Neutron and synchrotron X-ray scattering experiments on actinides

PHYSICA[

Physica B 186-188 (1993) 664-669 North-Holland

Neutron and synchrotron X-ray scattering experiments on actinides G.H. Lander Commission o f the European Communities, JRC, Institute for Transuranium Elements, Karlsruhe, Germany

The proximity of the 5f bands to E v in U, Np and Pu has the consequence that hybridization between the 5f and conduction electron states usually occurs in metallic compounds containing these elements. Neutron experiments with polarized neutrons have been successful in measuring the ratio of the orbital to spin moments at the actinide site in compounds such as UFe2, NpCo2 and PuF%, and this is found to be a sensitive measure of the hybridization. Anisotropic effects are found in the hexagonal system URhAI. A new technique measuring magnetic X-ray scattering with the energy tuned to the M~v and Mv resonances at a synchrotron source is particularly well adapted for studies of the actinides. Experiments on U and Np compounds are discussed.

1. Introduction

The large range of physical properties found in actinide (5f) systems has its origins in the special nature of the 5f electrons and their tendency to behave either as itinerant or localized electrons, depending on the nature of the ground-state wavefunction in a particular compound. Examples of unusual behavior start with uranium metal itself, which exhibits a chargedensity wave and superconductivity [1,2]. The majority of ionic compounds, e.g. UO 2, UF4, Pu203, can be thought of as localized with a certain number of 5f electrons acted upon by a (strong) crystal field (CF) interaction. The resulting crystal field parameters, and their comparison with isostructural and isoelectronic lanthanides, have been an active field for both optical [3] and neutron spectroscopy [4]. Despite some interesting questions raised by covalency, I shall not discuss this part of actinide research, but concentrate instead on metallic systems. It is in these that correlatedelectron behavior in its facets is found. The heavy fermions UPt 3, UBex3, URu2Si2 and U2Zn,7 are fascinating materials. At high temperature they show Curie-Weiss behavior and effective moments close to those expected for U 3+. At low temperature a correlated-electron system exists that suppresses the magnetism and gives rise to superconductivity. This extraordinary phenomenon is still not unCorrespondence to: G.H. Lander, Commission of the European Communities, JRC, Institute for Transuranium Elements, Postfach 23-40, 7500 Karlsruhe, Germany.

derstood and, quite rightly, is the subject of much research. Some interesting questions that are seldom asked are, for example, what is the ground-state wavefunction in UPt 3 even at high temperatures? and what role, if any, do the 5d electrons associated with Pt play? What gives rise to the anisotropy in the susceptibility in UPt3? And what, if any role do CF interactions play? I shall not address these questions directly, enough already is written about the heavy fermions in these proceedings. Instead I shall focus on other actinide compounds that exhibit their own unusual properties. The point of this is twofold; first, to illustrate that 5f electrons exhibit characteristics of both itinerant and localized behavior and, second to help place the heavy fermions in the context of the large effort in actinide research.

2. Orbital moments in itinerant 5f systems

In almost all lanthanide (4f) intermetallic compounds the CF interaction plays the major role in defining the magnetic properties. There are exceptions, of course; the biggest group being the Ce-based materials that exhibit heavy-fermion (e.g. CeCu6) or Kondo-like (e.g. CeAI~) behavior. If we consider the lanthanide compounds with the strongly magnetic 3d elements, the 3d electrons are itinerant and interact with the lanthanide 5d electrons, which are also itinerant, but the lanthanide 4f electrons are strictly localized [5]. Again Ce compounds, such as CeFe 2, are an

0921-4526/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

G.H. Lander / X-ray scattering experiments on actinides

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exception. The situation is quite different in the analogous actinide compounds. The 5f electrons in these are itinerant as well as the 3d electrons at the transition metal site. In the A n F e 2 compounds, where A n is an actinide (in this case U, Np, Pu or A m ) band structure calculations using the local density approximation, and including orbital polarization terms, show that the 5f electrons are really itinerant in as much as they hybridize with the 3d Fe electrons [6]. O n e signature of this hybridization is a reduction in the value of the orbital c o m p o n e n t P-L of the 5f electrons as compared to the free-ion value. A convenient measure is the ratio ~L/~S, where P-s is the spin component. T o determine the spin and orbital components individually we have used polarized neutrons to measure the spatial dependence of the magnetization. In those cases, such as the light actinides in which ~ and P-s are opposed to each other, the individual components may be determined by analyzing the shape of the magnetic form factor. A more direct m e t h o d involving X-rays (see below) is expected to become available with the new-generation synchrotron sources. The neutron m e t h o d is illustrated by the magnetic form factors [7] of U F e 2 and PuFe 2 shown in fig. 1. The

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Fig. 1. (a) Magnetic form factor for the U ion in U F e 2 a s a function of sin 0/A. The strong depression of the scattering at low angles is due to the cancellation of the ~t and ~s components to the total moment. The lines through the data represent vfirious fits. (b) Similar data for PuFe2. Here the cancellation of I~L and ~s is less complete than in the case of UFe 2. The dashed line is a fit to the data in PuSb, which has ~L/~S as expected from free-ion theory (see ref. [7] for more details and original references).

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666

G.H. Lander / X-ray scattering experiments on actinides

almost complete cancellation of /xL and /xs that happens in UFe 2 leaves a small amount of scattering from the more contracted orbital magnetization and this gives a maximum at sin 0/A -~ 0.3/~ i characteristic of a (j2) function. These form factors are most unusual; a typical one is a monotonically decreasing function of sin 0/A. We summarize this aspect of the work by plotting --/ZL//Zs versus the number of 5f electrons in fig. 2. The dashed line passes through the free-ion values. All lanthanide systems would lie on this line, provided the ground-state contains no contribution from excited-state J multiples. Within a single J multiplet, whatever the CF ground state, the ratio of/XL//Xs is the same and can be related directly to the Land6 gfactor: Ixu tz s

1 - g/2 g-

1

(1)

Many actinide compounds also fall on this line, but the itinerant magnets UFe 2, UNi 2, NpCo 2, PuFe 2 and AmFe 2 do not. In all cases k~ is reduced in magnitude because of the interaction between the actinide 5f electron and the transition metal 3d electrons [8]. A similar situation [9] exists for CeFe 2, although no measurements have been reported.

3. Anisotropic susceptibilities These studies have now been extended to the 1 : 1 : 1 intermetallic compound URhA1 [10]. A reduction in ~L/tz s is observed, but, equally interesting, is the observation of a large induced susceptibility at the Rh l site in the structure. The latter consists of alternate planes of U and Rh~ and Rh H and A1 stacked along the c-axis of the hexagonal structure. Although the U-Rh~ and U-RhII distances are essentially the same ( U - R h n is actually the shorter), the hybridization occurs completely within the U-Rh~ plane, i.e. in the plane perpendicular to the c-axis. This leads to a strongly enhanced susceptibility along the c-axis. An identical effect has been found in paramagnetic URuAI. These measurements have therefore given us a microscopic understanding of one of the unusual physical p r o p e r t i e s - t h e highly anisotropic suspectibility. The latter extends to very high fields; this is not surprising as it is a property of the ground-state wavefunction hybridization, rather than of a conventional CF interaction. Similar anisotropies exist in the susceptibility of UPt3, but form factor data of sufficient accuracy to determine whether there is hybridization of the 5f and Pt 5d electrons do not exist [11].

4. Magnetic X-ray scattering Neutron scattering has, and will continue to be, the single most important scattering probe in the study of the magnetism of the actinides. However, magnetic X-ray scattering is now becoming a complementary tool of considerable promise. There is not space to discuss this interaction in detail; I simply refer to some relevant papers [12]. Of particular importance is the presence of a strong resonant term [13-15] when the energy is tuned to the M~v and M v absorption energies in the actinides. By chance, these edges are in a range 3.5-4 keV in which scattering experiments can take place (for photons E = 12.4/A where E is in keV, A in ,~). Similar strong (dipolar) resonances in the 3d and 4f series lie in the energy range 0.5-1.5 keV and can be accessed only by reflection or the use of multilayer structures. Absorption measurements (at Q = 0, where Q is the momentum transfer) may use all these resonances and give rise to magnetic circular dichroism [16]. 4. I. Investigating the resonant scattering

In the short time since the first observation of resonant magnetic scattering in actinides [15], a number of experiments have been performed. First, there is the question of what we can learn from the resonance itself [17]. In fig. 3 we show the variation of intensity with energy as measured from single crystals of USb and NpAs. The solid line is a fit using two resonances, one at each absorption edge. The shift in energy between USb and NpAs signifies the one extra nuclear charge in going from U to Np. These resonances are then element specific and may be used to investigate random alloys in a way impossible with neutrons. Other features of the resonance are their width and intensity. So far the width appears similar to the experimental resolution ( - 5 eV); improvement of the resolution may give information on exchange processes and core-hole lifetimes. The ratio of the M W to the M~v resonant amplitudes is called the branching ratio and contains information on the electronic structure [17]. Although it is not easy to see from the logarithmic intensity scale in fig. 3, the branching ratio of NpAs is less (3.0 compared with 3.5) than that for USb, This reflects the 5f 4 state thought to exist in NpAs as compared to 5f 3 in USb. Both actinide ions are essentially trivalent. 4.2.

Using the resonant scattering

At the MIV r e s o n a n c e (fig. 3) the scattering is extremely intense. For example, despite considerable

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Fig. 3. Intensity of magnetic X-ray scattering as a function of energy from single crystals of USb (top) and NpAs (lower). The resonances correspond to those at the Mv and Mw edges. The solid lines are fits with two resonances located at the absorption edges and Lorentzian in form. Note the logarithmic intensity scale.

absorption through ~1.5 mm total of Be, the magnetic intensity from a small 12mg 'flake' of NpAs was >30,000 cts/s at resonance at the X22C (bending magnet) beamline at the NSLS, Brookhaven National Laboratory. Such intensities allow us to examine details of the magnetic structure, to examine the critical scattering above TN with the greater wavevector resolution available at a synchrotron source, and consider the possibility of detecting surface diffraction from antiferromagnets. All these are being activity explored at the Brookhaven synchrotron at the moment. Magnetic structure and magnetoelastic effects are an important aspect of characterizing actinide (and heavy-fermion) systems. The most notable example of progress in understanding magnetic structure with Xrays has been the study of holmium [18]. A good example of the power of the X-ray technique in the actinides is the study of URu2Si 2 by resonant scattering [19]. The authors were able to show that the 'ordered' state below T N was, in fact, not completely long-range ordered in the sense of the underlying atomic structure, but instead consisted of moments with a correlation length of --500 A. The absence of true long-range order has also recently been found in a study [20] of the complex magnetic phases present in the pseudobinary com-

pound U0.85Th0.15Sb. One of the scans at low temperature is shown in fig. 4 along the (00L) line in reciprocal space. The similar scan above T N (=200 K) is shown for comparison. The narrowness of the peaks is a consequence of the excellent wavevector resolution. New peaks corresponding to modulations of wavevector q = 1/4 and 1/2 are visible. Peaks arising from higher-order contamination, i.e. A/3 from the (008) at 8/3 may readily be identified by their T and E dependence. A further method available without too much difficulty is polarisation analysis. Combined with neutron and magnetization studies, the work on Uo.ssTholsSb was able to show a higher level of complexity in the magnetic structure than previously realized. In particular, the moments are modulated even at lower temperature. Such a modulation has been discussed in considerable detail, for example, in connection with CeAI2, and is thought to arise from a competition between the localized and conduction electrons, i.e. a manifestation of the Kondo effect. The most recent work on CeAI 2 proposes equal moments on each site [21], but transport measurements in the U S b - T h S b solid solutions have been interpreted as evidence for large Kondo effects [22]. Before turning to the lattice behavior it is important to stress that these X-ray measurements probe the

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the (00L) reciprocal lattice line from a single crystal of U0.ssTh015Sb: (a) at 220 K, above Try, (b) at 15 K. A number of additional peaks at the half and quarter integral values are evident in the lower plot. Note the logarithmic intensity scale (from ref. [20]).

668

G.H. Lander / X-ray scattering experiments on actinides

near-surface region only. For example, at resonance (3.73keV) the absorption coefficient for U is -25,000era -j. Recalling that the reduction of the beam goes as exp(-/~t), where t is the thickness, one can see that for reflection (in which the beam has to go both in and out of the material) the penetration depth does not exceed -2000 A,. The surface sensitivity of X-ray scattering in the study of magnetic effects has already been noted in connection with ordering effects in random-field systems [23], and we anticipate that differences between neutron and X-ray results may be due to the different length scales probed. This has become of particular concern in the study of critical phenomena, in which correlations rather than long-range order are studied. Coupling to the lattice is also important in magnetic studies and can be observed with X-rays by examining the charge peaks. Although the resolution exhibited in fig. 4 is already good, it can be improved with 8 keV X-rays and an analyzer. In an accompanying experiment [20] on the (U, Th)Sb system the results of transverse scans of the (002) and (004) reflections are shown as a function of temperature in fig. 5. At --155 K the material develops a ferromagnetic component, which results in a rhombohedral distortion. However, the (00L) d-planes abruptly change their value at this temperature, but, as expected do not split into more than one value. Longitudinal scans along the (00L) reciprocal lattice line (i.e. as in fig. 4) confirm that the width of the charge peaks Ad does

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not change with temperature. We find A d / d = 6 x 10 4 at all temperatures, a value close to the instrumental resolution. On the other hand, there is clearly a large increase in both the (002) and (004) transverse widths at the onset of the ferromagnetic component. Why? Arguments about strain can be advanced, but we should then expect the increase to be independent of the diffracting order. Instead, we believe strain is being produced by a re-orientation of the mosaic blocks at the surface because of the rhombohedral distortion. Because the photons penetrate less with the (002) than the (004) reflection, the former is more sensitive to the 'surface' strains. We can anticipate more studies of this sort that characterize the magnetic structure and its interaction with the lattice.

5. S u m m a r y

I have tried in this short paper to summarize some of the neutron experiments performed over the last three years (since Santa Fe in 1989) on actinide compounds which are not heavy fermions, but are nonetheless of considerable interest. I have briefly discussed the new technique of resonant X-ray magnetic scattering, which is complementary to neutron scattering, and which I expect to play an increasing role in the study of heavy fermions and actinides in general. One serious omission has been the lack of any discussion of neutron inelastic scattering. This activity is a difficult one as interest has turned to S(Q, w) within a particular Brillouin zone, i.e. as a function of the reduced wavevector q, rather than the total momentum transfer Q. Such studies, as reported, for example, in UPt 3 [24] and URuzSi 2 [25] demand single crystals and they are often difficult to make of sufficient size. On the other hand, the information content of these studies is considerable. We are now trying to perform such studies on systems such as UFe 2 (see section 2 above) but have so far failed to find any evidence for collective excitations despite efforts at both the Institute Laue-Langevin and Brookhaven National Laboratory. The thought is beginning to occur to us that the hybridization 'washes out' all the collective excitations, a frustrating possibility for the experimentalist! The neutron experiments described here were performed at RisO National Laboratory, Denmark; the ILL in Grenoble, and Saclay (Paris). The X-ray experiments were all performed at the NSLS, Brookhaven. The help of the Radioprotection staff in handling transuranium samples at these institutes is

G.H. Lander / X-ray scattering experiments on actinides

gratefully acknowledged. Many colleagues have contributed to the work described here. In particular I should like to thank Michael Wulff, Bente Lebech, Jane Brown, Jos6-Antonio Paix~o, Alain Delapalme, and Mike Brooks and Borje Johansson for theory in the work described in sections 2 and 3. Bill Stirling, Chiu Tang, Sean Langridge, D o o n Gibbs, and Paola Carra (theory) have been involved with me in the X-ray scattering. I should like to dedicate this article to my 'boss' and colleague Jean Fuger on his sixtieth birthday and in recognition of his (sometimes frustrating) efforts to follow my movements!

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