lines through spectra are guides to the eyes.
fourth peak near 400 cm -1 can be resolved from the background. For comparison the J-level excitations of the free E u 3+ ion (Dieke and Crosswhite 1963) are indicated by the dashed vertical lines in fig. 6 for J = 1 to J = 4.
In fig. 7 we show a schematic energy-level diagram explaining the electronic R a m a n scattering from the J-multiplet levels in an IV Eu compound by applying the interconfigurational fluctuation model of intermediate valence (Hirst 1970, see fi~. 1) to R a m a n scattering from IV Eu compounds. The (Eu 2+) 4f 7 and (Eu 3+) 4f + e - confgurations are nearly degenerate and separated by E x. W h e n E x # 0, two sets of inelastic energy losses E L i.tra and E L inter = EL intra - - gx are observ- able in R a m a n spectroscopy for the )-multiplet i'evels of the 4 f 6 configuration.
These are the intraconfigurational e x c i t a t i o n s (EL,intra) of the J = 1 , . . . , 6 levels with respect to the (4f 6) J = 0 initial state and the interconfigurational excitations (EL,inter) with respect to the (4f 7) J = 0 initial state. The interconfigurational excitation energy E x itself should also show up with respect to the J = 0 initial state. The inelastic scattering intensity of the interconfigurational excitations (4f7-->4f6+ e ) is obtained in second-order Perturbation theory and should be stronger than for the magnetic-dipole-allowed intraconfigurational excitations (J = 0---~ J ~ 0). The latter contribute to the scattering cross-section in third-order perturbation theory involving spin-orbit coupling.
L I G H T S C A T T E R I N G IN I N T E R M E T A L L I C C O M P O U N D S 173
Raman Scattering_
J = 7 / 2
4f7(8S7/2)
infer- infro- configurQtiona[
I I
He"tUs,infer
I INo I I
hwil
. .~[x-
4f6(7Fj lhws, intra I
i 3
I I
, 2
I
I EL,intra I J=O ) + e-(E F)
Fig. 7. Schematic representation of the electronic R a m a n scattering process in an intermediate- valence E u compound showing an interconfigura- tional excitation energy E x # 0. Indicated are the
intraconfigurational energy losses (EL,intr,) and the
interconfigurational energy losses (EL,into , = EL,intr a -- E x ) of the incident p h o t o n hwl, with re- spect to the J = 0 and J = 7 initial state, respec- tively.
We now turn to the interconfigurational excitation energy E x and its tempera- ture d e p e n d e n c e , which is given by the c o m m o n , rigid shift of all interconfigura- tional excitations (EL,inter) with respect to the intraconfigurational J-multiplet excitations (EL,intra). The latter have been indicated in figs 5 and 6 by the dashed vertical lines. F o r the case of EuPd2Si 2 at 300 K the more intense interconfigura- tional excitations EL,inte r (indicated by tick marks) are slightly shifted to lower energy with respect to the dashed lines, implying that E x = 5 0 cm -1 (70 K). At 2 0 0 K a further increase of E x ( E x = 1 5 0 K ) is indicated by the asymmetric broadening of the peaks at their low-energy side. The clearest evidence for a p r o n o u n c e d increase in E x ( E x = 350 K) is found in the spectrum at 145 K, in which the EL,intr a and EL,inte r peaks are clearly split. A t 77 K this splitting has disappeared, although the energy positions of the dominant interconfigurational excitations EL,inte r (see tick marks) imply that E x is still about the same as at 145 K. T h e spectrum at 5 K again shows rather narrow peaks near the positions of the dashed lines, implying that E x is about of the o r d e r of the r o o m t e m p e r a t u r e value. T h e t e m p e r a t u r e d e p e n d e n c e of the E , of EuPd2Si2, which is directly revealed in our R a m a n spectra, is plotted in fig. 8a.
Unlike EuPd2Si2, in the case of EuCu2Siz, EL,inte r and EL,intr a c a n only be distinguished at 300 and 77 K for the J = 4 level. For J = 1, 2 and 3 they cannot be separated due to the large inherent linewidths. F r o m the EL,intr a and EL,inte r
excitations of the J = 4 level one deduces an E . of about 400 K at T = 300 K and E x = 320 K at 77 K. Only one set of excitations is observable at 4 K, yielding an
174 E. ZIRNGIEBL and G. GI~INTHERODT (K)
400
¢ - 300
t t J
o
= 2 0 0 -4.-
1oo
ht
~_~ (K}
= 300"
¢ _
200
E I00 m
l - -
w_ o;
I [ I ] I
)
o)I I I I I
100 200 300
Temperature (K)
Fig. 8. Temperature dependence of (a) the interconfigurational excitation energy (Ex) and (b) the upper limit of the fluctuation temperature Tf of EuPd2Si 2 as directly re- vealed in the Raman spectra of fig. 5.
E x smaller than the linewidth of the narrowest peak ( J = 1). H e n c e we obtain E x ~< 80 K (see fig. 9a).
We shall now consider the t e m p e r a t u r e d e p e n d e n c e of
Tf,
which characterizes the quantum mechanical mixing of the two 4f configurations (see b o t t o m of fig.1). This information is mainly contained in the spectral width of the R a m a n peaks. Although for EuPd2Si e the experimentally observed widths of the different J-levels differ significantly at 300 K, their additional variations upon cooling below 300 K are very similar. Since we observe the joint mixing width of the initial and final states in the scattering process, we ascribe the t e m p e r a t u r e - d e p e n d e n t c o m m o n contribution to the width of all the energy-loss peaks primarily to Tf of the initial state (ground state). T h e u p p e r limit of Tf of the ground state of EuPd2Si 2 is set by the narrowest energy-loss peak observable, i.e., J = 1 at 300 and 5 K, and J = 3 at all o t h e r temperatures. The values of Tf of EuPdzSi e and EuCueSi z inferred from the spectral features are presented in figs. 8b and 9b, respectively, as a function of temperature. It has to be pointed out that these spectroscopically deduced values of E x and T~ show good qualitative agreement with those obtained by Schmiester et al. (1982) for EuPdaSi 2 and by R6hler et al.
(1982a) for EuCu2Si 2 (see also R6hler et al. 1982b) on quite different experimen- tal grounds. By use of the ionic ICF model, Schmiester et al. (1982) have deduced the t e m p e r a t u r e d e p e n d e n c e of E x and Tf for EuPd2Si 2 from the M6ssbauer isomer shift and the magnetic susceptibility.
Moreover, for EuPdeSi 2 there is at least basic agreement between the R a m a n scattering and the magnetic n e u t r o n scattering (Holland-Moritz et al. 1987)
LIGHT SCATFERING IN INTERMETALLIC COMPOUNDS 175
~oo
,a, 3 0 0 C
W
o 200
4--'
o
x 100
LLI
0
300 ,o
19
~ 200
01 I - -
c 100
0 0 , j
,7"
b)i
i- 0
T e m p e r o t u r e (K i)
Fig. 9. Temperature dependence of (a) the in- terconfigurational excitation energy E x and (b) an upper limit of the fluctuation temperature Tf of EuCu2Si 2 as directly revealed in the Raman spectra of fig. 6.
concerning the t e m p e r a t u r e d e p e n d e n c e of Tf and the existence of a J = 0--~ J = 1 transition of the E u 3+ configuration. Differences concerning the detailed transi- tion energy of the J = 0--~ 1 excitation and the l o w - t e m p e r a t u r e b e h a v i o r are unresolved and await further i clarification on m o r e theoretical grounds taking into account the different scatteiing m e c h a n i s m s of n e u t r o n and R a m a n scattering.
! i
2.4. Electronic R a m a n scattering in CeSI+ x and C e P d 3
J-multiplet level excitati0ns have also b e e n o b s e r v e d in intermetallic Ce c o m p o u n d s ( M 6 r k e et al. 1986, Zirngiebl et al. 1985b). T h e J - m u l t i p l e t structure of Ce 3+ ions is simple c o m p a r e d to that of E u 3+, since it consists only of the J = to J = 7 transition at an energy of a b o u t 2150 cm -~ ( D i e k e and Crosswhite 1963).
B o t h J-multiplet levels can l~e• split by crystalline electric fields ( C E F ) , which act m o r e strongly on the Ce 4~ a electron than on those in E u due to the m o r e e x t e n d e d 4f radius of Ce Icompared to Eu. Nevertheless, especially at low t e m p e r a t u r e s , only the transitions out of the ground state (CEF-split ground state of the J = ~ configuration) " ~nto the CEF-split states of the J = 7 configuration should be o b s e r v a b l e , wit~ the lowest transition energy being at roughly 2150 cm . 1
We shall first discuss the r~sults of M 6 r k e et al. (1986) o b t a i n e d on a series of stable valence CeSa+x c o m p q u n d s . CeS has the NaC1 structure and the first-order R a m a n effect is f o r b i d d e n b~ s y m m e t r y at the zone center. H o w e v e r , defects can b r e a k the translational s y m m e t r y of the lattice leading to a relaxation of the
/
176 E. ZIRNGIEBL and G. GIJNTHERODT
q-selection rule. The result is a weighted one-phonon density of states as found, e.g., in LaS (M6rke 1985). An example of CeS is shown in fig. 10 at the bottom.
The T h 3 P 4 crystal structure, within which C e 2 S 3 and C e 3 S 4 crystallize, can accommodate cations (M) and anions (S) in various stoichiometries with the nominal compositions M 2 S 3 and M 3 S 4. In the M 3 S 4 compounds both sublattices are filled, whereas in the M 2 S 3 compounds only the M sublattice contains vacancies. Therefore, it is better to denote this compound as M2.67S 4. For trivalent rare-earth ions the R 3 S 4 and R - S samples are metallic, whereas the R2S 3 compounds are semiconductors. The three CeyS 4 samples investigated had the following compositions according to wet chemical analysis:
C e 4 S 4 = Cel.ooSl.oo , a o = 5 . 7 7 7 2 A,
Ce2.996S4, a 0 = 8.622 ,~,
Ce2.71784, a 0 = 8.625 A.
)~
-p
c
© c
~ 3 C i_
©
O
l ~ T = t B K
÷ ~
N N
÷
N . . . . ~ . . . . . .
~ N
T T
÷ ÷
t
C e S
I I I I I
@ 5 0 0 1 0 0 0 ! 5 0 0 2 0 0 0 2 5 0 0 3 @ B B
F r e q u e n c y Sh i q t ( c m -1)
Fig. 10. Raman spectra of the series Ce2S3, Ce3S 4 and CeS at l0 K. Of particular interest are the CEF-split J-multiplet excitations above 2000 cm -1, after M6rke et al. (1986).
L I G H T S C A T F E R I N G IN I N T E R M E T A L L I C C O M P O U N D S 177
The second compound will be quoted as Ce3S 4 and the last one as Ce2S 3. Figure 10 shows the R a m a n spectra of all three compounds (M6rke et al. 1986). In the low-frequency range from 90 cm -~ to 650 cm -1 one observes light scattering from Raman-active phonons, defect-induced phonon density of states scattering and electronic R a m a n scattering from excitations within the J = ~ multiplet. Addition- al features are seen near 2200 cm -a, with their scattering intensity decreasing by going from the semiconducting C e 2 S 3 t o metallic C e 3 S 4 and CeS. These excita- tions are interpreted as electronic transitions from the ground state of the J = 152 configuration to the four doublets of the J = 7 configuration. With increasing metallic behavior not only does the R a m a n scattering intensity decrease, but also the overall crystal-field splitting decreases due to the increasing shielding of the sulphur charges by conduction electrons and by a change in the site symmetry.
The site symmetry of Ce in CeS in cubic (m3m), while in the other two compounds the Ce site symmetry is tetragonal (4). The decrease of the overall crystal-field splitting is confirmed by magnetic susceptibility measurements, which show a drastic decrease of the crystal-field splitting of the J = ~ ground state (M6rke et al. 1986).
The investigation of J-multiplet excitations of Ce has been extended to inter- mediate-valence CePd 3 by Zirngiebl and co-workers (Zirngiebl et al. 1985b).
Figure 11 shows the R a m a n spectrum of CePd 3 at 5 K for 5309 A (2.3 eV) laser excitation. A broad maximum is found near 2600 cm -1 (325 meV) as indicated by the dashed guide line. The full width at half maximum ( F W H M ) amounts to about 250 meV. Superimposed on this broad maximum is a relatively sharp peak near 2050 cm -1 (256 meV) with a F W M H of 48 meV. The two maxima in fig. 11 always appear in the R a m a n spectra for different laser excitation energies at the same energy loss AE R with respect to the incident photon energy hoJ i. Thus they are identified as electronic excitations (AER) with respect to the initial state in
"E
° ~
c
E
200 160 120 80 40
I I I I
2050 cm -1 tO-sl "-I~
C e P d 3 ~ 26oo cn~ 1 'h
SK .'f. l
toi• v :
--~-},,~.
• - . . . . : -
. " ' . . . ~ - . ~ . . . ~ . ,,.: . . . . , . . . "
' . . . . ~ . . . .
:... ~ :~2..,
"..%.
• .. .- ,,;Y.
'. :.'5,'.."'..
0 I I I i
1000 2000 3000 4000 5000 6000
F r e q u e n c y S h i f t (crn -1)
Fig. 11. R a m a n s p e c t r u m of C e P d 3 at 5 K, showing t h e 4f1---> 4f ° excitation n e a r 2600 cm -I (dashed guide line) a n d the J = ~ ~ 7 excitation n e a r 2050 cm -1. Inset: the energy difference b e t w e e n the incident (ho~i) and the scattered (hoJ,) p h o t o n yields the energy A E R of t h e R a m a n excitation.
178 E. ZIRNGIEBL and G. Gi0NTHERODT
Raman scattering (see inset of fig. 11). Within the nomenclature introduced for the interpretation of Raman scattering results of IV EuPd2Si 2 the broad max- imum near 2600 cm -1 in fig. 11 is attributed to the 4fl---~ 4f ° interconfigurational excitation energy E x of about 325 meV. The one-electron occupied 4f I state above E F has been observed in BIS (bremsstrahlung isochromatic spectroscopy) near 450 meV (Baer et al. 1981), in good agreement with our findings. Both results indicate that the 4f 1 level is well below the Fermi level, placing CePd 3 into the class of Kondo-like compounds and not into the class of strong IV compounds like EuPd2Si2, for which Ex is more than an order of magnitude smaller. The F W H M ~ 2 5 0 m e V of the interconfigurational excitation obtained in Raman scattering is smaller, by about a factor of three, than that in BIS, most probably due to the much better spectral resolution of Raman scattering. This value is of the order of magnitude of the estimated f - d hybridization width of CePd 3 with A ~ 100 meV from optical data at 4.2 K and A ~ 150 meV from X-ray photoemis- sion (XPS) data (Fuggle et al. 1983).
The peak near 2050 cm -1 in fig. 11 coincides with the 2F5/2 ~ 2F7/2 intra-ionic excitation energy of the Ce 3+ 4f I configuration. This confirms the previous tentative assignment in infrared spectroscopy (Hillebrands et al. 1982) and proves that ionic configurations may still be preserved in IV compounds. The F W H M 48 meV is of the same order of magnitude as 2T~ = 2 F ~ / 2 ~ 38 meV as obtained from quasielastic magnetic neutron scattering (Loewenhaupt and Holland-Moritz 1979a).
2.5. Light scattering f r o m C E F excitations in R B 6
The investigation of CEF levels in lanthanide intermetallic compounds is a classic domain of magnetic neutron scattering (Fulde and Loewenhaupt 1988).
The normal energy range of CEF level splitting is of the order of 100 K and is best suited for inelastic magnetic scattering experiments. From the transition energies and intensities one can identify quite unambiguously CEF level schemes, especial- ly for cubic compounds within the systematic treatment given by Lea, Leask and Wolf (Lea et al. 1962).
There is, however, a large number of examples, where due to the limited energy range available (the production rate of high-energy neutrons (E > 50 meV) is quite low at reactors) or due to the limited energy resolution of neutron scattering, light scattering can be a complementary tool in the investigation of CEF level schemes. In the following we shall discuss some of these cases where light scattering has helped to clarify unresolved questions.
2.5.1. CeB 6
The dense Kondo compound CeB 6 was first reported by Fisk in 1969 (Fisk 1969). In spite of the large body of thermal, magnetic and elastic data on CeB6, which has accumulated over the following years various diverging speculations have entered the literature concerning the CEF excitations (for a review see Zirngiebl et al. (1984)). Their absence in direct spectroscopic measurements
L I G H T S C A T T E R I N G I N I N T E R M E T A L L I C C O M P O U N D S 179
(Horn et al. 1981a) has been puzzling ever since. This led to a wide variety of proposed CEF splittings ranging from 10 K (Goto et al. 1983) to more than 400 K (Horn et al. 1981b) and gave rise to conjectures about anomalous broadening or splitting effects (Horn et al. 1981b, Fujita et al. 1980, Hanzawa and Kasuya 1984). This unresolved CEF level scheme was even more puzzling a s C e B 6
crystallizes in the cubic C a B 6 s t r u c t u r e (space group O1), where the sixfold-de- generate ground state 4f 1 (J = ~-) of Ce 3+ is expected to split only into two levels (a F 7 doublet and a F s quartet), giving rise to only one CEF excitation.
The first spectroscopic insight into the CEF level scheme of C e B 6 finally came from inelastic magnetic neutron scattering using high-energy incident neutrons up to 185 meV (Loewenhaupt and Carpenter 1983). An inelastic magnetic excitation was found near 530 K, still not yet allowing for a final conclusion about the CEF level scheme. This inelastic magnetic excitation has been further investigated by Raman spectroscopy (Zirngiebl et al. 1984), taking advantage of the high resolution as compared to neutron spectroscopy• The Raman measurements have been carried out on (100) faces of C e B 6 between 300 and 4.2 K using 5309 .~ Kr + laser excitation• At room temperature an inelastic excitation at 372 cm-1 (530 K) was found as shown in fig. 12. Below 20 K the peak shifts by about 10 cm -1 to higher energies. At 4.2 K it is much narrower and has an energy of 382 cm -1 (fig.
12). The intensity of the peak does not change between 4.2 and 300 K because of the high excitation energy (530 K) compared to the sample temperature• There- fore, one cannot distinguish between a CEF excitation and a phonon by the intensity variation alone. However, the unusually large peak shift and its onset below 20 K rules out a phononic excitation since no lattice anomaly has been observed in this temperature range (Fujita et al. 1980)• In addition, the non- magnetic reference compound LaB 6 shows no excitation in that energy range at
C
t -
"E
0 ' } C
0 u
{.n
372tcrKt~ '
300K
~ 2
~ K ~l
382 cm -~ ~
rv 5~SK
30K OK-
/ - - - " ~ : Lo B6
77K
I I I I
300 400 500 600
Frequency Shift (crn -I)
Fig. 12. R a m a n scattering intensities of CeB 6 and LaB 6 at different temperatures showing the Ce 3+ F s - F 7 C E F tran- sition. Inset: derived C E F level scheme of CeB 6.
180 E. Z I R N G I E B L and G. G O N T H E R O D T
any temperature (see fig. 12 for, e.g., 77 K). Hence, Zirngiebl and co-workers concluded that the excitation near 372 cm -1 in C e B 6 corresponds to the F s - F 7 CEF transition within the 4f ~ configuration.
In order to further corroborate their CEF level assignment a symmetry analysis by polarized Raman measurements was performed as shown in fig. 13. For comparison the well known three Raman-active phonons appearing above 600 cm -1 have been included. The 372 cm -1 peak appears in the F3(Eg ) and the F;(Yzg ) symmetry components. This is consistent with a F s - F 7 transition because the direct symmetry product of the initial and final states IF8 > ® < Fyl = F~- • F 4 • F~ contains the experimentally observed symmetries.
From the symmetry analysis it cannot be decided which is the electronic ground state. However, Zirngiebl and co-workers deduced this information from the anomalous shift of the 372 cm -1 peak in fig. 12 for temperatures below 20 K. This behavior is explained by a non-Kramers ground state of F 8 symmetry, which is split into two doublets £8,1 and Fs, 2 with a separation of about 30K. At temperatures well above 30 K, transitions from both Fs, 1 doublets to the high- lying F 7 level are possible, yielding the measured mean transition energy of 372 cm -1 (530 K). A double-peak structure could not be resolved even in Raman scattering (experimental resolution 3 cm-1) because of the large inherent width of the peaks. Upon cooling well below 3 0 K the upper doublet Fs, 2 becomes thermally depopulated and the scattering takes place between the lower F8,1
4--
g e
>,-
f i Z u.J i , i Z
Z i ' Y u J i , i L_,, C,")
5~ I I ~5 I I 5 5 L I I
C e B 6
F1 +
(A,g)_~_ 77~K
_3F3 (3Eg)
÷n
[-5 + (T2g) I ~ ~ I 5
J L
I I ~$I I ~ ' 13'00 5S300 400 600 700 I100
F R E Q U E N C Y SHIFT (cm -I)
Fig. 13. Symmetry analysis of the Fs- ~ CEF transition and the Raman-active phonons of CeB 6 at 77 K.
LIGHT SCATI'ERING IN INTERMETALLIC COMPOUNDS 181 doublet and the F 7 level. This yields a shift of the observed transition energy upon
a E
cooling by 5( s,2 - Es,1) = 15 K = 10 cm -1 towards higher energy. The new C E F level scheme derived from the R a m a n measurements is shown in the inset of fig.
12, providing so far the most simple interpretation of the measured thermal, elastic and magnetic data (Zirngiebl et al. 1984).
2.5.2. N d B 6
The Hund's rule 4f ground state of the Nd3+(419/2) is tenfold degenerate and splits when in a cubic crystal surrounding into two F s quartets and a F 6 doublet.
The corresponding three-level C E F scheme of NdB 6 has been investigated by several experimental methods, yielding very different results (Westrum et al.
1965, Fisk 1976). A C E F level scheme has also been proposed on the basis of neutron scattering (Loewenhaupt and Prager 1986). Within the examined energy range of 50meV ( = 4 0 0 c m -1) one broad magnetic excitation was detected at 12 meV (=95 cm-a). From the temperature dependence of the scattering intensity of the excitation and by comparison with the L e a - L e a s k - W o l f parameters of other RB 6 compounds the following level scheme was deduced: the ground state has F~ z) symmetry, the first excited state at 12 meV has F~ 1~ symmetry and the F 6 state lies 24 meV above the ground state. The excitation at 24 meV was not observed in neutron scattering because of the small transition matrix element F(s2) ~ F 6. Therefore three possible transitions can give rise to only one peak in the neutron scattering spectrum. This determination of the C E F level scheme is plausible. It would, however, be more desirable to separate in energy the two transitions F~2)--~ F(81) and F~l)----~ F 6 within the peak at 12 meV.
R a m a n scattering on NdB 6 has been reported by Pofahl et al. (1986). The R a m a n measurements were carried out on the (110) face of a NdB 6 single crystal which was prepared using the arc floating zone technique (Verhoeven et al. 1976).
The measurements were performed as a function of temperature between 300 K and 7 K, with the sample under vacuum. Several different laser wavelengths (5145 ~ , 5130 A, 5682 A) were used.
In fig. 14 the R a m a n spectra of the magnetic compounds CeB 6 and NdB 6 and of the non-magnetic compound LaB 6 are shown. The well known Raman-active T2g phonon of the rare-earth hexaborides is seen in all three spectra near 680 cm ~, together with the phonon density of states near 180 cm -a. The addition- al peak at 372 cm a in the spectrum of CeB 6 was attributed to the C E F excitation Fs(0 K)---~ F7(545 K) as discussed in sect. 2.5.1. The extra peak at 95 cm -1 in the spectrum of NdB 6 coincides with that observed in neutron scattering and was the subject of more detailed examinations, such as symmetry analysis and tempera- ture dependence. As the peak does not show up in the R a m a n spectra of either LaB 6 or CeB 6 it is reasonable to associate it with excitations within the 4f 3 configuration of the Nd 3+ ion.
Polarized Raman measurements and special crystal orientations have been used by Pofahl et al. (1986) to analyze the mode symmetries as shown in fig. 15. It is possible to determine by group theory the symmetry of the different C E F transitions: