Samarium

Section 4.3 Section 4.3 deals with measurements on anomalous lanthanide systems, where significant departures from the normal systems are encountered

5. Coulomb transitions

5.2.2. Samarium

Because of the high multiplicity of the two lowest terms in the Sm 3+ ion, 6I--I and 6F, the multiplet structure below 1.5 eV is relatively complicated. Above the J---~ J + 1 transition, the neutron cross-sections are dominated by the 6H5/2----~ 6F3/2,5/2 transitions which occur at 827 and 889 meV in Sm:LaF 3 (Carnall et al. 1989), along with weaker transitions to the

6F1/2,7/2

levels at 797 and 991 meV, respectively. Free-ion spectra are not available, but are not expected to be much different from the fluoride. Needham (1989) reports, in SmPd3, the observation of two peaks at 781 and 842 meV with some evidence of a third at 934 meV. The spectra were taken with an incident energy of 1250 meV, above the absorption resonance at 870 meV, with scattered energies lying in the transmission

"window" below the resonance. A detailed comparison with the calculated cross-sections has not been attempted because of the consequent energy depen- dence of the neutron absorption. Nevertheless, the data are consistent with a uniform reduction of the energies of all the Coulomb transitions by about 50 meV from the values in Sm:LaF3, in qualitative agreement with the praseodymium results. Once again, the values in Sm:LaC13 lie between the metal and the fluoride (Martin et al. 1978).

34 R. O S B O R N et al.

5.2.3. Thulium

The energy of the lowest Coulomb transition in trivalent thulium, t h e 3H 6 ~ 3F 4 transition, is at just under 700 meV with transitions to the 3F 3 and 3F 2 levels at just under 2eV. There are strong deviations from the Land6 interval rule [equation (6)] because of intermediate coupling. Moreover, the mixture of the 3H4, 3F 4 a n d XG 4 levels by the spin-orbit interaction substantially alters the transition intensities. Figure 6 shows the inelastic neutron scattering from a 100 g sample of thulium metal, measured at HET by Osborn et al (1990) with an incident energy of 2.14 eV. Four well defined transitions are observed at 684, 1018, 1560 and 1760 meV. Comparison with the transitions in Tm:LaF 3 (Carnall et al. 1989; see table 6) show that these peaks correspond closely in energy with the

20 t',5 ,3,

,~1c°

3 03

I I

400 600

I I I I I I

3H 5 3H 4 3F 3

* + -

8OO 1000 .1200 1400 1600 1800 2000

"hoJ rmeV]

Fig. 6. N e u t r o n scattering cross-section of intermulitplet transitions from the 3H 6 g r o u n d level in thulium m e t a l at 20 K, m e a s u r e d at an angle of 5 ° with an incident n e u t r o n energy of 2140 m e V on H E T . T h e i n s t r u m e n t a l resolution varies f r o m 56 to 27 meV as the energy transfer increases f r o m 500 to 1800 meV. T h e data have b e e n fitted by four G a u s s i a n s a n d a tail of low-energy scattering. T h e p e a k s are labelled by the final state of the transition.

TABLE 6

T h e e x p e r i m e n t a l a n d calculated energies (in meV) of inter- multiplet transitions from t h e 3H 6 g r o u n d state multiplet of the Tm 3+ ion: Tm doped in L a F a (Carnall et al. 1989); Tin metal ( O s b o r n et al. 1990); calculation using the following p a r a m e t e r s , F 2 = 5 9 . 3 m e V , F a = 8 . 1 9 m e V , F 6 = 0 . 8 9 6 m e V

and ~4f = 326.8 meV.

T m : L a F 3 T m m e t a l Calculation

3F 4 689,7 694 693.5

3H 5 1017.0 1018 1017.8

3H 4 1550.4 1560 1556.0

3F 3 1774.3 1760 1810.7

I N T E R M U L T I P L E T T R A N S I T I O N S 35 3H6---> 3 F 4 , 3 H 5 , 3H 4 a n d 3 F 3 transitions, respectively. Furthermore, the relative intensities of the

3H-> 3H

and the

3H----> 3F

transitions are in good agreement with a full intermediate coupling calculation, in contrast to the praseodymium results (fig. 7).

The energies of all the transitions are well reproduced with F 2 = 59.3 meV and ff4f = 326.8 meV. The remaining Slater integral parameters were kept fixed to their hydrogenic ratios (see sect. 2.1.1). The value of ff4f is identical to that determined by Carnall et al., although the Slater integrals are slightly different because of our neglect of the other weaker free-ion parameters.

Since the transition energies of Pr:LaF 3 are close to those of the free Pr 3+ ion, it is especially significant that there is no appreciable difference between thulium metal and the fluoride. This suggests that, in the heavy lanthanides, there is no additional screening of the Coulomb interaction to that occurring in the free ion.

Osborn et al. (1990) propose that this is a consequence of the lanthanide contraction making the f shell in the heavy lanthanides much less susceptible to perturbation by the external environment. The fact that there are no anomalies in the measured intensities confirms the existence of a correlation between the Slater parameter shifts and the intensity reductions inferred from the praseodymium results (Osborn 1989). Both are a consequence of increased hybridisation of the f states in the lighter lanthanides.

\

3H~ \

lo-S -

-

/ , /

10"4 ^_

~ I~, L I , v"~ ~ I , L , i I , I I I

0 5 10 15 20

Wavevector K ( A - l )

Fig. 7. Neutron inelastic structure factors for intermultiplet transitions in thulium. The lines represent the calculated intensites, taking intermediate coupling into account, of the 3H6----~ 3F 4 (smooth line), 3H6---~3H 5 (long-dashed line), 3H6--~3H 4 (chain line) and 3H6---~3F 3 (short-dashed line) transitions.

The calculated structure factors are normalised to the 3H6----~3H 6 intensity at K = 0 , which has a cross-section of 2769 mb sr -1. The measured intensities of transitions to the 3F 4 (filled circles), 3H 5 (filled triangles), 3H 4 (open circles) and 3F 3 level (filled square) levels are normalised to the calculated structure factor of the 3H6----> 3F 4 transition at K = 6.2 A-~.

36 R. OSBORN et al.

Investigations of Coulomb transitions in intermediate valent thulium (and samarium) compounds are an obvious development in this field.

5.3. Uranium alloys

The study of Coulomb transitions is especially valuable in actinide metals and intermetallic compounds (McEwen et al. 1990, Osborn et al. 1990). Because of the greater radial extent of the 5f charge distribution, the actinide f electrons tend to hybridise more strongly with band electron states than their lanthanide counterparts. In a number of actinide metals, it is evident that the f electrons contribute to the cohesive energy through the formation of 5f bands, either by direct f - f overlap, as in a-uranium, or by hybridisation with conduction bands, as in URu 3 or URh 3 (Oguchi and Freeman 1986, Johansson et al. 1987). In these cases, relativistic band theory is successful in predicting lattice constants, photo- emission and Fermi surfaces (Arko et al. 1985) provided the f states are included as itinerant.

On the other hand, good agreement with the de Haas-van Alphen measure- ments on UPd 3 (Ubachs et al. 1986) is only obtained by treating the f electrons as core states (Norman et al. 1987), whilst photo-emission results show that there is no f-electron density at the Fermi level in this compound (Baer et al. 1980). It is significant that UPd 3 is the only actinide metal in which well defined crystal-field excitations have been observed by neutron spectroscopy (Shamir et al. 1978, Murray and Buyers 1980, Buyers and Holden 1985). All these results indicate that the uranium ions in UPd 3 have a localised f2 configuration and behave more like stable lanthanide ions.

Although band theory cannot describe the f electrons in UPd 3 adequately, it can help to explain why they behave differently from the f electrons in other apparently similar compounds. Johansson et al. (1987) have shown that in UX 3 compounds, where X is a 4d transition metal, the d electrons hybridise to form two separate bands; a bonding band, largely composed of X-derived 4d states, and an anti-bonding band, composed of the U-derived 6d states. In most of the compounds, the 5f states hybridise with the 4d states spreading the f contribution to the electronic density of states over several electron volts. In UPd3, however, the f states lie in the gap between the two d bands and scarcely hybridise at all. In these circumstances, the f electrons gain correlation energy through the localisa- tion process. In a further study of the band structure of U(Pdl_xRhx) 3 alloys, Eriksson et al. (1988) have studied the Mott transition in which the f-electron character changes from localised to itinerant with increasing x as a consequence of the 4d band moving up in energy.

McEwen et al. (1988) have suggested that similar mechanisms are responsible for the change in magnetic behaviour in U(Pdl_xPtx) 3 alloys from localised magnetism for x = 0 to heavy-fermion superconductivity for x = 1. Franse et al.

(1985) have shown that the large electronic specific-heat enhancement in UPt 3 is not present until x > 0.7. The effect of increasing hybridisation is also evident in the crystal-field spectra (McEwen et al. 1988, 1990b), with the peak at 14 meV

I N T E R M U L T I P L E T T R A N S I T I O N S 37

shifting to lower energy and broadening as x increases, becoming quasielastic at x = 1. There is always the possibility that some of this broadening is due to lattice disorder, but the absence of well defined crystal-field transitions in UPt 3 confirms that much of the damping is due to the hybridisation.

These results encouraged the first investigation of intermultiplet excitations in a uranium compound (McEwen et al. 1990, Osborn et al. 1990). Whilst crystal-field studies can trace the development of hybridisation, they cannot show what happens to the 5f-electron ground state as it grows. The observation of inter- multiplet transitions, however, can establish whether intra-atomic correlations are maintained as the hybridisation is turned on, and gives information on the composition of the hybridised ground state. An estimate of the positions of the intermultiplet transitions in U 4+ ions can be obtained by using the free-ion parameters of UO 2 (Rahman and Runciman 1966). The lowest transitions are the 3H4----~ 3 F 2 a n d 3H 5 transitions at 448 and 692 meV, respectively. The former is a Coulomb transition and so would be significantly reduced in energy by hybridisa- tion. The observation of

the 419/2---~ 4Ill/2

transition, which occurs at 530 meV in U3+:LaC13 (Carnall and Crosswhite 1985), would imply the development of intermediate valency.

Figure 8a shows the neutron inelastic scattering from UPd 3. There is a peak at 385 meV with a width of about 60 meV sitting on a multiple scattering back- ground. McEwen et al. (1990a) ascribe the peak to t h e 3 H n - - - - ~ 3 F 2 transition, which requires F 2 = 19.7 meV, a 20% reduction from its value of 23.73 meV in UO 2. To reduce the number of free parameters to one, the ratios of F 4 and F 6 to F2, and the value of ~st are kept fixed to their ionic values. This Slater parameter

20[ I ,

^,

1(o )

15 10

il

, , , +

++, ,f,tt

"~00 500 400 500 600 700

h~ rmeV]

Fig. 8. N e u t r o n inelastic scattering f r o m (a) U P d 3 and (b) U P t 3 at 20 K, m e a s u r e d at an angle of 5 ° with an incident energy of 800 rneV on H E T . T h e data h a v e b e e n fitted to a G a u s - sian and a tail of low-energy scattering.

38 R. OSBORN et al.

shift is much larger than that found in the lanthanides but appears reasonable, given the greater spatial extent of the 5f wavefunctions. This result then confirms the earlier conclusions concerning the localised nature of the 5f shell in UPd 3.

McEwen et al. (1990a) performed equivalent scans for x = 0.37, 0.5, 0.75 and 1.0 in the alloy series U(Pdl_xPtx)3. A similar peak is seen in every sample although its energy falls to 375 meV at x--0.5. In U P t 3 , it is at 373 meV and is both broader and weaker (fig. 8b). The extra reduction of F 2 at x = 0.5 occurs in the same composition range as a change in the crystal structure from the dhcp phase of UPd 3 to a 10-layer structure (McEwen et al. 1990b). Nevertheless, apart from this small energy shift, the intermultiplet transition persists across the series, showing that the ground state of the heavy-fermion compound UPt 3 is, like UPd3, composed of highly correlated 5f states, with a major component formed from the 5f 2 3H 4 ground level. The measurements do not rule out the presence of a 5f 3 component, as well, i.e., that U P t 3 is an intermediate valence compound with a hybridised ground state composed of two configurations. However, the failure to observe any 5f3-derived peaks implies that the uranium ion is close to tetravalent.

The suggestion that UPt 3 has a fairly localised 5f 2 configuration is not entirely new. It was proposed by Johansson et al. (1986) after consideration of the molar volumes and crystal structures of similar tetravalent compounds. On the other hand, there is considerable evidence that the f electrons form itinerant bands, even if their contribution to the bonding is small. Most strikingly, de Haas-van Alphen studies (Taillefer and Lonzarich 1988) provide detailed measurements of the Fermi surface topology which are in excellent agreement with relativistic local-density functional band structures (Norman et al. 1988, Christensen et al.

1988) which treat the f electrons as itinerant. Therefore, in spite of the neglect of orbital correlations, which the neutron scattering results show are very strong, one-electron band theory predicts the correct Fermi surface. The resolution of this paradox, that the f electrons are both highly correlated and yet itinerant, is, of course, central to the understanding of heavy-fermion phenomena.

For UPt3, the resolution of this conflict appears to be rather subtle. Density functional band theory predicts the correct Fermi surface but not the correct quasiparticle masses. To do that requires a reduction of the band widths in a semi-empirical manner (Fulde et al. 1988, Zwicknagl 1988); in the case of U P t 3 the renormalised band widths are about 50 meV (Christensen et al. 1988). This is much less than the intermultiplet splitting so, whilst the f electrons may form bands through hybridisation with the ligand d orbitals, the resulting Fermi liquid must be derived from the f states comprising t h e 3H 4 ground level. It seems that the reason for the success of band theory may be fortuitous. Because of the strength of the spin-orbit interaction and relative weakness of the Coulomb interaction in the actinides compared to the lanthanides, the 5f electrons are closer to being in the jj-coupling states than their lanthanide counterparts, for which L S coupling is a much better approximation. In the limit of strong spin-orbit coupling, relativistic band theory will predict the correct jj-coupling ground state, which has both f electrons in the j = ~ state, and indeed Zwicknagl (1988) has shown that the Fermi surface of U P t 3 consists almost wholly of j =

INTERMULTIPLET TRANSITIONS 39 character. She concludes that the Fermi surface topology is given correctly by band theory provided the spin-orbit coupling is strong. To this should be added the condition that the Coulomb repulsion between the f electrons must be comparatively weak, so that it is reasonable to neglect the orbital correlations implied by Hund's rules.

Investigations of the intermultiplet transitions have only just begun, but it is already evident that they can help to clarify the nature of the 5f-electron ground states in actinide metals. The experience gained from measuring Coulomb transitions in the relatively stable configurations of lanthanide compounds has been essential in interpreting the scattering from more strongly hybridised configurations. So far, the similarities between actinide systems and their lantha- nide counterparts are more remarkable than their differences. As more actinide compounds are explored, it should be possible to determine the degree of correlation necessary for the development of a particular ground state, whether localised, heavy fermion or itinerant.