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X-rays and neutrons as complementary probes to muons in magnetism: A view from reciprocal space
Physica B 289}290 (2000) 1}9
X-rays and neutrons as complementary probes to muons in magnetism: A view from reciprocal space G.H. Lander* European Commission, JRC, Institute for Transuranium Elements, Postfach 2340, 76125 Karlsruhe, Germany
Abstract Twenty years ago magnetism and superconductivity appeared mutually exclusive and life was (relatively) simple. The discovery of heavy-fermion superconductivity (1979}1984) and high ¹ (1986), changed our perceptions. Gradually, it was realised that either ordered magnetism or magnetic correlations are found in most of these materials. Here I shall concentrate on heavy fermions, in which the f electrons are responsible for the magnetism as well as (probably) the superconductivity. Muons have played a key role in elucidating these the so-called `small momenta systems, such as UPt , URu Si , UPd Al , etc. Recenty, at the ILL we have measured the low-energy inelastic magnetic signal from UPd Al and the response will be compared to the conclusions derived from muon studies. Interestingly, it is accepted wisdom that muons will be sensitive to any small magnetic e!ects. UBe is fascinating as it has long been the `exceptiona, with no sign of any magnetism. Now, at Ris+ National Laboratory, we have found evidence with neutrons for weak magnetic correlations of a most unusual form in UBe } so that it no longer can be regarded as an exception. Neutrons, powerful though they are, are sometimes lost in reciprocal space. U Pt In is a non-Fermi liquid, and there is a strong muon anomaly below 10 K, but we have been unable to "nd the correlations with neutrons. Finally, NpO is one of the oldest `small-moment systemsa, and recently muons were able to see an asymmetry below 25 K, and suggested an ordered moment of 0.1l . However, the signal has been too small for neutrons. Here I will explain the emergence of a new technique, resonant magnetic X-ray scattering, that, especially in the actinides, has great promise. We have used this at the ESRF to determine the magnetic structure of NpO . 2000 Elsevier Science B.V. All rights reserved. Keywords: Heavy Fermions; Neutron scattering; Actinides
1. Introduction Since the discovery of heavy-fermion (HF) superconductors, exactly 20 years ago, by Frank Steglich and his colleagues, there has been an important change in our concept of the connection between magnetism and superconductivity. Originally
* Tel.: #49-7247-951-441; fax: #49-7247-951-599. E-mail address: [email protected] (G.H. Lander).
thought to be mutually exclusive, it is now realised that these two phenomena may co-exist and there is even a substantial body of work suggesting that antiferromagnetism (AF), either ordered or #uctuating, may provide the driving potential for unconventional (i.e. non s-state) superconductivity. Of course, the majority of both experimental and theoretical work has centered on high-¹ materials since if ¹ can be raised substantially above the present record of &130 K the dream of room temperature superconductivity may be reached.
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 2 3 1 - 3
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G.H. Lander / Physica B 289}290 (2000) 1}9
Unfortunately, making wires out of ceramics has proved technically frustrating and 13 years after high ¹ was discovered applications remain disap pointing } still hope persists. What has happened in heavy-fermion materials is that the superconductivity has been shown beyond all reasonable doubt to be non-s-state, and the magnetism, at least the ordered component of it, has been shown to involve very small moments. The discovery of these small moments has been one of the great successes of muon spectroscopy. Understanding why these moments are so small ((0.1l ) is still a problem. In terms of band structure we do know Ni has an ordered moment of 0.6l , but it seems hard to understand why the energy gain of stabilising moments an order of magnitude smaller would be so important, even though the ordering temperatures are so small. Table 1 gives the compounds that are HF-superconductors and some of their properties as we now understand them. Muons are, of course, a local probe. The information from such experiments actually does contain information on both the static and dynamic aspects of the magnetism, but it is di$cult to disentangle. The most general probe is neutron scattering, but there are severe disadvantages to this technique. First, intensities are low so that large samples are required. Second, for moments (0.5l it is virtually impossible to use polycrystalline samples. In contrast, all the early important muon experiments were performed on such sam-
Table 1 Heavy fermion superconductors showing the symmetry of the unit cell, the Sommerfeld coe$cient c (units of mJ/mol/K), the NeH el temperature, the superconducting transition temperature ¹ , and the ordered antiferromagnetic moment in Bohr mag netons per uranium or cerium
CeCu Si UBe UPt URu Si UPd Al UNi Al
Structure
c (mJ)
¹ (K) ,
¹ (K)
k
Tetragonal Cubic Hexagonal Tetragonal Hexagonal Hexagonal
1100 1100 450 180 150 120
&1 * 5.0 17.5 14.5 4.4
0.70 0.90 0.55 1.2 1.8 1.0
0.1 * 0.03 0.02 0.85 0.12
ples. So large crystals have to be available for neutrons, by large we mean volumes of '0.3 cm to observe small moments. Third, for signal/noise reasons it is almost impossible in neutrons to use a technique that surveys large parts of reciprocal space for small signals. The instrument of choice is the triple-axis spectrometer, little changed since its invention by Brockhouse in the 1950s, and which painstakingly scans through reciprocal space with at least 2}5 min spent at each value of Q, the momentum transfer, and E, the energy transfer. Since beamtime is at a premium it is not surprising that selection committees rarely give carte blanche for looking at all reciprocal space.
2. UPd2 Al3 This HF superconductor was discovered in (1991) [1] and it was rapidly established that the AF-ordered moment is relatively large (0.8l /U atom) below ¹ "14 K [2]. It was "rst suggested , from bulk measurements [3] that two subsystems coexist, both coming from the 5f electrons, one of which is more localised and responsible for the magnetic properties, and the other less localised being responsible for the superconductivity. One year later this idea was further ampli"ed by the muon study of Feyerherm et al. [4]. From independent muon studies with single crystals the muons are known to annihilate at the real-space position (0 0 ). Because this is between the antiparallel layers of uranium (see Fig. 1), there is almost no change in the muon spin relaxation below ¹ and, , most importantly, there is no change below ¹ " 1.8 K. This demonstrates homogeneous superconductivity. In transverse "eld the measurement of the Knight shift showed changes at ¹ that were opposite in sign for H#c and HNc. The authors ascribed this to partial reduction of the 5f susceptibility, v , in the superconducting state. The initial neutron inelastic studies by Petersen et al. [5,6] established that a heavily damped spinwave response existed below &¹ /2. This is in , itself rather unusual in these 5f compounds; mostly the response is so heavily damped that no sign of a propagating spin wave can be found [7] but quite clear modes can be seen, particularly along the
G.H. Lander / Physica B 289}290 (2000) 1}9
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Fig. 1. The hexagonal crystal structure of UPd Al . The large circles represent the positions of uranium ions with the bold arrows marking the relative directions of the magnetic moments. The smaller circles in the same planes represent the positions of the palladium ions, and, the smallest circles in the intercalating plane represent the aluminium ions. Note that the magnetic cell is doubled compared to the crystal unit cell. (Taken from Ref. [8]).
c-axis. In a qualitative sense these may be associated with localised 5f moments. At the zone boundary (along the [0 0 1] direction) the energy of these modes reach &8 meV (with a damping of &5 meV) and since this is considerably greater than the 1.5 meV represented by ¹ ("14 K) it is , clear that the exchange interactions are complex. These measurements were performed with an energy resolution of 0.3 meV and no di!erences were observed in the signal above and below ¹ . When the resolution was improved, "rst to 0.1 and later to 0.07 meV, the second component of the scattering was discovered [8]. Further experiments both by our group [9}11] and that of Metoki et al. [12}15] revealed that the quasielastic nature of the scattering in the region ¹ (¹(¹ changed be , low ¹ and a gap opened in the spectrum of this component. Some of the relevant data are shown in Fig. 2 as a function of temperature. These are taken around the point q"[0 0 ], which is the AF or dering wave vector. It is worth pointing out the complexity of these experiments; a relatively large AF moment of 0.8l contributes an enormous AF Bragg peak at q "[0 0 ] at an energy transfer of *E"0. At the same time for ¹'¹ there is scat tering around this point that can be characterised as quasielastic, i.e. it represents a #uctuation
Fig. 2. The temperature dependence of scattering at (0 0.5) as a function of neutron energy transfer. In the top frame, the scattering in the normal antiferromagnetic phase is dominated by a strong low-energy mode which, within our resolution is quasielastic. The solid lines are calculated as outlined in the text. Note the logarithmic vertical scale. The data have been displaced by 0.8 meV horizontally and 140 cts vertically for successive temperatures above 2.5 K. In the lower frame, the scattering in the superconducting antiferromagnetic phase is shown. Again the spectra have been displaced in a similar manner to the upper frame. The strong, low energy, feature at low temperatures below ¹ is clearly seen to have a qualitatively di!erent form from the response in the normal antiferromagnetic phase. The solid lines are model calculations including the experimental resolution in the energy momentum plane of the experiment. As described in the text, the model includes a Lorentzian centred at "nite frequency for both the spin wave and the pair breaking response together with a quasielastic mode which only becomes signi"cant near ¹ (Taken from Ref. [10]).
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G.H. Lander / Physica B 289}290 (2000) 1}9
spectrum with a mean energy width at 5 K of &0.3 meV, implying #uctuations on a time scale of &30 GHz. One can see on the same scale in Fig. 2 the spin wave of Petersen et al. [5,6]; both these signals are some 10\ of the AF Bragg peak. It is far too naive to regard these as independent responses and indeed Bernhoeft has shown convincingly that they interact strongly. Nevertheless, it seems plausible to assume that at the extreme level they represent the two #uid model suggested by Refs. [3,4]. In reciprocal space the gap opening is centred strongly at q ; i.e. if one goes slightly away from this point then not only is the quasielastic scattering much reduced, but also the gap is not present. The temperature dependence of the gap is shown in Fig. 3. This is not exactly the observed gap as seen in the experiments, but rather that deduced after taking into account the strong interaction between the quasielastic and spin-wave scattering. Surprisingly, it is quite similar to the standard BCS function and the gap is close to 3.5 k¹ . The observed gap is actually smaller, consistent with NMR measurements, but this energy shift is because of strong interactions between the two modes, the quasielastic and inelastic responses. This apparent similarity to BCS theory should not be pushed too far. It must be remembered that the gap is only at one place in the Brillouin zone (BZ), whereas s-state superconductivity would give a uniform gap throughout the BZ. Bernhoeft et al. [16] have extended this analysis to deduce the symmetry of the superconducting order parameter. There is, for example, excellent agreement between recent transport measurements [17], the neutron measurements, and the bandstructures proposed [18] for the 5f states in UPd Al . As mentioned above, all the action is centred close to q as far as superconductivity is concerned. In particular, there is a strong q dependence on going away from q along the cH-axis, i.e. q"[0, 0, #q ]. It appears that the AF repetition of Fig. A 1 de"nes a potential restricting q small. Recently, A we have explored the region Q"[q , 0, ] and ? found a rather di!erent situation [19]. The original work of Petersen [5,6] suggested strong damping of the (higher-energy) spin wave in this direction, and
Fig. 3. The thermal evolution of the low-energy Lorentzian pole in the superconducting state which is approximately given by twice the maximum energy gap. The solid line corresponds with the BCS form normalised to the value at low temperatures, 2D "3.86 k ¹ , with ¹ "1.8 K lying close to the estimated bulk ¹ "1.90$0.07 K (Taken from Ref. [10]).
we "nd a larger amount of scattering at low energy ((5 meV) for all values of q . (Note that q "1 is ? ? another magnetic zone centre, so that q " is the ? magnetic zone boundary.) Surprisingly, the scattering response is extremely strong at q ", and ? extends over a large frequency range from &0.5 to 5 meV, but peaked at &3 meV. This represents a strong pole of the susceptibility and presumably nesting of relevant pieces of Fermi surface. Metoki et al. [20] have suggested that this also represents a pole in the superconductivity potential, but our high-resolution measurements show that the scattering is always inelastic and no change occurs below ¹ . The strong susceptibility for q &0.5 implies that ? there is a tendency also for the moments to order AF in the hexagonal basal plane. Fig. 1 shows a ferromagnetic ordering in these planes (corresponding to q "0) but the AF exchange interac? tion clearly competes with this ferromagnetic exchange. Indeed, in UNi Al , which is both iso structural and isoelectronic with UPd Al , the or dering is incommensurate in the plane with q &0.61 [21,22]. In this material our experiments ? [23] have established a quasielastic component at the ordering wave vector, but we were unable to
G.H. Lander / Physica B 289}290 (2000) 1}9
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establish the presence of a gap below ¹ , probably because our resolution was not good enough. I have discussed UPd Al in considerable detail because it illustrates the complexity that can occur in reciprocal space. Our experiments con"rm the `two componenta model advanced by bulk [3] and muon [4] experiments and show unambiguously that the 5f states are involved in driving the superconductivity. Furthermore, the large amount of scattering, both quasielastic around q and inelas tic around [q , 0, ], especially near q " raises an ? ? interesting question about the very small moments found in such materials as URu Si (&0.02l ) and UPt (&0.03l ). The moment in the former is 40 times smaller than the ordered moment in UPd Al , so that the AF Bragg peak is 1600 times smaller. But suppose this represents the pole of the susceptibility rather than an ordered moment. This comes down to what resolution is used in the neutron experiments, so that the arguments are perhaps not quite over for these materials.
3. UBe13 The magnetic and superconducting phase diagram, as established by muon and bulk measurements of the (U Th )Be system is shown in \V V Fig. 4 [24]. The zero-"eld muon spin resonance measurements observed no change in line width at ¹ in any samples. However, at ¹ a change was observed for 0.02(x(0.04 Th concentration. This has been ascribed to magnetic ordering with a moment of 10\}10\l /U atom. The absence of any magnetic ordering in UBe has long been an outstanding anomaly. In fact, the absence of any evidence for magnetism, either static or dynamic, throws considerable doubt that any general theory involving a magnetic potential might be responsible for superconductivity. A number of e!orts have been made with single crystals in the past, mainly driven by Aeppli who was so successful in "nding the magnetism in UPt [7]. However, UBe resisted attack. Looking at the periodic table Gabe realised that isostructural NpBe was close by (the next element) and that it was both a heavy-fermion and ordered AF below 4.9 K [25]. The proposal was to set about "nding
Fig. 4. Phase diagram for U Th Be . Open symbols are \V V from muons. Squares, ¹ from s ; circles, ¹ from magnetiz ?A ation M (H); inverted triangles, ¹ from kink in H (¹). The solid upright triangles are ¹ and ¹ from speci"c heat. The symbol (*) at x"0.043 indicates a merging of ¹ and ¹ . ¹ "0.39 K for x"0.0600 was determined resistively (Taken from Ref. [24]).
the ordered wave vector of NpBe in the hope that it might give an idea where to look in reciprocal space for UBe . These experiments were successful [26], and the AF wavevector of NpBe is q "1, 0, 02. (The 1 2 here indicate that since these compounds are cubic, one may permute the indices to give three possible con"gurations.) Interestingly, this AF wave vector is the same as found in the heavy rare-earth Be compounds [27], so that one suspects that the wave vector is de"ned by aspects of the conduction}electron density, and the latter is strongly in#uenced by the 13 Be atoms in the asymmetric unit. Following the success of this work on NpBe , the UBe crystals were found in the cupboard at Ris+ National Laboratory, and experiments were started in 1998. Initially, they were not successful; indeed there is nothing at q"1, 0, 02. However, quite by chance an overnight scan picked up some
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G.H. Lander / Physica B 289}290 (2000) 1}9
the width of the peaks as a measure of the correlation length of the magnetic arrangement, we found a correlation length of &5 As , i.e. a single spin}spin correlation function [28]. There is another unusual feature of the studies so far and that is that no scattering intensity has been found along the direction [H H 0]. In a normal magnetic structure with a propagation vector q "[ 0] this signi"es that the moments are also parallel to this direction and modulated in length. (This comes from the basic neutron interaction with magnetic moments and the fact that one is sensitive only to components perpendicular to Q; thus if the moments are along this direction k#Q there is no magnetic scattering.) A model for the correlations is shown in Fig. 6. Our experiments have established that shortrange magnetic correlations exist in UBe but many more experiments are needed. Key questions are Fig. 5. A transverse scan at *E"1.5 meV and 1.5 K through the magnetic peaks along the lines [f f ¸] with ¸"2 and 2.5. The two scans are displaced by 100 cts. The reciprocal space is shown in the inset (solid circles } allowed nuclear Bragg re#ections; solid squares } positions of magnetic signal) (Taken from Ref. [28]).
(1) what is the energy pro"le of these correlations? (2) what happens below ¹ ? (3) are these correlations related to the AF order proposed by muons in Th doped UBe ? (4) why have these correlations not been detected by muons? Note that recently the phase diagram has been further modi"ed [29]. Recently, He!ner and colleagues [30] have observed an interesting change in the Knight shift below ¹ with transverse-"eld muon spectroscopy. Their measurements suggest the development of an internal magnetic "eld which scales with magnetic "eld. We need to extend the neutron experiments below ¹ before we can even attempt to draw conclusions between the results of these two di!erent techniques.
Fig. 6. One possible domain (out of 6) for the real-space moment arrangement for an ordered AF with q "1 02 and a longitudinal moment modulation. The arrows represent the moment direction on the ; sites whereas the Be sites are not shown. Two identical magnetic layers are stacked along the [0 0 1] axis (Taken from Ref. [28]).
weak signal at Q"[, , 2], and it is clear from Fig. 5 that these peaks are real. They disappear progressively until no signal is visible by 30 K. Using
4. U2 Pt2 In This material has been found to be a HF system with c"415 mJ/(mol. U-K) [31,32]. However, at lower temperature ((5 K) there is evidence that a non-Fermi liquid state forms [33}35]. The crystal structure of U Pt In is a slight modi"cation of the tetragonal P4/mbm structure of isoelectronic compounds like U Ni In and U Pd In [36] and this doubling of the tetragonal c-axis in the Pt
G.H. Lander / Physica B 289}290 (2000) 1}9
compound may change radically the electronic properties. Both the U Ni In and U Pd In com pounds order AF, whereas U Pt In does not [36]. Muon experiments in zero "eld have shown no depolarization e!ects, indicating no long-range order, but there is a line broadening below &7 K. There is a peak in s also at 10 K. These two ,A measurements suggest (although they do not prove) that AF yuctuations may be present. We set out to "nd evidence for such #uctuations using a large single crystal and the IN14 3-axis spectrometer at the ILL, Grenoble. So far we have failed to "nd any positive evidence. The di$culty is to know where to look in Q-space. If &10 K is the relative energy scale then that is &1 meV ("11.4 K) so the energy scale is probably OK for IN14, but even this may be too naive. Initially we searched around the AF wave vectors of U Ni In and U Pd In but then widened our search. These latter two, as we discussed above, have a di!erent (simpler) atomic structure so these wave vectors may not be relevant. Recently, after our experiments, we have learnt of the AF structure of the isostructural U Pt Sn compound [37] which is complicated with q "[0, 0, 0.1823]. Al though we have scanned over this position it perhaps warrants another look.
5. NpO2 Neptunium dioxide has an extraordinarily interesting history. At "rst glance it would appear simple. We assume Np>#20\ and since Np> : 5f is a Kramers ion the ground state at ¹"0 K should be magnetic. Speci"c heat on NpO was "rst reported in 1953 [38] and showed a large anomaly at 25 K. In 1968 MoK ssbauer experiments [39] showed that a very small hyper"ne "eld, corresponding to a moment of &0.02l appeared below 25 K. Many neutron e!orts were undertaken; the last one on the largest available crystal of 0.5 mm being reported in 1987 [40]. They all failed to observe any peaks from an ordered moment. Although there were many ideas about NpO in recent years (see Ref. [41] for more details) the initial breakthrough on NpO came with the muon
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experiments at PSI of Kopmann et al. (1998) [42]. By measuring the zero-"eld spectra of both UO and NpO they showed that a very similar signal developed in NpO below 25 K as was found in UO below 30 K, except that the signal was much weaker in NpO . Since both these materials are semiconductors (and if they could be obtained 100% pure and defect free one might expect they would be insulators), then there is always the risk of muonium production when muon experiments are attempted. Fortunately, this appears not to be the case, as the experiment on UO , which has a well-charac terised AF con"guration, show. The close similarity of the ZF spectra leads to the suggestion that the AF arrangements in these two materials is the same, but that the ordered moment in NpO is about 5%, i.e. &0.1l , compared to that in UO . We have been working a lot recently with RXMS-resonant X-ray magnetic scattering, which is a technique in which the photons are tuned to an absorption edge of the material in question and a large (depending on the edge in question) enhancement of the magnetic response occurs. Numerous reviews of this technique exist (see for e.g., Refs. [43,44]) and I have even presented a short review speci"c to actinides [45]. Because of the special conditions that the actinide M edges, which represent transitions from the core 3d to the partially occupied 5f shells, have an energy (&4 keV) that can be used for di!raction experiments, studies of the actinides are particularly powerful. Photon beams from 3rd generation machines, like the ESRF in Grenoble, have very small beams (0.2;0.2 mm) so small samples of much less than 1 mg can be used. This is an advantage in NpO where only small crystals are avail able. In 1998 at the ID20 beamline of the ESRF we did such an experiment with the photon energy tuned to the Np M edge of 3.845 keV on a crystal of NpO and almost immediately found a strong re#ection at the (structurally forbidden) (0 0 1) and (0 0 3) re#ections. The intensity as a function of Q and temperature is shown in Fig. 7(a) and the exact AF con"guration worked out by comparing the relative intensities of a number of peaks is shown in Fig. 7(b). It is di!erent from that of UO , where the #!#! sequence is the same but the
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G.H. Lander / Physica B 289}290 (2000) 1}9
Although the RXMS technique has many advantages, it has one considerable disadvantage and that is that the signal cannot (yet) be related to the magnetic moment [43}45]. Thus, we cannot tell the moment in NpO even though we know the mag netism is long range. We therefore fall back on the MoK ssbauer and muon values of 0.02 and &0.10l , respectively. Our experiments shed no light on why this small moment exists. NpO is, of course, not a HF mater ial so another mechanism, perhaps quadrupolar ordering as has been proposed for the small moments in UPd [46], are the answer, but at least both muons and a scattering technique have observed the ordered magnetism.
6. Conclusions
Fig. 7. (a) Normalised temperature dependence of the (0 0 1) (open triangles) and (0 0 3) (open circles) magnetic Bragg intensities. The straight line corresponds to the exponent b"0.5, which is the molecular "eld value, with ¹ "25.3(1) K. The , inset shows data for the specular (0 0 3) re#ection at 10 K as a function of the momentum transfer component, ¸; (b) The #uorite crystal structure of NpO is shown. The larger circles represent oxygen, and the 8 oxygen atoms surrounding the Np atom on the top face are shown. The arrows indicate the components of the magnetic structure propagating along the [0 0 1] axis. This is a simple #!#! (type-I) alternating sequence of ferromagnetic planes. The real-magnetic structure is triple-q, i.e. all three equivalent 10 0 12 components exist simultaneously (Taken from Ref. [41]).
moments in UO are perpendicular to the propa gation direction, whereas they are parallel to this direction in NpO .
The enigma of superconductivity together with magnetism, or at least magnetic correlations, remains a common theme of both heavy Fermions and high ¹ , and, as such, remains one of the greatest challenges in solid state physics at the end of this century. The last 10 years have established that the superconductivity is not s-wave (BCS), but there is little agreement on what is the correct symmetry. Indeed, it seems likely that a variety of symmetries are possible. Small moments } or at least correlations between spins } appear a likely key for a potential to drive the superconductivity. Muons have played a key role in showing the presence of such small internal magnetic "elds. Neutrons have then been able to amplify the form of the correlations as they are measuring in both Q and E space. Often the results from the two can be reconciled, but not always. UBe is a case in point. I have also introduced a new technique, resonant X-ray scattering, using tunable photons from synchrotron sources, as this is especially powerful in studies of actinide materials.
Acknowledgements I am particularly indebted to my colleagues in these endeavors. In rough order of the projects they are: N. Bernhoeft (CEA-Grenoble), A. Hiess (ILL,
G.H. Lander / Physica B 289}290 (2000) 1}9
Grenoble), B. Roessli (PSI, Switzerland), N. Sato (Tohoku Univ., Sendai, Japan), S. Coad and A. MartmH n-MartmH n (ITU and ILL), D. McMorrow (Ris+ National Laboratory), G. Aeppli (NEC, Princeton), D. Mannix (ITU and ESRF, Grenoble), C. Vettier (ESRF), R. Caciu!o (Univ. Ancona, Italy), and F. Wastin and J. Rebizant of ITU, Karlsruhe. Despite the long hours and frequent frustration these experiments have been both rewarding and fun! Many thanks to all of them.
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[27] F. Vigneron et al., J. Phys. F 12 (1982) 223. [28] S. Coad et al., Presented at European Conference on Neutron Scattering, Budapest, Sept. 1999, Physica B 276}278 (2000) 764. [29] F. Kromer et al., Phys. Rev. Lett. 81 (1998) 4476. [30] R. He!ner, private communication and PSI-Report, 1998, p. 48. [31] L. Havela et al., J. Appl. Phys. 76 (1994) 6214. [32] L. Havela et al., J. Magn. Magn. Mater. 140}144 (1995) 1367. [33] A.M. Strydom, P. de V. du du Plessis, Physica B 223}224 (1996) 222. [34] A.M. Strydom, P. de V. du Plessis, Physica B 230}232 (1997) 62. [35] P. Estrela et al., Physica B 259}261 (1999) 409. [36] A. MartmH n-MartmH n et al., Phys. Rev. B 59 (1999) 11818. [37] K. Prokes et al., J. Magn. Magn. Mater. 202 (1999) 451. [38] E.F. Westrum et al., J. Chem. Phys. 21 (1953) 419, 1884. [39] B.D. Dunlap et al., J. Phys. Chem. Solids 29 (1968) 1365. [40] R. Caciu!o et al., Solid State Commun. 64 (1987) 149. [41] D. Mannix et al., Phys. Rev. B 60 (1999) 15187. [42] W. Kopmann et al., J. Alloys Compounds 271-273 (1998) 463. [43] M. Blume, C. Vettier, in: G. Materlik et al. (Eds.) Resonant Anomalous X-ray Scattering, Elsevier Science, Amsterdam, 1994, p. 495, 513. [44] D. McMorrow, D. Gibbs, J. Bohr in: K. Gschneidner, L. Eyring (Eds.), Handbook of Physics and Chemistry of Rare Earths, Elsevier, Amsterdam, 1999, p. 1. [45] G.H. Lander, J. Alloys Compounds 250 (1997) 544. [46] K.A. McEwen et al., J. Magn. Magn. Mater. 177}181 (1998) 37.
Comments G.M. Luke: Is there evidence that the inelastic response in UBe13 is of magnetic origin? G.H. Lander: Normally this is easy to distinguish as magnetic ewects decrease slowly with Q (momentum transfer) whereas charge ewects increase as Q2. Our measurements are at small Q, where charge ewects are usually hard to see. Also the extinction rule (no scattering along [1 1 0]) would be very dizcult to understand if the ewects were charge related. The more dirct method of polarisation analysis is probably impossible with such a weak signal.
X-rays and neutrons as complementary probes to muons in magnetism: A view from reciprocal space G.H. Lander* European Commission, JRC, Institute for Transuranium Elements, Postfach 2340, 76125 Karlsruhe, Germany
Abstract Twenty years ago magnetism and superconductivity appeared mutually exclusive and life was (relatively) simple. The discovery of heavy-fermion superconductivity (1979}1984) and high ¹ (1986), changed our perceptions. Gradually, it was realised that either ordered magnetism or magnetic correlations are found in most of these materials. Here I shall concentrate on heavy fermions, in which the f electrons are responsible for the magnetism as well as (probably) the superconductivity. Muons have played a key role in elucidating these the so-called `small momenta systems, such as UPt , URu Si , UPd Al , etc. Recenty, at the ILL we have measured the low-energy inelastic magnetic signal from UPd Al and the response will be compared to the conclusions derived from muon studies. Interestingly, it is accepted wisdom that muons will be sensitive to any small magnetic e!ects. UBe is fascinating as it has long been the `exceptiona, with no sign of any magnetism. Now, at Ris+ National Laboratory, we have found evidence with neutrons for weak magnetic correlations of a most unusual form in UBe } so that it no longer can be regarded as an exception. Neutrons, powerful though they are, are sometimes lost in reciprocal space. U Pt In is a non-Fermi liquid, and there is a strong muon anomaly below 10 K, but we have been unable to "nd the correlations with neutrons. Finally, NpO is one of the oldest `small-moment systemsa, and recently muons were able to see an asymmetry below 25 K, and suggested an ordered moment of 0.1l . However, the signal has been too small for neutrons. Here I will explain the emergence of a new technique, resonant magnetic X-ray scattering, that, especially in the actinides, has great promise. We have used this at the ESRF to determine the magnetic structure of NpO . 2000 Elsevier Science B.V. All rights reserved. Keywords: Heavy Fermions; Neutron scattering; Actinides
1. Introduction Since the discovery of heavy-fermion (HF) superconductors, exactly 20 years ago, by Frank Steglich and his colleagues, there has been an important change in our concept of the connection between magnetism and superconductivity. Originally
* Tel.: #49-7247-951-441; fax: #49-7247-951-599. E-mail address: [email protected] (G.H. Lander).
thought to be mutually exclusive, it is now realised that these two phenomena may co-exist and there is even a substantial body of work suggesting that antiferromagnetism (AF), either ordered or #uctuating, may provide the driving potential for unconventional (i.e. non s-state) superconductivity. Of course, the majority of both experimental and theoretical work has centered on high-¹ materials since if ¹ can be raised substantially above the present record of &130 K the dream of room temperature superconductivity may be reached.
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 2 3 1 - 3
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Unfortunately, making wires out of ceramics has proved technically frustrating and 13 years after high ¹ was discovered applications remain disap pointing } still hope persists. What has happened in heavy-fermion materials is that the superconductivity has been shown beyond all reasonable doubt to be non-s-state, and the magnetism, at least the ordered component of it, has been shown to involve very small moments. The discovery of these small moments has been one of the great successes of muon spectroscopy. Understanding why these moments are so small ((0.1l ) is still a problem. In terms of band structure we do know Ni has an ordered moment of 0.6l , but it seems hard to understand why the energy gain of stabilising moments an order of magnitude smaller would be so important, even though the ordering temperatures are so small. Table 1 gives the compounds that are HF-superconductors and some of their properties as we now understand them. Muons are, of course, a local probe. The information from such experiments actually does contain information on both the static and dynamic aspects of the magnetism, but it is di$cult to disentangle. The most general probe is neutron scattering, but there are severe disadvantages to this technique. First, intensities are low so that large samples are required. Second, for moments (0.5l it is virtually impossible to use polycrystalline samples. In contrast, all the early important muon experiments were performed on such sam-
Table 1 Heavy fermion superconductors showing the symmetry of the unit cell, the Sommerfeld coe$cient c (units of mJ/mol/K), the NeH el temperature, the superconducting transition temperature ¹ , and the ordered antiferromagnetic moment in Bohr mag netons per uranium or cerium
CeCu Si UBe UPt URu Si UPd Al UNi Al
Structure
c (mJ)
¹ (K) ,
¹ (K)
k
Tetragonal Cubic Hexagonal Tetragonal Hexagonal Hexagonal
1100 1100 450 180 150 120
&1 * 5.0 17.5 14.5 4.4
0.70 0.90 0.55 1.2 1.8 1.0
0.1 * 0.03 0.02 0.85 0.12
ples. So large crystals have to be available for neutrons, by large we mean volumes of '0.3 cm to observe small moments. Third, for signal/noise reasons it is almost impossible in neutrons to use a technique that surveys large parts of reciprocal space for small signals. The instrument of choice is the triple-axis spectrometer, little changed since its invention by Brockhouse in the 1950s, and which painstakingly scans through reciprocal space with at least 2}5 min spent at each value of Q, the momentum transfer, and E, the energy transfer. Since beamtime is at a premium it is not surprising that selection committees rarely give carte blanche for looking at all reciprocal space.
2. UPd2 Al3 This HF superconductor was discovered in (1991) [1] and it was rapidly established that the AF-ordered moment is relatively large (0.8l /U atom) below ¹ "14 K [2]. It was "rst suggested , from bulk measurements [3] that two subsystems coexist, both coming from the 5f electrons, one of which is more localised and responsible for the magnetic properties, and the other less localised being responsible for the superconductivity. One year later this idea was further ampli"ed by the muon study of Feyerherm et al. [4]. From independent muon studies with single crystals the muons are known to annihilate at the real-space position (0 0 ). Because this is between the antiparallel layers of uranium (see Fig. 1), there is almost no change in the muon spin relaxation below ¹ and, , most importantly, there is no change below ¹ " 1.8 K. This demonstrates homogeneous superconductivity. In transverse "eld the measurement of the Knight shift showed changes at ¹ that were opposite in sign for H#c and HNc. The authors ascribed this to partial reduction of the 5f susceptibility, v , in the superconducting state. The initial neutron inelastic studies by Petersen et al. [5,6] established that a heavily damped spinwave response existed below &¹ /2. This is in , itself rather unusual in these 5f compounds; mostly the response is so heavily damped that no sign of a propagating spin wave can be found [7] but quite clear modes can be seen, particularly along the
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3
Fig. 1. The hexagonal crystal structure of UPd Al . The large circles represent the positions of uranium ions with the bold arrows marking the relative directions of the magnetic moments. The smaller circles in the same planes represent the positions of the palladium ions, and, the smallest circles in the intercalating plane represent the aluminium ions. Note that the magnetic cell is doubled compared to the crystal unit cell. (Taken from Ref. [8]).
c-axis. In a qualitative sense these may be associated with localised 5f moments. At the zone boundary (along the [0 0 1] direction) the energy of these modes reach &8 meV (with a damping of &5 meV) and since this is considerably greater than the 1.5 meV represented by ¹ ("14 K) it is , clear that the exchange interactions are complex. These measurements were performed with an energy resolution of 0.3 meV and no di!erences were observed in the signal above and below ¹ . When the resolution was improved, "rst to 0.1 and later to 0.07 meV, the second component of the scattering was discovered [8]. Further experiments both by our group [9}11] and that of Metoki et al. [12}15] revealed that the quasielastic nature of the scattering in the region ¹ (¹(¹ changed be , low ¹ and a gap opened in the spectrum of this component. Some of the relevant data are shown in Fig. 2 as a function of temperature. These are taken around the point q"[0 0 ], which is the AF or dering wave vector. It is worth pointing out the complexity of these experiments; a relatively large AF moment of 0.8l contributes an enormous AF Bragg peak at q "[0 0 ] at an energy transfer of *E"0. At the same time for ¹'¹ there is scat tering around this point that can be characterised as quasielastic, i.e. it represents a #uctuation
Fig. 2. The temperature dependence of scattering at (0 0.5) as a function of neutron energy transfer. In the top frame, the scattering in the normal antiferromagnetic phase is dominated by a strong low-energy mode which, within our resolution is quasielastic. The solid lines are calculated as outlined in the text. Note the logarithmic vertical scale. The data have been displaced by 0.8 meV horizontally and 140 cts vertically for successive temperatures above 2.5 K. In the lower frame, the scattering in the superconducting antiferromagnetic phase is shown. Again the spectra have been displaced in a similar manner to the upper frame. The strong, low energy, feature at low temperatures below ¹ is clearly seen to have a qualitatively di!erent form from the response in the normal antiferromagnetic phase. The solid lines are model calculations including the experimental resolution in the energy momentum plane of the experiment. As described in the text, the model includes a Lorentzian centred at "nite frequency for both the spin wave and the pair breaking response together with a quasielastic mode which only becomes signi"cant near ¹ (Taken from Ref. [10]).
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spectrum with a mean energy width at 5 K of &0.3 meV, implying #uctuations on a time scale of &30 GHz. One can see on the same scale in Fig. 2 the spin wave of Petersen et al. [5,6]; both these signals are some 10\ of the AF Bragg peak. It is far too naive to regard these as independent responses and indeed Bernhoeft has shown convincingly that they interact strongly. Nevertheless, it seems plausible to assume that at the extreme level they represent the two #uid model suggested by Refs. [3,4]. In reciprocal space the gap opening is centred strongly at q ; i.e. if one goes slightly away from this point then not only is the quasielastic scattering much reduced, but also the gap is not present. The temperature dependence of the gap is shown in Fig. 3. This is not exactly the observed gap as seen in the experiments, but rather that deduced after taking into account the strong interaction between the quasielastic and spin-wave scattering. Surprisingly, it is quite similar to the standard BCS function and the gap is close to 3.5 k¹ . The observed gap is actually smaller, consistent with NMR measurements, but this energy shift is because of strong interactions between the two modes, the quasielastic and inelastic responses. This apparent similarity to BCS theory should not be pushed too far. It must be remembered that the gap is only at one place in the Brillouin zone (BZ), whereas s-state superconductivity would give a uniform gap throughout the BZ. Bernhoeft et al. [16] have extended this analysis to deduce the symmetry of the superconducting order parameter. There is, for example, excellent agreement between recent transport measurements [17], the neutron measurements, and the bandstructures proposed [18] for the 5f states in UPd Al . As mentioned above, all the action is centred close to q as far as superconductivity is concerned. In particular, there is a strong q dependence on going away from q along the cH-axis, i.e. q"[0, 0, #q ]. It appears that the AF repetition of Fig. A 1 de"nes a potential restricting q small. Recently, A we have explored the region Q"[q , 0, ] and ? found a rather di!erent situation [19]. The original work of Petersen [5,6] suggested strong damping of the (higher-energy) spin wave in this direction, and
Fig. 3. The thermal evolution of the low-energy Lorentzian pole in the superconducting state which is approximately given by twice the maximum energy gap. The solid line corresponds with the BCS form normalised to the value at low temperatures, 2D "3.86 k ¹ , with ¹ "1.8 K lying close to the estimated bulk ¹ "1.90$0.07 K (Taken from Ref. [10]).
we "nd a larger amount of scattering at low energy ((5 meV) for all values of q . (Note that q "1 is ? ? another magnetic zone centre, so that q " is the ? magnetic zone boundary.) Surprisingly, the scattering response is extremely strong at q ", and ? extends over a large frequency range from &0.5 to 5 meV, but peaked at &3 meV. This represents a strong pole of the susceptibility and presumably nesting of relevant pieces of Fermi surface. Metoki et al. [20] have suggested that this also represents a pole in the superconductivity potential, but our high-resolution measurements show that the scattering is always inelastic and no change occurs below ¹ . The strong susceptibility for q &0.5 implies that ? there is a tendency also for the moments to order AF in the hexagonal basal plane. Fig. 1 shows a ferromagnetic ordering in these planes (corresponding to q "0) but the AF exchange interac? tion clearly competes with this ferromagnetic exchange. Indeed, in UNi Al , which is both iso structural and isoelectronic with UPd Al , the or dering is incommensurate in the plane with q &0.61 [21,22]. In this material our experiments ? [23] have established a quasielastic component at the ordering wave vector, but we were unable to
G.H. Lander / Physica B 289}290 (2000) 1}9
5
establish the presence of a gap below ¹ , probably because our resolution was not good enough. I have discussed UPd Al in considerable detail because it illustrates the complexity that can occur in reciprocal space. Our experiments con"rm the `two componenta model advanced by bulk [3] and muon [4] experiments and show unambiguously that the 5f states are involved in driving the superconductivity. Furthermore, the large amount of scattering, both quasielastic around q and inelas tic around [q , 0, ], especially near q " raises an ? ? interesting question about the very small moments found in such materials as URu Si (&0.02l ) and UPt (&0.03l ). The moment in the former is 40 times smaller than the ordered moment in UPd Al , so that the AF Bragg peak is 1600 times smaller. But suppose this represents the pole of the susceptibility rather than an ordered moment. This comes down to what resolution is used in the neutron experiments, so that the arguments are perhaps not quite over for these materials.
3. UBe13 The magnetic and superconducting phase diagram, as established by muon and bulk measurements of the (U Th )Be system is shown in \V V Fig. 4 [24]. The zero-"eld muon spin resonance measurements observed no change in line width at ¹ in any samples. However, at ¹ a change was observed for 0.02(x(0.04 Th concentration. This has been ascribed to magnetic ordering with a moment of 10\}10\l /U atom. The absence of any magnetic ordering in UBe has long been an outstanding anomaly. In fact, the absence of any evidence for magnetism, either static or dynamic, throws considerable doubt that any general theory involving a magnetic potential might be responsible for superconductivity. A number of e!orts have been made with single crystals in the past, mainly driven by Aeppli who was so successful in "nding the magnetism in UPt [7]. However, UBe resisted attack. Looking at the periodic table Gabe realised that isostructural NpBe was close by (the next element) and that it was both a heavy-fermion and ordered AF below 4.9 K [25]. The proposal was to set about "nding
Fig. 4. Phase diagram for U Th Be . Open symbols are \V V from muons. Squares, ¹ from s ; circles, ¹ from magnetiz ?A ation M (H); inverted triangles, ¹ from kink in H (¹). The solid upright triangles are ¹ and ¹ from speci"c heat. The symbol (*) at x"0.043 indicates a merging of ¹ and ¹ . ¹ "0.39 K for x"0.0600 was determined resistively (Taken from Ref. [24]).
the ordered wave vector of NpBe in the hope that it might give an idea where to look in reciprocal space for UBe . These experiments were successful [26], and the AF wavevector of NpBe is q "1, 0, 02. (The 1 2 here indicate that since these compounds are cubic, one may permute the indices to give three possible con"gurations.) Interestingly, this AF wave vector is the same as found in the heavy rare-earth Be compounds [27], so that one suspects that the wave vector is de"ned by aspects of the conduction}electron density, and the latter is strongly in#uenced by the 13 Be atoms in the asymmetric unit. Following the success of this work on NpBe , the UBe crystals were found in the cupboard at Ris+ National Laboratory, and experiments were started in 1998. Initially, they were not successful; indeed there is nothing at q"1, 0, 02. However, quite by chance an overnight scan picked up some
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G.H. Lander / Physica B 289}290 (2000) 1}9
the width of the peaks as a measure of the correlation length of the magnetic arrangement, we found a correlation length of &5 As , i.e. a single spin}spin correlation function [28]. There is another unusual feature of the studies so far and that is that no scattering intensity has been found along the direction [H H 0]. In a normal magnetic structure with a propagation vector q "[ 0] this signi"es that the moments are also parallel to this direction and modulated in length. (This comes from the basic neutron interaction with magnetic moments and the fact that one is sensitive only to components perpendicular to Q; thus if the moments are along this direction k#Q there is no magnetic scattering.) A model for the correlations is shown in Fig. 6. Our experiments have established that shortrange magnetic correlations exist in UBe but many more experiments are needed. Key questions are Fig. 5. A transverse scan at *E"1.5 meV and 1.5 K through the magnetic peaks along the lines [f f ¸] with ¸"2 and 2.5. The two scans are displaced by 100 cts. The reciprocal space is shown in the inset (solid circles } allowed nuclear Bragg re#ections; solid squares } positions of magnetic signal) (Taken from Ref. [28]).
(1) what is the energy pro"le of these correlations? (2) what happens below ¹ ? (3) are these correlations related to the AF order proposed by muons in Th doped UBe ? (4) why have these correlations not been detected by muons? Note that recently the phase diagram has been further modi"ed [29]. Recently, He!ner and colleagues [30] have observed an interesting change in the Knight shift below ¹ with transverse-"eld muon spectroscopy. Their measurements suggest the development of an internal magnetic "eld which scales with magnetic "eld. We need to extend the neutron experiments below ¹ before we can even attempt to draw conclusions between the results of these two di!erent techniques.
Fig. 6. One possible domain (out of 6) for the real-space moment arrangement for an ordered AF with q "1 02 and a longitudinal moment modulation. The arrows represent the moment direction on the ; sites whereas the Be sites are not shown. Two identical magnetic layers are stacked along the [0 0 1] axis (Taken from Ref. [28]).
weak signal at Q"[, , 2], and it is clear from Fig. 5 that these peaks are real. They disappear progressively until no signal is visible by 30 K. Using
4. U2 Pt2 In This material has been found to be a HF system with c"415 mJ/(mol. U-K) [31,32]. However, at lower temperature ((5 K) there is evidence that a non-Fermi liquid state forms [33}35]. The crystal structure of U Pt In is a slight modi"cation of the tetragonal P4/mbm structure of isoelectronic compounds like U Ni In and U Pd In [36] and this doubling of the tetragonal c-axis in the Pt
G.H. Lander / Physica B 289}290 (2000) 1}9
compound may change radically the electronic properties. Both the U Ni In and U Pd In com pounds order AF, whereas U Pt In does not [36]. Muon experiments in zero "eld have shown no depolarization e!ects, indicating no long-range order, but there is a line broadening below &7 K. There is a peak in s also at 10 K. These two ,A measurements suggest (although they do not prove) that AF yuctuations may be present. We set out to "nd evidence for such #uctuations using a large single crystal and the IN14 3-axis spectrometer at the ILL, Grenoble. So far we have failed to "nd any positive evidence. The di$culty is to know where to look in Q-space. If &10 K is the relative energy scale then that is &1 meV ("11.4 K) so the energy scale is probably OK for IN14, but even this may be too naive. Initially we searched around the AF wave vectors of U Ni In and U Pd In but then widened our search. These latter two, as we discussed above, have a di!erent (simpler) atomic structure so these wave vectors may not be relevant. Recently, after our experiments, we have learnt of the AF structure of the isostructural U Pt Sn compound [37] which is complicated with q "[0, 0, 0.1823]. Al though we have scanned over this position it perhaps warrants another look.
5. NpO2 Neptunium dioxide has an extraordinarily interesting history. At "rst glance it would appear simple. We assume Np>#20\ and since Np> : 5f is a Kramers ion the ground state at ¹"0 K should be magnetic. Speci"c heat on NpO was "rst reported in 1953 [38] and showed a large anomaly at 25 K. In 1968 MoK ssbauer experiments [39] showed that a very small hyper"ne "eld, corresponding to a moment of &0.02l appeared below 25 K. Many neutron e!orts were undertaken; the last one on the largest available crystal of 0.5 mm being reported in 1987 [40]. They all failed to observe any peaks from an ordered moment. Although there were many ideas about NpO in recent years (see Ref. [41] for more details) the initial breakthrough on NpO came with the muon
7
experiments at PSI of Kopmann et al. (1998) [42]. By measuring the zero-"eld spectra of both UO and NpO they showed that a very similar signal developed in NpO below 25 K as was found in UO below 30 K, except that the signal was much weaker in NpO . Since both these materials are semiconductors (and if they could be obtained 100% pure and defect free one might expect they would be insulators), then there is always the risk of muonium production when muon experiments are attempted. Fortunately, this appears not to be the case, as the experiment on UO , which has a well-charac terised AF con"guration, show. The close similarity of the ZF spectra leads to the suggestion that the AF arrangements in these two materials is the same, but that the ordered moment in NpO is about 5%, i.e. &0.1l , compared to that in UO . We have been working a lot recently with RXMS-resonant X-ray magnetic scattering, which is a technique in which the photons are tuned to an absorption edge of the material in question and a large (depending on the edge in question) enhancement of the magnetic response occurs. Numerous reviews of this technique exist (see for e.g., Refs. [43,44]) and I have even presented a short review speci"c to actinides [45]. Because of the special conditions that the actinide M edges, which represent transitions from the core 3d to the partially occupied 5f shells, have an energy (&4 keV) that can be used for di!raction experiments, studies of the actinides are particularly powerful. Photon beams from 3rd generation machines, like the ESRF in Grenoble, have very small beams (0.2;0.2 mm) so small samples of much less than 1 mg can be used. This is an advantage in NpO where only small crystals are avail able. In 1998 at the ID20 beamline of the ESRF we did such an experiment with the photon energy tuned to the Np M edge of 3.845 keV on a crystal of NpO and almost immediately found a strong re#ection at the (structurally forbidden) (0 0 1) and (0 0 3) re#ections. The intensity as a function of Q and temperature is shown in Fig. 7(a) and the exact AF con"guration worked out by comparing the relative intensities of a number of peaks is shown in Fig. 7(b). It is di!erent from that of UO , where the #!#! sequence is the same but the
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G.H. Lander / Physica B 289}290 (2000) 1}9
Although the RXMS technique has many advantages, it has one considerable disadvantage and that is that the signal cannot (yet) be related to the magnetic moment [43}45]. Thus, we cannot tell the moment in NpO even though we know the mag netism is long range. We therefore fall back on the MoK ssbauer and muon values of 0.02 and &0.10l , respectively. Our experiments shed no light on why this small moment exists. NpO is, of course, not a HF mater ial so another mechanism, perhaps quadrupolar ordering as has been proposed for the small moments in UPd [46], are the answer, but at least both muons and a scattering technique have observed the ordered magnetism.
6. Conclusions
Fig. 7. (a) Normalised temperature dependence of the (0 0 1) (open triangles) and (0 0 3) (open circles) magnetic Bragg intensities. The straight line corresponds to the exponent b"0.5, which is the molecular "eld value, with ¹ "25.3(1) K. The , inset shows data for the specular (0 0 3) re#ection at 10 K as a function of the momentum transfer component, ¸; (b) The #uorite crystal structure of NpO is shown. The larger circles represent oxygen, and the 8 oxygen atoms surrounding the Np atom on the top face are shown. The arrows indicate the components of the magnetic structure propagating along the [0 0 1] axis. This is a simple #!#! (type-I) alternating sequence of ferromagnetic planes. The real-magnetic structure is triple-q, i.e. all three equivalent 10 0 12 components exist simultaneously (Taken from Ref. [41]).
moments in UO are perpendicular to the propa gation direction, whereas they are parallel to this direction in NpO .
The enigma of superconductivity together with magnetism, or at least magnetic correlations, remains a common theme of both heavy Fermions and high ¹ , and, as such, remains one of the greatest challenges in solid state physics at the end of this century. The last 10 years have established that the superconductivity is not s-wave (BCS), but there is little agreement on what is the correct symmetry. Indeed, it seems likely that a variety of symmetries are possible. Small moments } or at least correlations between spins } appear a likely key for a potential to drive the superconductivity. Muons have played a key role in showing the presence of such small internal magnetic "elds. Neutrons have then been able to amplify the form of the correlations as they are measuring in both Q and E space. Often the results from the two can be reconciled, but not always. UBe is a case in point. I have also introduced a new technique, resonant X-ray scattering, using tunable photons from synchrotron sources, as this is especially powerful in studies of actinide materials.
Acknowledgements I am particularly indebted to my colleagues in these endeavors. In rough order of the projects they are: N. Bernhoeft (CEA-Grenoble), A. Hiess (ILL,
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Grenoble), B. Roessli (PSI, Switzerland), N. Sato (Tohoku Univ., Sendai, Japan), S. Coad and A. MartmH n-MartmH n (ITU and ILL), D. McMorrow (Ris+ National Laboratory), G. Aeppli (NEC, Princeton), D. Mannix (ITU and ESRF, Grenoble), C. Vettier (ESRF), R. Caciu!o (Univ. Ancona, Italy), and F. Wastin and J. Rebizant of ITU, Karlsruhe. Despite the long hours and frequent frustration these experiments have been both rewarding and fun! Many thanks to all of them.
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Comments G.M. Luke: Is there evidence that the inelastic response in UBe13 is of magnetic origin? G.H. Lander: Normally this is easy to distinguish as magnetic ewects decrease slowly with Q (momentum transfer) whereas charge ewects increase as Q2. Our measurements are at small Q, where charge ewects are usually hard to see. Also the extinction rule (no scattering along [1 1 0]) would be very dizcult to understand if the ewects were charge related. The more dirct method of polarisation analysis is probably impossible with such a weak signal.