Heavy-electron metals: new highly correlated States of matter.

New data on the three major determinants of the carbon release from tropical forest clearing are used in a comput er model that simulates land use change and its effects on the carbon content of vegetation and soil in order to calculate the net ßux of carbon dioxide between tropical ecosystems and the atmosphere. The model also permits testing the sensitivity of the calculated ftu.x to uncertain ties in these data. The tropics were a net source of at least 0.4 x 10 15 grams but not more than 1.6 x 10 15 grams of carbon in 1980, considerably less than previous estimates. Decreases in soil organic matter were responsible for 0.1 x 10 15 to 0.3 x 10 15 grams of the release, while the burning and decay of cleared vegetation accounted for 0.3 x 10 15 to 1.3 x 10 15 grams. These estimates are low er than many previous ones because lower biomass esti mates and slightly lower land clearing rates were used and because ecosystem recovery processes were included. These new estimates of the biotic release allow for the possibility of a balanced global budget given the large remaining uncertainties in the marine, terrestrial, and fossil fuel components of the carbon cycle.

At room tempcrarures and above, hcavy-clcctron systcms bchavc as a wcak1y interacting collcction of f-clcctron momcnts and conduction dcctrons with quite ordinary masscs; at low tcmpcrarures the f dcctron moments bccome strongly couplcd to the conduction clcctrons and to onc another, and the conduction-dcctron cffcctivc mass is typically 10 to 100 times the bare clcctron mass (3). A numbcr of thesc systems bccomc supcrconducting, a quitc surprising rcsult given the fact that in ordinary supcrconduaors a dilutc conccntration of magnctic impurities dcstr0ys supcrconductivity (18). Indccd in both UPt 3 (19) and URu2Si2 (S) rccent cxpcriments suggcst that on lowering the tempcrarure an antiferromagnctic transition is followcd by a transition to the supcrconducting statc, whercas in U 0 . 97 1bo. 03 Bcll the order of the transitions is rcvcrscd (9). Morcovcr, wc shall sec that thc physical mcchanism rcsponsiblc for supcrconductivity is an anractive interaction bctwccn elcctrons that rcsults from a virtual cxchange of local momcnt 6uauarions, rather than the cxchangc of phonons that lcads to supcrconductivity in ordinary mctals.
Thus in hcavy-clcetron systems one sces realiud two long- cherished beliefs of the late Bernd Matthias: that superconductivity and magnetism are not murually inimical, and that a magnetic interaction can give rise to superconductivity. Matthias (20) first put magnetic impurities into superconductors some 30 years ago to explore these possibilities. Although he did not discover heavyelectron superconductors, Jus seminal investigations and his drive to explore new materials have been a continuiog source of inspiration. Figure 1 illustrates the richness of response of heavy-electron systems to the addition of impurities. There one sees that at zero pressure on adding minute amounts of thorium ( a nonmagnetic impurity, which primarily acts to increase the system volume) to Uße 13 , the transition temperature decreases markedly until, at an impuriry concentration of-2%, a cusp in the transition temperarure (Tc) curve appears: further additions of thorium lead to an increase in Tc, accompanied by a second transition at T-0:4 K (11). Rcccnt muon spin relaxation experiments (9) show that the second transition is accompanied by the onset of magnetism. The application of pressure P (21) to the system shifts the transitions; for P ;;::; 9 kbar, superconductivity is completely absent for a range of conccntrations; at 12 kbar that range is berween -2.5% and -4.5% of thorium. This remarkable phase diagram results from the highly concentration-dependent intcrplay berween antiferromagnetic moment flucruations and superconductiviry.

Normal State Behavior
Some unique fearures of the low-temperarure normal state properties of heavy-electron systems [ Fig. 2 and Table 2; see (22-39)] include: 1) An anomalously !arge specific heat. The ratio of specific heat to temperamre, C(T)IT = -y(T), is a measure of the temperaruredependent electronic density of states near thc Fermi surface, and as shown in Tablc 2, for tcmperatures bclow 10 K is somc two or more orders of magpirude in excess of that observed in ordinary metals. Moreover, -y(T) continues to be highly temperaturc-depcndent for temperarurcs below 10 K-a striking contrast to the temperarureindependent -y usually observed in a meta! (Fig. 2).
2) Highly temperature-dependent de Haas-van Alphen oscillation amplitudcs measured at T ~ 0.1 K in UPt3 (40) and CeCu6 (41) that confirm the presence of conduction clectrons with cffo:tive masses one to rwo orders of magnirude greater than observed in ordinary metals.
3) A magnetic susceptibility, x(T), that continues to vary with 34 temperature bclow 20 K, and is somc rwo or more orders of magnitude !arger than the temperature-independent Pauli susceptibility observed in this rcgion in an ordinary metal. The susceptibility is highly pressure-dependent, as evidenced by a magnetostriction (42) that exceeds that of a transition meta! by rwo or more orders of rnagnirude. 4) A usually negative thermal expansion, the magnin1de ofwhich dwarfs the positive thermal expansion of an ordinary meta! by some four orders of magnitude (43) . 5) Low-temperarure transport properties that diffcr markedly from those of ordinary metals. For exarnple, the rcsistivity displays a rapid variation with temperature below 10 K, whereas the resistivity of a normal meta!, dominated by impurity scattering, is nearly constant over this region. For a number of heavy-fennion systems, the low-temperarure resistivity takes the form p = p 0 + PeeT 2 at the Jowest temperarures. The temperarure-independent contribution, p 0 is comparable to rhat found in moderatcly pure ordinary metals, whereas the coefficient, Pee, which measures the importance of electron-electron scattering, is six to nine orders of magnirude !arger than its value in an alkali metal.
6) A remarkable sensitiviry to impurities. For example, the substimtion of3.4% ofthe uranium in UBe 13 by thorium leads to a 37% increase in -y(O), whereas the substitution of a similar amount of lutetium depresses -y by the same amount (44).
2) A !arge, nearly temperature-independent resistivity at room cemperarure, wluch is some two orders of magnirude !arger than that of sodium, and an order of magnirude !arger than that of palladium. Moreover, in all heavy-fermion compounds other than UPt 3 and UA1 2 , the resistiviry near room temperarure increases as the temperarure is decreased, whereas in normal metals the opposite behavior is observed.
2) In materials that do not order magnetically, a peak in the specific heat at roughly the same temperature as the resistivity maximum.
2) A simple arrangement of the ordered moments. The ordered moments are commensurate with the uranium sitcs. In U 2 Zn 17 , the direction of the moment alternatcs from uranium site to uranium site (55), but in UCu 5 tbe moments are aligned ferromagnetically within a plane and anriferromagnetically berween planes (56).

4)
A total entropy that is very much Jess than that one would expect for a collection of disordered moments. Moreover, the total entropy below T N is approximately 25 to 30% less than 'Y(T N)T N· This has led to the speculation (57) that were it not for the onset of magnetic ordering, 'Y(T) would continue increasing with decreasing temperature. 5) A TN that is in general weakly prcssure-dependent, the exception being UCd 11 , which develops rwo additional phase transitions ( at 3 kbar and at 16 kbar) below T N ( 58).
6) An unusual sensitivity to impurities. For example, in U 2 Zn 17 , replacement of 2% of the zinc atoms by copper (which has no magnetic moment) totally supprcsscs the magnetic state, whereas 'Y(O) is increased by some 10% (59). 7) A !arge linear contribution to the specific heat below T N. Extrapolarions of 'Y(T) ro zero temperature from specific heat data obtained in the antiferromagnetic states ofU 2 Zn 17 and UCd 11 give a finite -y(O) that is some 40% of that obtained by extrapolating the paramagnetic specific heat data to T = 0 ( 60). This suggests that heavy electrons exist in the antiferromagnetic state. Moreover, for UAgCu 4 and UCu 5 , -y(T) increases with decreasing T for T :S 0.2 T N (4).

Systematics
lt is known that cerium and uranium, and in a few cases other f elements, can form heavy-electron compounds. Although we have little predictive capability concerning the formation of heavyelectron statcs, certain patterns in their occurrence are clear. Hili (61) first pointed out that when the ff spacing in cerium and uranium intermetallic compounds is lcss than approxin1ately 3.4 A, fbands can form, and nonmagnetic behavior results. Magnetic behavior occurs at !arger separations. For hcavy-electron behavior it appears tobe necessary for thefatoms tobe beyond rhis Hill limit of 3.4 A, whereas the absence of fatom near neighbors seems necessary for vcry !arge 'Y· (UAl 2 , whose ' Y = 140 mJ mo1-1 K -2 , docs have uranium-uranium near neighbors.) The magnctic bchavior of both cerium and uranium varics strongly with thcir apparent atomic radii in the compounds; !arge radii favor local momcnt behavior and the formation of heavy-electron states.
3) A magnetic moment in the ordered state at most only 40% of the cffective moment deduced from the high-temperarure susceptibility.
Another regularity emergcs when one examincs where elements rhat form heavy-electron binary compow1ds with uranium occur in the periodic table. These are found at the end of the d-block and the beginning of the .rp-blocks where few statcs are available for hybridization with the f eleetrons. This ha~ led to the suggestion Table 2. Some low-temperature properties of heavy-electron compounds comparcd with those of palladium and sodium. All quantitics arc infcrrcd from mcasurements at the lowest temperaturcs for which the normal state has been investigated. Nurnbers in parenthcscs are literarure citations. Multiple values separared by slashes indicate different crysta!Jographic directions.
The local chemical envirorunent of the f atom is clearly important.
An example (14) of how sensitive the many-body effects can be to this is provided by UPt 5 . This cubic compound has a slight!y enhanced -y of 85 mJ mo1-1 K-2 • Substitution of platinum by gold to form UAuPt.i, which has the same crystal structure, changes -y to 700 mJ mo1-1 K-2 • lt is believed that here uranium is tetrahedrally coordinated by gold. AJthough many of the bulk properties of the heavy-e!ectron comp9unds are extreme, ratios such as -y/x have values similar to those of simple metals (60). lt is instructive to tabulate the heavyelectron compounds wich respect to "'(v, the -y per unit volume (see Table 2). The tabulation (60,62) for the uranium heavy-electron compounds shows a surprising regularity as "Yv increascs, from spin fluctuating systems to magnetically ordered heavy-fermion systems to superconducting heavy-fermion systems. lt is a task of theory to understand why the superconductors occur at largest "Yv, and why, additionally, these particular hcavy-clectron compow1ds seem to have -ylx closcst to the free-electron value.

Physical Picture
W e have seen that the physical behavior of heavy-electron systems changes dramatically as the temperature is lowered. Consider the magnetic susceptibility: at high temperatures its temperature dependence is that of a collection oflocal moments, whose magnirudes are close to those found in free atoms; at low temperatures its large and nearly temperamre-independent value is of the same order of magnitude as a meta! in which the itinerant electron density of states is two or more orders of magnitude !arger than that cncountered in normal metals. The fact that in the nonmagnetic normal state at low tempcratures, the specific hcat has a !arge contribution, which varies as Tin many cases, suggests that itinerant electrons, wich an effective mass comparable to the muon mass, dominate the thermal behavior there. In similar fashion, ehe low-temperature transport properties exhibit ehe behavior expectcd (63) for a Fenni liquid made up of heavy clectrons that scatter against impurities, against localized spin fluctuations, and against one another.
Tims, at high temperatures, hcavy-elcctron systems bchave like a weakly interacting colkction of local moments and conduction electrons, whereas at low temperatures, so far as the. rmal and transport properties are concemed, thcse systems behave like a collection of heavy itinerant clectrons that scatter against one another and may, under some circtunstances, exhibit a transition to a superconducting state. Accounting for the transition between thcse two regin1es is a central problem in w1dcrstanding heavy-electr~n systems. The transition is not a sharp one (in the sense of ordinary phase transitions) and may be viewed as a transformation or metamorphosis, a reversible analogue of the process in the chrysalis by which a caterpillar becomes a buttcrfly. In both cascs the end product can be simply characterized, whercas the physical behavior evidenced during the transformation is complex and de.fies simple characterization.

Kondo Systems
lt is natural to inquire whether there are any other systems that display similar behavior. One dass, which is frequemly mentioned in conncction with hcavy-clectron systems, is simple mctals containing dilutc conccntrations of magnetic impuritics. The physical properties of these systems arc successfully described by the Kondo model ( 64) in which a d-or f Ievel of thc impurity has an energy just below the Fermi level. At high temperatures the impurity displays localmoment bchavior, whcreas at low ccmperatures the spin of the impurity is compensated by a conduction electron cloud, and the magnetic susceptibility is independent of tcmpcrature and has a higher value than its free-electron value. The increase reflects the exiscence of a narrow resonance, of width -T K, d1e Kondo tcmperarurc, in ehe scattcring of conduction electrons by the impurity spin and its compcnsating cloud; thc increase is of order X;mp T FIT K , where Ximp is the impurity concentration and k 8 T Fehe conductionelectron Fermi energy. An additional contribution to the magnetic susccptibility, which can be of d1e same ordcr of magnitudc, comes from an induced effective interaction between thc conduction electrons, which is produced by a polarization of the compcnsated impurity spins. A final contribution to the magnetic susceptibility comes from the polarization of the compensated impurity spins by the extemal magnctic ficld.
Kondo systems have a finite electrical resistivity as a consequence of the scattering of the conduction electrons by thc compcnsated impurity spin. The resistivity is a maximum at zero temyerature, where thc scattering is resonant, and it falls off as (TIT K) , in part bccause tl1e scattering is off rcsonance, and in part because of the importancc of inelastic scattering. On the other hand, the spcci.fic heat, linear in temperature at low temperaturcs, rcachcs a maximum at tcmpcratures -T K, bcyond which it falls off with increasing temperature. Nozieres (65) has constructed a Fermi liquid model for the behavior ofthe conduction electrons around thc impurity, and has shown how the low-temperature behavior of tl1e spccific heat, SCIENCE, VOL. 239  resistivity, and magnctic susccptibility, brought about by thc tcmperaturc-dcpcndent Kondo resonance, can be cxprcssed in tcrms of a few Fermi Liquid paramctcrs. At first sight onc might hopc to explain the propertics of hcavyfermion systems by regarding thcm as a collection of independent compcnsatcd spins, with propertics sinular to thosc dcscribcd above, placed on a lattice. [Calculations based on such a modcl are reviewcd in Fulde et at. (3).] Howcvcr, this picturc cannot be true in dctail.
First, in this picrurc one would cxpcct all heavy-fermion systems to exlubit maxima in the resistivity, a prcdiction in conf!ict with experimcnts. This maximum would come about because scattering from a magnctic site is partly elastic and partly inelastic. Whcn thc sitcs are in a periodic array, only thc inelastic scattering lcads to real scattcring proccsscs, whcreas the elastic scattering creates band structure in the clectron spectrum. The total cross scction for a singlc magnetic site to scatter an electron increascs as thc tcmpcrature decreases, and the scattcring bccomcs increasingly elastic at tempcratures below the Kondo temperarure. At high tempcratures thc significant scattcring is inelastic, whereas at T = 0 it is completely elastic. Consequcntly, as the temperaturc decrcases, the inelastic scattering cross section first increascs, rctlccting the incrcase in the total cross section, and thcn dccrcases to zcro at T = 0.
Sccond, with a finite density of magnetic impurity sitcs, thc interaction berwecn the itincrant electrons is no langer determincd by the polarization of a single compensatcd impurity spin, but rathcr retlects the presence of other compensated spins, whcreas the repcated interaction of the itinerant electron-holc pairs can botl1 scrcen thc cffectivc intcraction between compcnsatcd spins, and give tcmperarures are superpositions of localized clectrons and conduction electrons. Thcir quite strong interaction reflects not so much their direct Coulomb interaction, as it does an interaction induccd by their coupling to spin fluctuations on tllc magnetic sitcs, and it providcs a natural cxplanation for tl1c large finitc-temperature corrections to thc low-tempcrature form of tlle specific heat, and tllc strong temperarure dependence of tlle clectrical resistivity and otllcr transport coefficients.

Fermi Liquid Theory
In tlle low-temperature limit the tllem1al and transport properties of heavy-fermion systems in tlle normal state should be tllosc cxpccted for hcavy-clectron Fermi liquids. However, in most cases expcrirncnts have not yet been carried out in tllc Landau Limit, that is, at tempcratures sufficiently low tl1at one can neglect, in first approximation, tlle frequency dependence of tlle quasiparticlc energies and quasiparticle scattering amplitudes associated witll tlle coupling of tlle conduction electrons to tlle localized f electrons. If WC definc ecoh as tlle temperature below which tllc eJectrOruC specific heat is Linear in T, and tllc elcctrical and tl1crmal rcsistivities fall off sharply witll decreasing tempcrature, tllcn it is only at temperatures T < < ecoh tllat one expects to observe tlle Landau tcmpcrarure dependcnce, in which tllc finite temperature corrections to tllc low-temperaturc limiting behavior of tlle electrical resistivity, p (Fig. 5), tlle tllermal resistivity times tlle temperature, WT, and tlle ultrasonic attenuation coefficient ex (Fig. 6) arc proportional to T 2 • Such Landau limiting bchavior is observed for UPt 3 at temperarures below -1.5 K (31 ), but UBe 13 at zcro prcssure bccomes a supcrconductor well before it reaches a temperaturc at which Landau thcory would apply (63,67).
Landau tl1eory is a very gencral framework tllat makes few spccific assumptions about tllc nature of tlle system to bc dcscribcd; detailed microscopic physics is contained in tllc paramctcrs tllat cntcr tllc tlleory (68). It has proved to bc highly successful in providing an account of tllc low-tcmperamrc propertics of tlle "canonical" Fermi liquid, 3 He (69). Q uite generally, it predicts a low-tcmperaturc specific heat containing tllc well-known term Linear in T. Interactions between quasiparticles lcad to T 3 ln(I) contributions to tlle specific heat as weil as a quasiparticlc collision rate proportional to T 2 • In 3 He tlle most important contribution to tllc quasiparticle scattcring amplitude is tlle exchangc of spin flucmation excitations, risc, at low tcmperatures, to markedly enhanced low-frcqucncy spin ~ 4 f:Juctuation cxcitations.  and it is this interaction that is responsible for the !arge T 3 ln(1) contribution to the specific heat, and for the transition to the superfluid state. The appearance in UPt 3 of a !arge T 3 ln(1) term in the specific heat and superconductivity led Stewart et td. ( 13) to suggest that spin fiuctuations might play a role in this heavy-fermion compound comparable to that in 3 He. At first sight one might hope to be able to make quantitative calculations for heavy-electron systems by straightforward application of Landau theory. However, there are significant differences between hcavy-fermion systems and 3 He that make Landau theory for heavy-ferm.ion system.s much more complicated than for 3 He. As a result of the crystal lanice, heavy-ferm.ion systems are intrinsically anisotropic and the electrons are not Galilean invariant. One consequence of the latter effect is that the elcctron effective mass is not simply related ro a moment of the quasipartide interaction. Because of spin-orbit coupling, the nature of the quasipartide states is difficult to specify and their magneric moments are not sirnply rclated to d1e free-electron moment, and, more important, there are significant nonquasipartide contributions to the static magnetic susceptibility, so that quasiparticle properties cannot bc deduced direcdy from measurements of the susccptibility.
An initial anempt at applying Fermi liqltid theory to UPt 3 has been made by Pethick et al. (70) and by Hess (71). They have approximated UPt 3 as an isotropic Fermi liquid of pseudo-spin 1/2 partides and have shown that it is possible to obtain a quantitative account of the compound's low-temperature thermal and transport properties, and of the quasipartide contribution to the spin fluctuation excitation spectrum, starting with a single Fermi liquid paran1eter [ for a review of this approach, sce ( 63 )]. The recent de Haas-van Alphen measurements ofTaillefer et td. (40) show that the Fermi surface is multisheeted, consistent with density-functional calculations. Thc Fermi surface, therefore, is more complicated than assumed in the earlier cakulations and is characterized by considerably smaller values of Fermi wave number kF and effective mass m*. Consequently, the agreement with experiment may prove to be fortuitous.

Magnetic Properties
W e turn now to a consideration of the magnetic properties of heavy electrons. Here one needs to take into account cxplicitly the presence of compensated local moments at each lattice site. We recall that the same strong coupling between the felectrons and thc conduction electrons, which is responsiblc for tl1e heavy itinerant quasiparticles, will give risc to a compensating electron doud that will alter the magnetic response of the local moments. If magnetiza- 38 tion were a conserved quantity, the local moments and their compcnsating elcctron clouds would not contributc to the long wavelength magnetic susceptibility, x(1), at low temperatures; that quantity would be cntirely determincd by the heavy-electron quasipartide contriburion, Xqp· Because magnetization is not conscrved, thcrc can be a significant nonquasipartide contribution, Xioc to x(1), which arises from thc polarization of the local moments and their compensating clouds (that is, from virtual excitations at finite frequencies). This polarization, in the Kondo model, would corrcspond to finite-energy transitions betwcen the singlct ground state and finite spin excitcd states.
In neutron scattering experirnents, which measure the spin flucruation cxcitation speetrum, onc would thereforc expect to sec long wavelength excitations of two sorts: (i) thosc associated with itinerant heavy electron-hole pairs, whose frequency vanishes in thc long wavelength limit, and (ii) those from the compensated moments of the felectrons at magnetic sites, whosc frequency remains finite in the long wavelcngth limit. Thc prcsent evidencc is that in the four heavy-electron systems for which detailed ncutron scattering experiments have been carried out [UPt 3 (72), U 2 Zn 17 (73), URu 2 Si 2 (74), and CeCu 6 (75)], the dominant contributions to the measured spin fluctuation excitation spectra are those of thc compensated local moments. Evidencc for antiferromagnetic coupling between locaJ moments on different sites is found for all thcse systems. As was thc case at high tcmperatures, tlus intcraction reflects not a direct exchange, but rather one induced by the coupling of the local momcnts to the itinerant electrons. A model in which that intcraction is constant between nearest neighbors has been shown (75) to provide a fit to the data in CeCu6' whereas for U 2 Zn 17 a temperature-dependent nearest ncighbor intcraction that incrcascs with dccrcasing temperature below 18 K has been found (73) to drive thc antiferromagnetic transition at 9.7 K.
The presence ofheavy itinerant electrons in the antifcrromagnctic state is consistent with the above picnire, since it is the local moments that order antiferromagnetically as a result of nearest neighbor coupling. The observed reduced statc dcnsity could result from eithcr a change in thc area of the Fermi surface occupicd by the heavy electrons, or may reflect a change in the average Fermi vclocity VF of these electrons. To the extcnt that the physical origin of the antiferromagnetic behavior is the local moment interaction, it is likely that nesting of the Fermi surface plays little rolc; hencc it would seem plausible that the Fermi surface area occupied by the heavy electrons is relatively unchanged, and what is observed is a substantial incrcase of their average Fermi vclocity. A change in VF should not be surprising, since it is the coupling between rhe itincrant electrons and the local moments that is responsiblc for the heavy-electron mass, and this coupling will change below TN, since there the spectrom of local moment fluctuations will change, as a consequencc of tl1c appcarance of antiferromagnetic spin waves characteristic of the ordcred magnetic state.
The compound URu 2 Si 2 is a particularly intercsting systcm because it exhibits both an antifcrromagnctic transition at 17.5 K and a subsequent supcrconducting transition at T 0 = 1.2 K (5). In this system the attractive interaction bctwccn tl1c heavy itincrant electrons induced by their coupling to the antiferromagnetic spin waves would seem a srrong candidate for the physical origin of the superconducting transition.
1n UPt 3 , one can show (72) from the ncutron scancring rcsults for X1oc that thc magnitude of the locaJ fluctuating magnetic moment is considerably lcss than its high-temperature value, whereas the quasipartide effective magnetic momcnr is markcdly rcduccd below a Bohr magneton. Neithcr of these reductions should be regardcd as especially surprising, given the antiferromagnetic nature of the correlations that characterizc hcavy-clcctron behavior. SCIENCE, VOL. 239 To put in perspective the ways in which heavy-fermion superconductivity differs from that of ordinary metals, wc review the salient features of the successful microscopic theory of superconducrivity developcd by Bardeen, Coopcr, and Schrieffer (BCS) (76). Thc attractive interaction betwecn electrons that is brought about by exchange of virtual phonons gives rise to an instability in the bchavior of pairs of electrons near the Fermi surface in singlet states, and Jeads to a gap in the electron spectrum at the Fermi surface. This gap is finite everywherc on thc Fermi surface, and as a consequence many properries, such as the specific heat and transpon coefficients, fall off exponentially with decreasing tcmpcrature. Tbc orbital part of the wave function associated with the pairs has s-Jike charactcr, and the gap is essentially constant over thc Fermi surface. In some mctals the crystal Jatticc can introduce some anisotropy in the gap, but in most cascs this is modest.
In the decade or so following the development of BCS theory, and especially after the experimental discovery of thc superfluid phascs of liquid 3 Hc (77), thcorists explorcd the possibility of pairing with a more complicated orbital structure (jJ-wave or dwave, for example), in which the gap can vary in both magnitude and phase with position on thc Fermi surfacc. (In the case of odd partial wave pairing, the pairs are forced by the Pauli principle to have triplet, rather than singlet, spin wave functions.) Many of these states have nodcs of the gap at points or on lines on thc Fermi surface, and conscquently thc numbcr of excitations in such statcs at low temperatures varies as a power of the temperarure, rather than exponenrially. Following a rather hecric 2-year period of exploration of possible states, it was escablished (78) that the pairing in liquid 3 He is in two distinct p-wave states, the A phase corresponding to the Anderson-Brinkman-Morcl (ABM) statc (78), which has point oodes on the Fermi surface, and the B phasc to thc Balian-Wcrthamer state (79), which has a gap of constant magnimdc ovcr the Fermi surface, but varying phase. In these p-wave states the pairs arc in triplet states, as required by the Pauli principle, and they possess magnetic properries very difterent from singlet pairing states; these provided invaluable clues in the detectivc work to pin down thc nature of thc scaces.
Research on the supcrconducting phases of the heavy-fermion superconductors is currently in a period rcminiscent of the years immediately following the discovery of the supcrfluid phases of 3 He. Thcorists arc studying the microscopic origin of the interactions responsible for superconductivity and the nature of the resuJting pairing states, and experimcntalists are searching for phenomena that may provide evidence for the nature of the encrgy gap.
A fundamental question in conncction with the observation of supcrconductivity in heavy-electron systems is whethcr it is the heavy elcctrons thcmsclves that become superconducting. Clcar 1 JANUARY 1988 evidencc for the pamng of the heavy electrons is provided by measurements of the jump in the specific heat at the transition temperaturc, Tc, to the supcrconducting phasc. Quite gcnerally in pairing theories of superconductivity, such as the BCS theory and its generalization to anisotropic states, one expects a specific heat jump proportional co the normal state specific heac of the electrons that bccomc supcrconducting. The fact that the measurcd jumps (5,10,12,13) are comparablc to thc specific heat in the normal state above Tc shows conclusively that the superconductivity is associated with the heavy elecrrons, rather than a possible band of light electrons that wouJd provide but a small patt. of the normal state specific heat.
A second fundamental question is whcther the superconducting cnergy gap has nodcs on thc Fermi surfacc, and, if so, what thcir character is. Experimentally, no equilibrium or transport properties in the heavy-fermion superconductors exhibit the exponential behavior expected for states with a nonzero energy gap everywhere on the Fermi surface; rather both specific heat and transport measurements display the power-law behavior that is characteristic of states with gaps that vanish at points or along lines on the Fermi surface. Spccific hcat mcasurements at low temperarurcs, which rcflcct thc density of quasiparticle states at encrgics of ordcr k 8 T, give direct evidence about the nodes of the gap. At low temperaturc, the only quasiparticles excited will be those in the vicinity of nodes of the gap. These states possess an encrgy less than kaT and lie within an angle -Tl 6. of a node, wherc 6. is the maximum value of the energy gap oo the Fermi surfacc. A simple geometric argumcnt shows that the density of quasiparticles varies as T 2 for nodes at points and as T for nodes on lines, and the corresponding variacion of the specific heat is as T 3 and T 2 , respectively. In this way the experimental measuremcnt ( 80) of a T 2 dependence of the specific heat for UPt 3 shows that thc encrgy gap vanishes on a line or Jines, wlule the T 3 depcndence found (44) in UBe 13 is indicative of a gap that vanishes at points. Thus heavy-fermion systems posscss at least two superconducting staces. Since Uße 13 possesses cubic symmetry, whercas UPt 3 is hexagonal, it is possible thac crystal scructure plays a role in determining the nature of thc superconducting statc. Evidence that suggests the possible existence of two superconducting statcs in a singlc sysccm is provided by specific heat (44) and critical field cxpcrimcnts (81) on U1-xThxBe 1 3, where x lies between 2 and 4% (Fig. 7).
A third question of interesc is where the nodcs lic on thc Fermi surface. Information about this is contained in mcasurements of transport coefficients such as acoustic attenuarion. In UPt 3 thc attcnuation, ex, of transvcrse ultrasound propagating in thc basal plane (82) shows a different temperarure dependence according to whether ehe sound wave is polarizcd in the basal plane (ex oc T) or pcrpendicular co it (ex oc T2). These results suggest that quasiparriclcs movc morc freely in the basal plane than pcrpendicular to it, which w' mld be consistent with a quasiparticle gap having nodcs on Jines on thc Fermi surface perpendicular to the hexagonal axis. Further evidence for this bchavior of thc gap is provided by the reccnt tunneling measurements (83) that give no evidencc for a gap whcn quasiparricles are injected across crystal faces with normals perpendicular to thc hexagonal axis, but show a distinct gap when quasiparticles are injccted across faccs with normals parallel to the hexagonal axis.
Considerable effort has gone into trying to understand transport in the supcrconducting states. Under circumstanccs in which scattering by impurities is thc dominant process, as is tl1e case in UPt 3 at cemperacures of the order of Tc and lower, the temperature dependence of the transport coefficients seems to disagrce with calcuJations for any ruusotropic superfluid State if the scattering is trcated in the Born approximation. In this approximation the Jowest order swave scattering by a single in1purity is considered; the cakulated ARTICLES 39 Flg. 8. Uppcr critical magnetic field 10 ~~~~~~~~~~ Hc2 versus temperarure T for UBe13. 8 UBe In gencral, fearures around ehe nodcs arc smcared out by impuricy scactering. Evidence for this physical cffcct on thc densicy of scatcs in ehe superconducting state of UBc 13 has bcen found (88) in experimental measuremencs of ehe specific hcac at low temperarurcs (T c: 50 mK); ehe experimental rcsults are in excellent agreemcnt with cheoretical calculations of ehe scacc densicy thac assume an axial stace, in which ehe energy gap has poinc nodes, and clcctron impuricy scattering chac is near ehe unicaricy limit.
Therc can bc little doubt that ehe superconducting staccs obscrvcd in ehe hcavy-clcctron systcms are unconventional, whcn comparcd to cypicaJ metallic superconduccors. lt is therefore narural to inquire whecher ehe physicaJ origin of superconductivicy is likewisc unconventional, in that it docs not arise from an attractivc phononinduccd intcraction bctween clectrons. Although there is as yet no theoretical proof or dircct experimental demonstration that electron-phonon interactions are csscntially irrelevant to heavy-fcrmion supcrconduccivicy, in view of thc persuasive physicaJ argurnencs that ehe origin of the !arge masscs is ehe coupling of conduction cleccrons to ehe local moment fluccuations, and that ehe virrual cxchangc of such spin flucruarions givcs risc to an attractive interaction bccwcen heavy-clectron quasipartidcs, it would seem highly likcly that it is ehe eleccron locaJ momcnc fluccuacion coupling that is rcsponsible for heavy-elcctron supcrconductivicy. Whether ehe resuJting pairing statc is "p-like" o r "d-like" depends on ehe details of ehe wavevector dcpcndencc of ehe cffcctive attractive interaction.
3) The superconduccing propcrtics of UPt 3 are remarkably sensitive to small concentrations of impurities; for examplc, substitution (93) of less than 1 % palladium for platinum reduccs Tc to bclow 20 mK, and in general magnetic and nonmagnetic impurities both tcnd to strongly depress ehe transition cempcrarure.

Concluding Remarks
The qualitative description wc havc of heavy-clcctron systcms is attraccivcly simple. At high temperarurcs ehe fatoms bchave as a collcction of nearly indepcndcnc magnetic moments. Bccausc of the interaction becween fclcctrons and conduction electrons, ac lower tcmpcracurcs of o rdcr d1e Curie-Weiss temperarure 0 cw, thcse momcncs beco me scrccncd by ehe formation of a cloud of conduction electrons wich antiparallcl spin. At still lower tempcratures, cypicaJJy of ehe order of 0 cw/10, ehe residual interaction bcrwcen ehe fclectron momencs lcads to significant antiferromagnetic corrc-Jations among ehern. Thc interaction induced bctwcen itinera.nt eleccrons by the antiferromagnetic flucruations associaccd wich ehe correlacions is responsiblc for ehe enhanced electronic spccific hcat and thc superconducting transition. Such an interaccion inhibics ehe usual isotropic BCS pairing scatc but favors anisotropic pairing states characterized by ehe vanishing of ehe energy gap at points or on lines on ehe Fermi surface. For these anisotropic staccs, unlike ehe isotropic one, there is no confücc bcrween magnetic o rdering and superconductivicy, so that ehe cocxistencc of antifcrromagnctism and superconductivicy in somc heavy-clectron syscems may be vicwed as a naruraJ consequence of ehe fact thac a single inceraction is rcsponsible for both phenomena.
What is the relationship berwccn hcavy-elcccron syscems, ehe mixed-valence compounds and ehe transition metals? In mixedvalcncc compounds dor f shcU cnergy bands lie close eo ehe Fernl.i surface, and ehe Coulomb hybridization of eleccrons bclonging to ehe different encrgy bands plays a donl.inant rolc in dctcrmining system behavior. In heavy-clectron systcms, it is ehe magnctic SCIENCE, VOL. 239 interactions bcrween thc f electrons and the conduction electrons that are the dominant ones; to the extent that one tries to make a heavy-clectron system with an felectron band near the Fermi surfacc, Coulomb hybridization will inhibit the physical processes rcsponsible for the onset of the antiferromagnetic correlations that set the Stage for the appearance of characteristic heavy-ciectron phenomena. What makes the transition mctals so interesting (and makes it so difficult to develop a first-principles description of them), is that both Coulomb hybridization and magnetic interactions play a significant role in dctermining thcir bchavior.
What is the rclationship between heavy-electron superconductors, "ordinary" superconductors, and the very recently discovered (94,95) high Tc superconducring oxidcs? Somc 37 years after the discovery of the isotope effect (96) on the transition temperarurc of metallic superconductors, which demonstrated the important role played by phonons in determining the transition to the superconducting state, and 30 years after the microscopic BCS theory (76), which took as its starting point an attractive phonon-induced interaction berween electrons near the Fermi surface, a new mechanism for supcrconductiviry and new superconducting pairing states in metals have been identificd in the hcavy-electron sysrcms. lt is natural to inquire whether the high Tc superconducting oxides bclong to the same family as the heavy-electron superconductors (97); the detection of anrifcrromagnetic ordering (98) in pure La2Cu04 would seem to suggest this might bc thc case, but the isotropy of the energy gap inferred (99) from penetration depth measurcmcnts would appcar to argue againsr this possibility. lt rook some 3 years of intensive experimental and theoretical invcstigations for researchers ofheavy-electron materials to arrivc at a consensus on the physical picrure we have set forth in this artide; it would not bc surprising if a similar period of time might be required to arrive at a similar conscnsus on thc new high Tc marerials.

Tropical Forests and the Global Carbon Cycle
R. P. DE1WILER AND CHARLES A. S. HALL New data on the three major determinants of the carbon release from tropical forest clearing are used in a computer model that simulates land use change and its effects on the carbon content of vegetation and soil in order to calculate the net ßux of carbon dioxide between tropical ecosystems and the atmosphere. The model also permits testing the sensitivity of the calculated ftu.x to uncertainties in these data. The tropics were a net source of at least 0.4 x 10 15 grams but not more than 1.6 x 10 15 grams of carbon in 1980, considerably less than previous estimates. Decreases in soil organic matter were responsible for 0.1 x 10 15 to 0.3 x 10 15 grams of the release, while the burning and decay of cleared vegetation accounted for 0.3 x 10 15 to 1.3 x 10 15 grams. These estimates are lower than many previous ones because lower biomass estimates and slightly lower land clearing rates were used and because ecosystem recovery processes were included. These new estimates of the biotic release allow for the possibility of a balanced global budget given the large remaining uncertainties in the marine, terrestrial, and fossil fuel components of the carbon cycle.

HB CONCENTRATION OF CARBON DIOXIDE IN THE ATMO·
sphere has increased from about 280 parts per million (ppm) circa 1750 to about 345 ppm in 1984 (1). Because C0 2 and other trace gases (for exan1ple, methane, nitrous oxides, and chloro· fiuorocarbons) produced by industrial and agriculrural processes absorb thermal radiation emitted by the earth's surface (2), researchers have predicted that the increasing concentrations of these gases in the am1osphere will result in significant changes in climate (3), which in rum may produce substantial changes in the Jocation of agriculrural zones and shorelines ( 4). Because the effeas of C0 2 on climate are in some dispute (5), determining how carbon cycles among the armosphere, hydrosphere, and biosphere is of continuing interest.
Since 1977 this interest in the global cycling of carbon has involved a controversy between tcrrestrial ecologists and geochem- 42 ists. All panicipants agree that the principal cause of the increase in atmospheric C0 2 in recent years has bcen the combustion of fossil fuels, which relcased about 5.2 gigarons (GT; 1 GT = 1 x 10 15 g) of carbon during 1980. The kilning of limcstone for the production of cemcnt rcleased an additional 0.1 GT, for a total of 5.3 GT from industrial processes in 1980 (6). But long-term srudies of atJno· spheric C0 2 conducted at Mauna Loa since 1958 indicate that only 55 percent of the C0 2 released from industrial activities remains in the atmosphere (7). The most likely repository of some or all the remaining 45 percent is the oceans. Because it is not possible at present to measure directly the increase in inorganic carbon dissolved in seawater (8), estimates of the ocean's uptake of C0 2 have been based on models, most of which predict relatively small oceanic uptake (9). Present versions of these models estimate that the oceans sequester approximately 35 percent ofthe C0 2 released by industry (10). To balance their global carbon budgets, a number of geochemists posrulated that terrestrial ecosystems, like plants in greenhouses, increase tl1eir rate of photosynthesis in tl1e presence of increasingly elevated levels of C0 2 (11).
In 1977, however, several terrestrial ecologists conduded tl1at not only was it unlikely tl1at terrestrial ecosystems would increase their carbon storage in response ro increased at1nospheric C0 2 but that the destruction of these ecosystems, primarily tropical forests, was releasing nearly as much C0 2 into tl1e am10sphere as were industrial processes (12). In their view, the oceans were the only likely sink for both the fossil fuel C0 2 not found in the at1nosphere and the C0 2 released from forest clearing (12,13). Two early srudies suggested that the annual releases from forest clearing could be as !arge as two to four times those from fossil fuels and limestone (14), although these estimates were later revised downward (15). The geochemists, however, believed that their models of oceanic C0 2 uptake were sufficiently accurate to exclude the possibility of such a !arge crror in tl1eir estimates, and they attacked both conclusions of tl1e ecologists. They argued that too little was known about rares of forest