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Photoemission and bremsstrahlung isochromat spectroscopy of 5f electron systems
Journal of Magnetism and Magnetic Materials 52 (1985) 129-134 North-Holland, Amsterdam
INVITED
129
PAPER
PHOTOEMISSION AND BREMSSTRAHLUNG 5t' E L E C T R O N SYSTEMS F.U. HILLEBRECHT
*, D . D . S A R M A
ISOCHROMAT
and N. M~,RTENSSON
SPECTROSCOPY
OF
+
lnstitut fftr FestkOrperforschung, KFA J~lich, P.O. Box 1913, 5170 J~lich, Fed. Rep. Germany + Physics Institute, Uppsala Unioersity, Box 530, S-751 21 Uppsala, Sweden
The core levels and valence states of U compounds have been studied using XPS and BIS. The unoccupied valence states give a clear indication of the degree of localization of the 5f states. In general, the influence of f-ligand hybridization is stronger for U compounds than for Ce compounds.
1. Introduction The purpose of this p a p e r is to discuss some aspects of the electronic structure of 5f electron systems as o b t a i n e d from X-ray photoemission a n d inverse p h o t o emission in the soft X-ray regime, which is usually termed Bremsstrahlung Isochromat Spectroscopy. f electrons occur in the rare earth a n d actinide series of the periodic system, a n d play a decisive role mainly for the magnetic behaviour, but also for other properties of these elements and their c o m p o u n d s . In several cases, especially for some rare earth compounds, the magnetic b e h a v i o u r is clearly connected to a fully localized f level exhibiting a well-defined angular m o m e n t u m a n d associated localized magnetic m o m e n t . These m o m e n t s interact with each other via R K K Y coupling or a similar mechanism, leading to a large n u m b e r of ordered structures [1,2]. For actinides the situation is more complicated. It has been deduced from b a n d - s t r u c t u r e calculations that at the beginning of the actinide series the 5f states are delocalized [3,4]. The overlap between n e i g h b o u r i n g 5f wave functions is sufficient for a 5f b a n d to be formed. F o r the heavier actinides the 5f shell is more contracted, a n d the 5f states are localized, similar to the 4f states of rare earths. The transition to localized 5f states occurs between U and A m [3,4]. Consequently, U can be classified as a 5f metal. It has been suggested that in U c o m p o u n d s the 5f states m a y b e c o m e localized, if the separation between n e i g h b o u r i n g U atoms is larger than
* Present address: IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA. 9 3 0 4 - 8 8 5 3 / 8 5 / $ 0 3 . 3 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)
3.4 to 3.6 A [5]. A l t h o u g h it is a very plausible a r g u m e n t to relate the width of the 5f b a n d to the U - U separation, we shall d e m o n s t r a t e that u n d e r certain circumstances the 5f states are delocalized even if the U - U separation is large. Rare earth metals and their c o m p o u n d s are quite often taken as model substances for actinides, a n d the concepts used there are transferred to 5f systems. However, as we have said at the beginning of the actinides series the 5f states are delocalized, whereas the 4f states are - u n d e r normal conditions at least - highly localized, even in Ce. In some cases it h a p p e n s that two different f occupancies are nearly degenerate, and the material is mixed valent. This affects e.g. the magnetic susceptibility and the lattice volume. Photoemission spectra of such materials show the distinct multiplet structure characteristic of the f" final states [6,7]. The intensity ratio observed in the spectra can be used to deduct the average valence in a straightforward manner. T h e loss of m a g n e t i s m in some Ce c o m p o u n d s a n d the smaller volume of n o n - m a g n e t i c Ce ions as c o m p a r e d to the magnetic case was originally attributed to a p r o m o tion of the f state above the Fermi level ( E v L a n d a transfer of the f electron to the c o n d u c t i o n band. This so-called p r o m o t i o n a l model of mixed valence is not able to explain experimental results, e.g. photoemission results. W i t h i n this model one expects to find f related features near the Fermi level in photoemission for nonmagnetic materials. It appears, however, that in all cases a significant part of the emission is always well below E v. Hybridization between the 4f a n d conduction states plays a decisive role here [8-12]. If hybridization is i m p o r t a n t for Ce, it should be m u c h more i m p o r t a n t for U c o m p o u n d s because of the
130
F. U. Hillebrecht et al. / Electronic structure of 5f electron systems
larger 5f radius. We expect therefore to find a stronger tendency towards delocalization in those U c o m p o u n d s whose Ce analogs showed signs of a delocalized contribution. These were n o n - m a g n e t i c c o m p o u n d s like CeNi 5 [12]. A l t h o u g h we will make extensive use of the Ce results, this is not the place to repeat the discussion. Instead we present recent results on U c o m p o u n d s and refer to review articles or the original works where necessary.
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For Ce c o m p o u n d s it has proved very revealing to analyze core level spectra [8 11,13]. Especially X-ray photoemission and absorption of the 3d levels indicated the presence of f 0 fl a n d f2 configurations in the final state. The intensity of the various final states differs d e p e n d i n g on what kind of experiment one does, and also does not agree with estimates of average f occupancy derived from e.g. lattice c o n s t a n t measurements. This led to the conclusion that hybridization affects the weights of the final states [9]. For U comp o u n d s core level spectroscopy should also provide relevant information [14-18]. If the 5f states are bandlike, we expect a fairly simple spectrum, similar to core level spectra of transition metals. If, however, they are localized, we expect to find some signs of m u h i p l e t splitting, provided the splitting is large e'nough. Furthermore, in analogy to Ce compounds, one may expect to find final states corresponding to different f occupancies [8-10,13]. The core level spectra of U c o m p o u n d s show pronounced variations as is illustrated in fig. 1 for the U 4f levels in UCo5. 5 and UCu s. The spectrum of the first c o m p o u n d looks at first sight rather simple: there are two sharp lines, split by the spin orbit interaction. M u h i p l e t splitting seems to be smaller than for the rare earth 3d levels [10,19]. U C u 5 clearly shows additional structure [14], but - again in contrast to rare earths only at higher binding energies. To obtain a clearer picture of the size and shape of the satellite c o n t r i b u t i o n we fitted the main lines with two D o n i a c h - S u n j i c profiles convoluted with Lorentzian and G a u s s i a n curves to simulate lifetime b r o a d e n i n g and experimental resolution. An integral b a c k g r o u n d was also included. After o b t a i n i n g a close agreement between calculated and experimental spectrum in the region of the main lines the calculated spectrum was subtracted leaving b e h i n d the satellite spectrum shown in the b o t t o m part of fig. l. We note that both satellites are similar in shape, a n d the intensity ratio is similar to that for the main lines.
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Fig. 1. Uranium 4f core level spectra excited with monochromatized AI K s radiation for UCo55 and UCu 5. Also shown are the satellite contributions which have been determined by subtracting a background and fitting the main lines with Doniach-Sunjic profiles with Lorentzian and Gaussian broadening to simulate finite lifetime and resolution. Performing the same procedure for UCo5 s we find that the spectrum still contains a small satellite contribution. Its shape is similar to that of the UCu s satellites, but its intensity is much smaller. It appears that spectra of m a n y other c o m p o u n d s [14] are intermediate between these two prototypes. An additional effect which can be seen e.g. for UPt 3 [20] is a very large asymmetry of the main line which is presently not fully understood. We note that the " m a i n line" i.e. the d o m i n a n t c o n t r i b u t i o n is always the one at the lowest excitation energy. In Ce the main line is not the one with the lowest excitation energy. The 4f binding energy for the main line of the c o m p o u n d s is in m a n y cases similar to that for U metal, or it is shifted by a certain a m o u n t similar to the 4f BE shift found for isostructural Th compounds. This means that the final state associated with this line is the same in all cases. In U metal this state certainly has an f4 local configuration, and we assign the same state to the main lines in the compounds. The core level spectra tell us that in general the coupling between 5f and extended states is sufficient to ensure in all cases that the d o m i n a n t screening channel is screened by an f electron. In rare earths this was not the case, a n d the decrease of the well screened peak with increasing Z can be correlated with the shrinking of the 4f shell [8]. As a next step in the interpretation of the U core level spectra one can propose that the additional structure seen in U C u 5 is due to f3 and f4 configurations, in analogy to the fl a n d f0 configurations seen in Ce
F.U. Hillebrecht et al. / Electronic structure of 5f electron systems
spectra. However, as we have noted above, in UCos. 5 there still is a remnant of both features. If we were to interpret the satellite contribution in the spectra in terms of f2 and f3 configurations, we would expect the f2 contribution to be smallest. Obviously, the f3 contribution is very small in UCos. 5, and so it is astonishing to find any f 2 at all. This interpretation also yields an estimate for the 5f intra shell Coulomb interaction U. From the spectrum we find the feature which would be assigned to f2 at 6.8 eV above the main line, and the f3 feature at 3.2 eV. For the fa_f3 separation we get U f c - 3 U , and for the f3_f2 separation Ufc - 2U. Ufc is the Coulomb interaction between the core hole and the 5f electrons. This results in U = 0.6 eV. Herbst and Watson [21] calculated U = 1.8-2.5 eV. The simple interpretation of the satellites cannot account for the peak separations found in the spectrum. It is possible that the small value of U which comes about through the position of the main line indicafes that this particular final state is not an atomic 5f 4 configuration. The fixed shape of the satellite spectrum leads us to suggest that one should think of one satellite spectrum containing both f2 and f3 contributions, which are strongly mixed. This is supported by results for Th compounds [22] which show clearly that the Coulomb interactions in actinides are such that the configurations mix much more strongly than for rare earth materials. To understand the core level spectra properly it is necessary to incorporate multiplet and crystal field splitting into the theory of Gunnarsson and Sch6nhammer [9,23].
3. Valence band spectra We now turn to a discussion of the valence states. The occupied valence states can be probed by photoemission, and the unoccupied states by inverse photoemission. In this experiment the sample is irradiated with electrons and the photons emitted are detected. For f states a suitable energy range is the soft X-ray regime, since the cross section at these energies is comparatively high. In fig. 2 the density of occupied and unoccupied states is shown for two U - C o compounds, as obtained by X-ray photoemission and Bremsstrahlung Isochromat Spectroscopy (BIS). The part below the Fermi level ( E F ) is dominated by Co 3d states, firstly, because their cross section is high, and secondly, because the Co concentration is high. We note that the U 5f to Co 3d cross section ratio is not as low as the Ce 4f to Co 3d ratio. Comparison to isostructural Th compounds shows
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additional intensity for the U compounds which is to be attributed to U 5f states. Nevertheless, it is still difficult to extract detailed information solely on the basis of spectra of the occupied states. Spectra of the unoccupied states, also shown in fig. 2, are dominated by U 5f states. We know that from cross sections as well as from a comparison to Th compounds, which differ from U compounds with respect to the 5f position and shape. U C o 2 crystallizes in the C15 structure. The U - U distance in this structure is about 3.2 ,~. Applying the concept of Hill [5] we expect a 5f band for U C o 2. A 5f band in U C o 2 might be anticipated to be slightly narrower than in U metal, and possibly shifted upward in energy by a small amount. This can be reconciled with the BI spectrum of U C o 2. UCos. 5 has a rather complicated rhombohedral structure [24], and the U - U distance is probably similar to that in UNis,owhich is larger than the critical value by more than 1 A. Consequently, we expect a localized spectrum for UCo5. 5. The spectrum of a transition to an f4 localized final state should be governed by multiplet splitting, and should show an atomic Coulomb correlation energy characteristic for the localized f state. Multiplets for the 5f states have been calculated [25] for f" to f " - ~ transitions which are observed in photoemission. Making use of the equivalence of electrons and holes we can use the fll to fl0 transition as an indication of what the BI spectrum should look like if the transition is f3 to f4. The overall splitting calculated by Gerken for the fl0 final state is about 4 eV. The calculation was performed for a nuclear charge of 99, whereas U only has a nuclear charge of 92. The scaling of the splitting with
F. U. Hillebrecht et al. / Electronic structure of 5f electron ,2vsterns
132
final state. It is identical to the bandlike spectrum of U C o 2, and clearly must be interpreted in the same way as U C o 2. That means that the spectrum seen in the BIS experiment is caused by a 5f band. The question is how does this 5f band come about? The Hill plot is based on the notion that overlap between 5f wave functions leads to b a n d formation, and above 3.6 A U - U distance this overlap becomes negligible. The only way in which a band can form in this situation is by hybridization with the ligand states. We conclude that in UCos. 5 a 5f band is formed by hybridization with Co 3d states. In princi-
nuclear charge can be inferred from the variation of the splitting parameter with Z , which is also given in ref. [25]. Using this argument we arrive at a value of 4 - 5 eV. Because this procedure relies heavily on calculations which so far could not be compared extensively to experimental values [26,27], we compare the experimental BI spectrum of U O : to the calculated spectrum for the f12 to fll transition. The calculated spectrum is about 5 eV wide, whereas the measured spectrum is about 4 eV wide [17]. The BI spectrum of UCo55 clearly cannot be reconciled with what we expect for a localized
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F.U. Hillebrecht et al. / Electronic structure of 5f electron systems
pie it is more appropriate to speak of a combined U 5 f - C o 3d band, which indicates that above E v there must also be some Co 3d character. The next question is whether there is any truth in the Hill plot at all, or whether 5f band formation does occur in general, even if the U - U distance is large. This does not happen. For a significant mixing between 5f and ligand states two requirements must be fulfilled. Firstly, a high density of ligand states must be present, and secondly, it must be close in energy to the occupied 5f states. We can check on this prediction by looking at a series of compounds where the density of d states shifts away from the Fermi level. In fig. 3 the BI spectra for the quasibinary series of compounds U N i x C u s _ ~ are shown, together with the XPS spectra of the occupied states [20]. The occupied states show clearly the shift of the d band away from the Fermi level with increasing Cu content. In the BI spectra, the 5f band is seen for U N i 5, but diminishes as more and more Cu is added. For UCu 5 we only find a small bump on top of a broad structure. A small amount of oxygen (2 L) quenches this bump completely. The broad structure which is the main contribution in the BI spectrum of U C u 5 is due to a transition into a localized 5f 4 final state. The structure has about the width expected for this transition, 4 eV, and its shape is obviously not due to a single Lorentzian, but contains several lines. Lifetime broadening a n d / o r insufficient resolution do not allow to observe all the details one might expect on the basis of a calculation [25]. This is also true for U O 2 [17]. Finally, we turn to the heavy Fermion superconductor UPt 3 [29,30]. Fig. 4 shows the occupied and unoccupied density of states. Below E v, the main contribution to the spectrum comes from Pt 5d states. There are two features at 0.7 and 3 eV which are not present in ThPt 3 [16]. On this basis we attribute these features to U 5f states. The Bi spectrum consists of a broad structure with two peaks at 1.6 and 2.5 eV above E v. The o 5[
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peak at 1.6 eV is quenched by a small amount of oxygen, as indicated schematically by the dashed line. This spectrum consists mainly of a 5 f 4 localized final state, with a small contribution of the delocalized final state, which accounts for the oxygen sensitive peak at 1.6 eV. The high degree of localization in this compound is caused by the large U - U distance, The mechanism which could lead to a delocalization despite the large U - U distance is not operative here because the density of ligand states is low in the region of the occupied 5f state. The Pt 5d DOS in UPt 3 falls off sharply towards E v which is more obvious in the ThPt 3 spectrum [16,20,28]. Experiments on a number of other heavy fermion systems show that a nearly completely localized f shell is a common property of these materials.
4. Summary We have presented some examples of photoemission and bremsstrahlung isochromat spectra of U compounds and discussed similarities and differences to Ce compounds. Very naively one can anticipate a stronger influence of f-ligand hybridization for U than for Ce. This influence can be seen in core level spectra where the "well-screened peak" [13] is always the dominant one. Also, final states with differing f occupancy are more strongly mixed so that it is not possible to assign a unique configuration to some of them. To fully understand the core level spectra of uranium multiplet splitting has to be incorporated into a theoretical treatment. The unoccupied states as monitored by B1S are dominated by the U 5f states. The spectra show localized as well as delocalized contributions, which can be easily distinguished. Under certain circumstances the 5f states can be delocalized even though one would expect localized states on the basis of the U - U distance alone. The delocalization occurs due to interaction with the extended states of the ligand, and therefore the detailed structure of the ligand states is very important for the properties of the 5f states. It appears that a number of heavy Fermion systems have nearly completely localized f states, or a small f-ligand hybridization. The authors are grateful to M. Campagna for supporting this research.
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Fig. 4. Occupied and unoccupied valence states of the heavy Fermion superconductor UPt 3. The dashed line in the BI spectrum shows the change in the spectrum upon exposure to a small dose of oxygen.
References [1] W.E. Wallace, Rare Earth Intermetallics (Academic Press, New York, 1973).
134
F.U. Hillebrecht et a L / Electronic structure of 5f electron :~vstems
[2] K.A. Gschneidner, Jr. and L.R. Eyring, eds., Handbook on the Physics and Chemistry of the Rare Earths (NorthHolland, Amsterdam, 1978). [3] B. Johansson, H.L. Skriver, N. M~rtensson, O.K. Andersen and O. Gl6tzel, Physica 102B (1980) 12. [4] B. Johansson, J. Magn. Magn. Mat. 47&48 (1985) 231. [5] H.H. Hill, in: Plutonium 1970 and other Actinides, ed. W.N. Miner (AME, New York, 1970) p. 2. [6] M. Campagna, G.K. Wertheim and Y. Bear, in: Photoemission in Solids, vol. II, eds. L. Ley and M. Cardona (Springer, Berlin, 1979) chap. 4. [7] J.C. Fuggle, J. Less Common Metals 93 (1983) 159. [8] F.U. Hillebrecht and J.C. Fuggle, Phys. Rev. B25 (1982) 3550. [9] O. Gunnarsson, K. SchOnhammer, J.C. Fuggle, F.U. Hillebrecht, J.-M. Estava and R.C. Karnatak, Phys. Rev. B28 (1983) 7330. [10] J.C. Fuggle, F.U. Hillebrecht, Z. Zo/tnierek, R. L~sser, O. Gunnarsson and K. Sch6nhammer, Phys. Rev. B27 (1983) 7330. [11] J.C. Fuggle, F.U. Hillebrecht, J.-M. Esteva, R.C. Karnatak, O. Gunnarsson and K. Sch6nhammer, Phys. Rev. B27 (1983) 4637. [12] F.U. Hillebrecht, J.C. Fuggle, G.A. Sawatzky, M. Campagna, O. Gunnarsson and K. SchiSnhammer, Phys. Rev. B30 (1984) 1777. [13] J.C. Fuggle, M. Campagna, Z. Zolnierek, R. Lasser and A. Platau, Phys. Rev. Lett. 45 (1980) 1597. [14] H. Grohs, H. H~3chst, P. Steiner, S. H~fner and K.H.J. Buschow, Solid State Commun. 33 (1980) 573. [15] W.-D. Schneider and C. Laubschat, Phys. Rev. Lett. 46 (1981) 1023. [16] W.-D. Schneider and C. Laubschat, Phys. Rev. B23 (1981) 997.
[17] Y. Baer and J. Schoenes, Solid State Commun. 33 (1980) 885. [18] Y. Baer, H.R. Ott and K. Andres, Solid State Commun. 36 (1980) 387. [19] C. Bonnelle, R.C. Karnatak and J. Sugar, Phys. Rev. A9 (1974) 1920. [20] F.U. Hillebrecht, D.D. Sarma and N. M~.rtensson, to be published. [21] J.F. Herbst and R.E. Watson, Phys. Rev. Lett. 34 (1975) 1395. [22] O. Gunnarsson, K. Sch6nhammer, D.D. Sarma, F.U. Hillebrecht and M. Campagna, Phys. Rev. B (submitted). [23] O. Gunnarsson and K. Sch6nhammer, Phys. Rev. Lett. 50 (1983) 604; Phys. Rev. B29 (1983) 4685. [24] A.W. Derjagin and A.B. Andrejev, Zh. Eksp. Teo. Fiz. 71 (1976) 1166. Quoted by W. Trzebiakowski, in: Ferromagnetic Materials, vol. 1, ed. E.P. Wohlfarth (North-Holland, Amsterdam, 1980) chap. 5. [25] F. Gerken and J. Schmidt-May, J. Phys. F 13 (1983) 1571. [26] B.W. Veal, D.J. Lam, H. Diamond and H.R. Hoekstra, Phys. Rev. B 15 (1977) 2929; this work is on oxides, and the overall splitting may be different from metallic systems. [27] J.R. Naegele, L. Manes. J.C. Spirlet and W. Mialler, Phys. Rev. Lett. 52 (1984) 1834. [28] D.D. Sarma, R.U. Hillebrecht and N. M~.rtensson, to be published. [29] G.R. Stewart, Z. Fisk, J.O. Willis and J.C. Smith, Phys. Rev. Lett. 52 (1984) 679. [30] T.T.M. Palstra, P.H. Kes, J.A. Mydosh, A. de Visser, J.J.M. Franse and A. Menovsky, Phys. Rev. B 30 (1984) 1986.
INVITED
129
PAPER
PHOTOEMISSION AND BREMSSTRAHLUNG 5t' E L E C T R O N SYSTEMS F.U. HILLEBRECHT
*, D . D . S A R M A
ISOCHROMAT
and N. M~,RTENSSON
SPECTROSCOPY
OF
+
lnstitut fftr FestkOrperforschung, KFA J~lich, P.O. Box 1913, 5170 J~lich, Fed. Rep. Germany + Physics Institute, Uppsala Unioersity, Box 530, S-751 21 Uppsala, Sweden
The core levels and valence states of U compounds have been studied using XPS and BIS. The unoccupied valence states give a clear indication of the degree of localization of the 5f states. In general, the influence of f-ligand hybridization is stronger for U compounds than for Ce compounds.
1. Introduction The purpose of this p a p e r is to discuss some aspects of the electronic structure of 5f electron systems as o b t a i n e d from X-ray photoemission a n d inverse p h o t o emission in the soft X-ray regime, which is usually termed Bremsstrahlung Isochromat Spectroscopy. f electrons occur in the rare earth a n d actinide series of the periodic system, a n d play a decisive role mainly for the magnetic behaviour, but also for other properties of these elements and their c o m p o u n d s . In several cases, especially for some rare earth compounds, the magnetic b e h a v i o u r is clearly connected to a fully localized f level exhibiting a well-defined angular m o m e n t u m a n d associated localized magnetic m o m e n t . These m o m e n t s interact with each other via R K K Y coupling or a similar mechanism, leading to a large n u m b e r of ordered structures [1,2]. For actinides the situation is more complicated. It has been deduced from b a n d - s t r u c t u r e calculations that at the beginning of the actinide series the 5f states are delocalized [3,4]. The overlap between n e i g h b o u r i n g 5f wave functions is sufficient for a 5f b a n d to be formed. F o r the heavier actinides the 5f shell is more contracted, a n d the 5f states are localized, similar to the 4f states of rare earths. The transition to localized 5f states occurs between U and A m [3,4]. Consequently, U can be classified as a 5f metal. It has been suggested that in U c o m p o u n d s the 5f states m a y b e c o m e localized, if the separation between n e i g h b o u r i n g U atoms is larger than
* Present address: IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA. 9 3 0 4 - 8 8 5 3 / 8 5 / $ 0 3 . 3 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)
3.4 to 3.6 A [5]. A l t h o u g h it is a very plausible a r g u m e n t to relate the width of the 5f b a n d to the U - U separation, we shall d e m o n s t r a t e that u n d e r certain circumstances the 5f states are delocalized even if the U - U separation is large. Rare earth metals and their c o m p o u n d s are quite often taken as model substances for actinides, a n d the concepts used there are transferred to 5f systems. However, as we have said at the beginning of the actinides series the 5f states are delocalized, whereas the 4f states are - u n d e r normal conditions at least - highly localized, even in Ce. In some cases it h a p p e n s that two different f occupancies are nearly degenerate, and the material is mixed valent. This affects e.g. the magnetic susceptibility and the lattice volume. Photoemission spectra of such materials show the distinct multiplet structure characteristic of the f" final states [6,7]. The intensity ratio observed in the spectra can be used to deduct the average valence in a straightforward manner. T h e loss of m a g n e t i s m in some Ce c o m p o u n d s a n d the smaller volume of n o n - m a g n e t i c Ce ions as c o m p a r e d to the magnetic case was originally attributed to a p r o m o tion of the f state above the Fermi level ( E v L a n d a transfer of the f electron to the c o n d u c t i o n band. This so-called p r o m o t i o n a l model of mixed valence is not able to explain experimental results, e.g. photoemission results. W i t h i n this model one expects to find f related features near the Fermi level in photoemission for nonmagnetic materials. It appears, however, that in all cases a significant part of the emission is always well below E v. Hybridization between the 4f a n d conduction states plays a decisive role here [8-12]. If hybridization is i m p o r t a n t for Ce, it should be m u c h more i m p o r t a n t for U c o m p o u n d s because of the
130
F. U. Hillebrecht et al. / Electronic structure of 5f electron systems
larger 5f radius. We expect therefore to find a stronger tendency towards delocalization in those U c o m p o u n d s whose Ce analogs showed signs of a delocalized contribution. These were n o n - m a g n e t i c c o m p o u n d s like CeNi 5 [12]. A l t h o u g h we will make extensive use of the Ce results, this is not the place to repeat the discussion. Instead we present recent results on U c o m p o u n d s and refer to review articles or the original works where necessary.
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For Ce c o m p o u n d s it has proved very revealing to analyze core level spectra [8 11,13]. Especially X-ray photoemission and absorption of the 3d levels indicated the presence of f 0 fl a n d f2 configurations in the final state. The intensity of the various final states differs d e p e n d i n g on what kind of experiment one does, and also does not agree with estimates of average f occupancy derived from e.g. lattice c o n s t a n t measurements. This led to the conclusion that hybridization affects the weights of the final states [9]. For U comp o u n d s core level spectroscopy should also provide relevant information [14-18]. If the 5f states are bandlike, we expect a fairly simple spectrum, similar to core level spectra of transition metals. If, however, they are localized, we expect to find some signs of m u h i p l e t splitting, provided the splitting is large e'nough. Furthermore, in analogy to Ce compounds, one may expect to find final states corresponding to different f occupancies [8-10,13]. The core level spectra of U c o m p o u n d s show pronounced variations as is illustrated in fig. 1 for the U 4f levels in UCo5. 5 and UCu s. The spectrum of the first c o m p o u n d looks at first sight rather simple: there are two sharp lines, split by the spin orbit interaction. M u h i p l e t splitting seems to be smaller than for the rare earth 3d levels [10,19]. U C u 5 clearly shows additional structure [14], but - again in contrast to rare earths only at higher binding energies. To obtain a clearer picture of the size and shape of the satellite c o n t r i b u t i o n we fitted the main lines with two D o n i a c h - S u n j i c profiles convoluted with Lorentzian and G a u s s i a n curves to simulate lifetime b r o a d e n i n g and experimental resolution. An integral b a c k g r o u n d was also included. After o b t a i n i n g a close agreement between calculated and experimental spectrum in the region of the main lines the calculated spectrum was subtracted leaving b e h i n d the satellite spectrum shown in the b o t t o m part of fig. l. We note that both satellites are similar in shape, a n d the intensity ratio is similar to that for the main lines.
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Fig. 1. Uranium 4f core level spectra excited with monochromatized AI K s radiation for UCo55 and UCu 5. Also shown are the satellite contributions which have been determined by subtracting a background and fitting the main lines with Doniach-Sunjic profiles with Lorentzian and Gaussian broadening to simulate finite lifetime and resolution. Performing the same procedure for UCo5 s we find that the spectrum still contains a small satellite contribution. Its shape is similar to that of the UCu s satellites, but its intensity is much smaller. It appears that spectra of m a n y other c o m p o u n d s [14] are intermediate between these two prototypes. An additional effect which can be seen e.g. for UPt 3 [20] is a very large asymmetry of the main line which is presently not fully understood. We note that the " m a i n line" i.e. the d o m i n a n t c o n t r i b u t i o n is always the one at the lowest excitation energy. In Ce the main line is not the one with the lowest excitation energy. The 4f binding energy for the main line of the c o m p o u n d s is in m a n y cases similar to that for U metal, or it is shifted by a certain a m o u n t similar to the 4f BE shift found for isostructural Th compounds. This means that the final state associated with this line is the same in all cases. In U metal this state certainly has an f4 local configuration, and we assign the same state to the main lines in the compounds. The core level spectra tell us that in general the coupling between 5f and extended states is sufficient to ensure in all cases that the d o m i n a n t screening channel is screened by an f electron. In rare earths this was not the case, a n d the decrease of the well screened peak with increasing Z can be correlated with the shrinking of the 4f shell [8]. As a next step in the interpretation of the U core level spectra one can propose that the additional structure seen in U C u 5 is due to f3 and f4 configurations, in analogy to the fl a n d f0 configurations seen in Ce
F.U. Hillebrecht et al. / Electronic structure of 5f electron systems
spectra. However, as we have noted above, in UCos. 5 there still is a remnant of both features. If we were to interpret the satellite contribution in the spectra in terms of f2 and f3 configurations, we would expect the f2 contribution to be smallest. Obviously, the f3 contribution is very small in UCos. 5, and so it is astonishing to find any f 2 at all. This interpretation also yields an estimate for the 5f intra shell Coulomb interaction U. From the spectrum we find the feature which would be assigned to f2 at 6.8 eV above the main line, and the f3 feature at 3.2 eV. For the fa_f3 separation we get U f c - 3 U , and for the f3_f2 separation Ufc - 2U. Ufc is the Coulomb interaction between the core hole and the 5f electrons. This results in U = 0.6 eV. Herbst and Watson [21] calculated U = 1.8-2.5 eV. The simple interpretation of the satellites cannot account for the peak separations found in the spectrum. It is possible that the small value of U which comes about through the position of the main line indicafes that this particular final state is not an atomic 5f 4 configuration. The fixed shape of the satellite spectrum leads us to suggest that one should think of one satellite spectrum containing both f2 and f3 contributions, which are strongly mixed. This is supported by results for Th compounds [22] which show clearly that the Coulomb interactions in actinides are such that the configurations mix much more strongly than for rare earth materials. To understand the core level spectra properly it is necessary to incorporate multiplet and crystal field splitting into the theory of Gunnarsson and Sch6nhammer [9,23].
3. Valence band spectra We now turn to a discussion of the valence states. The occupied valence states can be probed by photoemission, and the unoccupied states by inverse photoemission. In this experiment the sample is irradiated with electrons and the photons emitted are detected. For f states a suitable energy range is the soft X-ray regime, since the cross section at these energies is comparatively high. In fig. 2 the density of occupied and unoccupied states is shown for two U - C o compounds, as obtained by X-ray photoemission and Bremsstrahlung Isochromat Spectroscopy (BIS). The part below the Fermi level ( E F ) is dominated by Co 3d states, firstly, because their cross section is high, and secondly, because the Co concentration is high. We note that the U 5f to Co 3d cross section ratio is not as low as the Ce 4f to Co 3d ratio. Comparison to isostructural Th compounds shows
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additional intensity for the U compounds which is to be attributed to U 5f states. Nevertheless, it is still difficult to extract detailed information solely on the basis of spectra of the occupied states. Spectra of the unoccupied states, also shown in fig. 2, are dominated by U 5f states. We know that from cross sections as well as from a comparison to Th compounds, which differ from U compounds with respect to the 5f position and shape. U C o 2 crystallizes in the C15 structure. The U - U distance in this structure is about 3.2 ,~. Applying the concept of Hill [5] we expect a 5f band for U C o 2. A 5f band in U C o 2 might be anticipated to be slightly narrower than in U metal, and possibly shifted upward in energy by a small amount. This can be reconciled with the BI spectrum of U C o 2. UCos. 5 has a rather complicated rhombohedral structure [24], and the U - U distance is probably similar to that in UNis,owhich is larger than the critical value by more than 1 A. Consequently, we expect a localized spectrum for UCo5. 5. The spectrum of a transition to an f4 localized final state should be governed by multiplet splitting, and should show an atomic Coulomb correlation energy characteristic for the localized f state. Multiplets for the 5f states have been calculated [25] for f" to f " - ~ transitions which are observed in photoemission. Making use of the equivalence of electrons and holes we can use the fll to fl0 transition as an indication of what the BI spectrum should look like if the transition is f3 to f4. The overall splitting calculated by Gerken for the fl0 final state is about 4 eV. The calculation was performed for a nuclear charge of 99, whereas U only has a nuclear charge of 92. The scaling of the splitting with
F. U. Hillebrecht et al. / Electronic structure of 5f electron ,2vsterns
132
final state. It is identical to the bandlike spectrum of U C o 2, and clearly must be interpreted in the same way as U C o 2. That means that the spectrum seen in the BIS experiment is caused by a 5f band. The question is how does this 5f band come about? The Hill plot is based on the notion that overlap between 5f wave functions leads to b a n d formation, and above 3.6 A U - U distance this overlap becomes negligible. The only way in which a band can form in this situation is by hybridization with the ligand states. We conclude that in UCos. 5 a 5f band is formed by hybridization with Co 3d states. In princi-
nuclear charge can be inferred from the variation of the splitting parameter with Z , which is also given in ref. [25]. Using this argument we arrive at a value of 4 - 5 eV. Because this procedure relies heavily on calculations which so far could not be compared extensively to experimental values [26,27], we compare the experimental BI spectrum of U O : to the calculated spectrum for the f12 to fll transition. The calculated spectrum is about 5 eV wide, whereas the measured spectrum is about 4 eV wide [17]. The BI spectrum of UCo55 clearly cannot be reconciled with what we expect for a localized
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F.U. Hillebrecht et al. / Electronic structure of 5f electron systems
pie it is more appropriate to speak of a combined U 5 f - C o 3d band, which indicates that above E v there must also be some Co 3d character. The next question is whether there is any truth in the Hill plot at all, or whether 5f band formation does occur in general, even if the U - U distance is large. This does not happen. For a significant mixing between 5f and ligand states two requirements must be fulfilled. Firstly, a high density of ligand states must be present, and secondly, it must be close in energy to the occupied 5f states. We can check on this prediction by looking at a series of compounds where the density of d states shifts away from the Fermi level. In fig. 3 the BI spectra for the quasibinary series of compounds U N i x C u s _ ~ are shown, together with the XPS spectra of the occupied states [20]. The occupied states show clearly the shift of the d band away from the Fermi level with increasing Cu content. In the BI spectra, the 5f band is seen for U N i 5, but diminishes as more and more Cu is added. For UCu 5 we only find a small bump on top of a broad structure. A small amount of oxygen (2 L) quenches this bump completely. The broad structure which is the main contribution in the BI spectrum of U C u 5 is due to a transition into a localized 5f 4 final state. The structure has about the width expected for this transition, 4 eV, and its shape is obviously not due to a single Lorentzian, but contains several lines. Lifetime broadening a n d / o r insufficient resolution do not allow to observe all the details one might expect on the basis of a calculation [25]. This is also true for U O 2 [17]. Finally, we turn to the heavy Fermion superconductor UPt 3 [29,30]. Fig. 4 shows the occupied and unoccupied density of states. Below E v, the main contribution to the spectrum comes from Pt 5d states. There are two features at 0.7 and 3 eV which are not present in ThPt 3 [16]. On this basis we attribute these features to U 5f states. The Bi spectrum consists of a broad structure with two peaks at 1.6 and 2.5 eV above E v. The o 5[
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peak at 1.6 eV is quenched by a small amount of oxygen, as indicated schematically by the dashed line. This spectrum consists mainly of a 5 f 4 localized final state, with a small contribution of the delocalized final state, which accounts for the oxygen sensitive peak at 1.6 eV. The high degree of localization in this compound is caused by the large U - U distance, The mechanism which could lead to a delocalization despite the large U - U distance is not operative here because the density of ligand states is low in the region of the occupied 5f state. The Pt 5d DOS in UPt 3 falls off sharply towards E v which is more obvious in the ThPt 3 spectrum [16,20,28]. Experiments on a number of other heavy fermion systems show that a nearly completely localized f shell is a common property of these materials.
4. Summary We have presented some examples of photoemission and bremsstrahlung isochromat spectra of U compounds and discussed similarities and differences to Ce compounds. Very naively one can anticipate a stronger influence of f-ligand hybridization for U than for Ce. This influence can be seen in core level spectra where the "well-screened peak" [13] is always the dominant one. Also, final states with differing f occupancy are more strongly mixed so that it is not possible to assign a unique configuration to some of them. To fully understand the core level spectra of uranium multiplet splitting has to be incorporated into a theoretical treatment. The unoccupied states as monitored by B1S are dominated by the U 5f states. The spectra show localized as well as delocalized contributions, which can be easily distinguished. Under certain circumstances the 5f states can be delocalized even though one would expect localized states on the basis of the U - U distance alone. The delocalization occurs due to interaction with the extended states of the ligand, and therefore the detailed structure of the ligand states is very important for the properties of the 5f states. It appears that a number of heavy Fermion systems have nearly completely localized f states, or a small f-ligand hybridization. The authors are grateful to M. Campagna for supporting this research.
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References [1] W.E. Wallace, Rare Earth Intermetallics (Academic Press, New York, 1973).
134
F.U. Hillebrecht et a L / Electronic structure of 5f electron :~vstems
[2] K.A. Gschneidner, Jr. and L.R. Eyring, eds., Handbook on the Physics and Chemistry of the Rare Earths (NorthHolland, Amsterdam, 1978). [3] B. Johansson, H.L. Skriver, N. M~rtensson, O.K. Andersen and O. Gl6tzel, Physica 102B (1980) 12. [4] B. Johansson, J. Magn. Magn. Mat. 47&48 (1985) 231. [5] H.H. Hill, in: Plutonium 1970 and other Actinides, ed. W.N. Miner (AME, New York, 1970) p. 2. [6] M. Campagna, G.K. Wertheim and Y. Bear, in: Photoemission in Solids, vol. II, eds. L. Ley and M. Cardona (Springer, Berlin, 1979) chap. 4. [7] J.C. Fuggle, J. Less Common Metals 93 (1983) 159. [8] F.U. Hillebrecht and J.C. Fuggle, Phys. Rev. B25 (1982) 3550. [9] O. Gunnarsson, K. SchOnhammer, J.C. Fuggle, F.U. Hillebrecht, J.-M. Estava and R.C. Karnatak, Phys. Rev. B28 (1983) 7330. [10] J.C. Fuggle, F.U. Hillebrecht, Z. Zo/tnierek, R. L~sser, O. Gunnarsson and K. Sch6nhammer, Phys. Rev. B27 (1983) 7330. [11] J.C. Fuggle, F.U. Hillebrecht, J.-M. Esteva, R.C. Karnatak, O. Gunnarsson and K. Sch6nhammer, Phys. Rev. B27 (1983) 4637. [12] F.U. Hillebrecht, J.C. Fuggle, G.A. Sawatzky, M. Campagna, O. Gunnarsson and K. SchiSnhammer, Phys. Rev. B30 (1984) 1777. [13] J.C. Fuggle, M. Campagna, Z. Zolnierek, R. Lasser and A. Platau, Phys. Rev. Lett. 45 (1980) 1597. [14] H. Grohs, H. H~3chst, P. Steiner, S. H~fner and K.H.J. Buschow, Solid State Commun. 33 (1980) 573. [15] W.-D. Schneider and C. Laubschat, Phys. Rev. Lett. 46 (1981) 1023. [16] W.-D. Schneider and C. Laubschat, Phys. Rev. B23 (1981) 997.
[17] Y. Baer and J. Schoenes, Solid State Commun. 33 (1980) 885. [18] Y. Baer, H.R. Ott and K. Andres, Solid State Commun. 36 (1980) 387. [19] C. Bonnelle, R.C. Karnatak and J. Sugar, Phys. Rev. A9 (1974) 1920. [20] F.U. Hillebrecht, D.D. Sarma and N. M~.rtensson, to be published. [21] J.F. Herbst and R.E. Watson, Phys. Rev. Lett. 34 (1975) 1395. [22] O. Gunnarsson, K. Sch6nhammer, D.D. Sarma, F.U. Hillebrecht and M. Campagna, Phys. Rev. B (submitted). [23] O. Gunnarsson and K. Sch6nhammer, Phys. Rev. Lett. 50 (1983) 604; Phys. Rev. B29 (1983) 4685. [24] A.W. Derjagin and A.B. Andrejev, Zh. Eksp. Teo. Fiz. 71 (1976) 1166. Quoted by W. Trzebiakowski, in: Ferromagnetic Materials, vol. 1, ed. E.P. Wohlfarth (North-Holland, Amsterdam, 1980) chap. 5. [25] F. Gerken and J. Schmidt-May, J. Phys. F 13 (1983) 1571. [26] B.W. Veal, D.J. Lam, H. Diamond and H.R. Hoekstra, Phys. Rev. B 15 (1977) 2929; this work is on oxides, and the overall splitting may be different from metallic systems. [27] J.R. Naegele, L. Manes. J.C. Spirlet and W. Mialler, Phys. Rev. Lett. 52 (1984) 1834. [28] D.D. Sarma, R.U. Hillebrecht and N. M~.rtensson, to be published. [29] G.R. Stewart, Z. Fisk, J.O. Willis and J.C. Smith, Phys. Rev. Lett. 52 (1984) 679. [30] T.T.M. Palstra, P.H. Kes, J.A. Mydosh, A. de Visser, J.J.M. Franse and A. Menovsky, Phys. Rev. B 30 (1984) 1986.