Superconductivity: PuCoGa5 to diamond

Superconductivity: PuCoGa5 to diamond

Journal of Physics and Chemistry of Solids 67 (2006) 557–561 www.elsevier.com/locate/jpcs Superconductivity: PuCoGa5 to diamond J.D. Thompson a,*, E...

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Journal of Physics and Chemistry of Solids 67 (2006) 557–561 www.elsevier.com/locate/jpcs

Superconductivity: PuCoGa5 to diamond J.D. Thompson a,*, E.A. Ekimov b, V.A. Sidorov a,b, E.D. Bauer a, L.A. Morales a, F. Wastin c, J.L. Sarrao a a

Los Alamos National Laboratory, Los Alamos, NM 87454 USA Institute for High Pressure Physics, 142190 Troitsk, Moscow Region, Russia c EC, JRC, Institute for Transuranium Elements, Post Box 2340, 76125 Karlsruhe, Germany b

Abstract We review experimental and theoretical studies of two new superconductors, B-doped diamond and PuMGa5 (MZCo, Rh). The pairing mechanism responsible for superconductivity in these materials remains ambiguous. Though electron–phonon pairing in B-doped diamond is a viable candidate, the Coulomb interaction in this poor metal must be understood before definitive conclusions can be drawn. The 5f electrons of Pu appear to play a decisive, but uncertain, role in producing superconductivity in PuMGa5. The possibility of magnetically mediated superconductivity in these materials is suggested by analogy to the evolution of superconductivity and magnetism in isostructural Ce- and actinide-based materials. q 2005 Elsevier Ltd. All rights reserved.

Superconductivity has been discovered recently in two extremely different and rather unlikely materials: PuCoGa5 [1] and B-doped diamond [2]. PuCoGa5 and subsequently discovered PuRhGa5 [3] are the first superconductors based on Pu and have transition temperatures of 18.5 and 8.7 K, respectively. These Tc’s are nearly an order of magnitude higher than found in any heavy-fermion systems based on Ce or U but are comparable to those in some conventional superconductors. This raises the question of whether superconductivity in these Pu-based materials is conventional or not. As will be discussed, there is growing evidence that these Pu superconductors are closely related to the isostructural compounds CeMIn5 in which unconventional superconductivity appears in proximity to a magnetic-non-magnetic boundary [4]. In contrast, superconductivity below 4 K in B-doped diamond emerges beyond a metal–insulator boundary. Though superconductivity in diamond may be conventional, possibly a three-dimensional analog of MgB2 [5,6], a more exotic pairing mechanism also has been proposed [7]. Here, we briefly review existing and new evidence pointing toward the origin of superconductivity in these disparate materials, beginning with B-doped diamond. Boron, with one less electron than C, acts as an acceptor and hole-dopes diamond. With increasing B, there is a metal– * Corresponding author. Tel.: C505 667 6416; fax: C505 665 7652. E-mail address: [email protected] (J.D. Thompson).

0022-3697/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2005.10.105

insulator (Mott) transition at a B concentration n z2! 1020 cmK3, beyond which the impurity band formed by donor states begins to overlap the valence band edge [8]. Though B-doped diamond is prepared most commonly by chemical vapor deposition, high-pressure, high-temperature synthesis techniques are particularly effective approaches to incorporating greater concentrations of B into diamond. In the initial report of superconducting diamond [2], B concentrations of z4.9!1021 cmK3 (0.028 B/C) were achieved by reacting graphite and B4C at high pressures (8–9 GPa) and temperatures (2500–2800 K) for about 5 s. Under these conditions, small B-doped diamond aggregates formed that were sufficiently large for electrical transport and magnetic susceptibility measurements. These experiments showed the onset of a resistive transition to the superconducting state near 4 K and zero-resistance below 2.3 K where a strong diamagnetic response developed. Though these measurements provided strong evidence for bulk superconductivity, the small sample mass and small heat capacity of B-doped diamond prevented the detection of a clear specific heat anomaly at Tc that would confirm the bulk nature of superconductivity. Subsequent to this initial report, we have prepared B-doped diamond using similar high-pressure, high-temperature conditions but with a starting mixture of 4% amorphous B powder in graphite. Analysis of X-ray diffraction patterns on the resulting diamond aggregates gives a cubic lattice parameter of ˚ , which is larger than the lattice constant of pure 3.573 A ˚ ) and indicates that B is incorporated into diamond (3.5664 A the diamond lattice. The lattice parameter of these new samples

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˚ reported earlier. however, is slightly smaller than 3.5755 A Hall-effect measurements on the new samples give, within a single band approximation, a carrier concentration of z1.8! 1021 cmK3, which is less than half the carrier concentration inferred from estimates of the B concentration in samples prepared with B4C. Additional, systematic studies are required to understand if this apparent discrepancy in carrier concentration is real or, more realistically, that it is an artifact of assumptions, e.g. that all B atoms were incorporated into the diamond lattice and that a single-band approximation is reasonable. In either event, the carrier concentration in both sets of samples appears to be above the Mott limit [8]. Fig. 1a shows the temperature dependence of the electrical resistivity of the new sample prepared with B powder. The overall shape of the curve, including a metallic-like resistivity (a)

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above about 250 K, is very similar to that reported earlier [2]. However, the magnitude of the resistivity in this sample is nearly four times lower, a discrepancy that probably arises from extrinsic effects. The inset shows the onset of a transition near 4.5 K to an immeasurably small resistance below 2.5 K. Both temperatures are comparable to but somewhat higher than those reported earlier. This broad resistive transition indicates an inhomogeneous distribution of B (charge carriers) that is reflected as well in ac susceptibility cac measurements given in Fig. 1b. In contrast to the very sharp transition at 7.2 K in a comparably sized piece of Pb in the measurement coil, cac of B-doped diamond starts to deviate from its temperatureindependent value near 4.5 K and is followed at 2.2 K by a much steeper transition to a fully diamagnetic state. These resistance and ac susceptibility measurements establish that superconductivity in B-doped diamond is a robust result that does not depend quantitatively on starting materials. We also have succeeded in finding clear evidence in specific heat for bulk superconductivity in these new samples. As seen in Fig. 2, there are anomalies in specific heat divided by temperature C/T that correspond closely in temperature to those observed in resistance and cac. Though two specific heat anomalies could imply unconventional superconductivity, a more likely interpretation is that there is approximately a bimodal B distribution in the sample, but the origin of this possibility needs to be investigated. A fit of these data above 4.5 K to C/TZgCbT2 gives an average electronic contribution gZ0.113 mJ/mol K2 and, from the value of b, a sampleaverage Debye temperature QDZ1439 K, which is about 23% smaller than the Debye temperature of undoped diamond. Assuming an ideal, uniformly B-doped sample with a Tc of 4 K, we construct a curve shown in Fig. 2 that conserves measured entropy in the superconducting and normal states. This idealized curve provides an estimate of the specific heat

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T(K) Fig. 1. (a) Resistivity as a function of temperature for B-doped diamond prepared by reacting B powder and graphite at high pressures and temperatures. The inset shows the onset of a superconducting transition near 4.5 K below which the resistivity becomes immeasurably small at 2.5 K. (b) AC susceptibility of the B-doped diamond and a comparably sized piece of Pb in a counter-wound coil. The inset shows the onset of a diamagnetic response in B-doped diamond at 4 K that is followed below 2.3 K by a response comparable to that of Pb with TcZ7.22 K. Diamagnetic signals from diamond and Pb are of the opposite sense because one is in that part of the counterwound coil having right-handed helicity and the other is in that part of the coil with left-handed helicity.

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T(K) Fig. 2. Specific heat divided by temperature versus temperature for B-doped diamond prepared by reacting B powder and graphite. Two anomalies, corresponding closely in temperature to those found in resistivity and ac susceptibility, confirm the bulk nature of superconductivity. The dashed line is an entropy-conserving construction, assuming an idealized transition at 4 K. A linear fit of C/T versus T2 for TR4.5 K, plotted in the inset, gives a sampleaveraged electronic Sommerfeld coefficient gZ0.113 mJ/mol K2 and QDZ 1439 K.

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jump at this Tc, DC/gTc Z0.5, which is about one-third of the value 1.43 expected for weak coupling superconductivity. A small but finite density of states at the Fermi energy, implied by a non-zero g, and high Debye temperature are consistent with the plausibility of conventional electron– phonon mediated superconductivity in diamond. Lee and Pickett [5] as well as Boeri et al. [6] have considered this possibility theoretically. Though taking different approaches to the problem, both sets of authors arrive at similar conclusions, namely that superconducting diamond is analogous to MgB2. The basic pairing mechanism in these models is the coupling of doped holes in diamond’s three-dimensional s-bands to optical (bond-stretching) phonon modes. The same mechanism produces superconductivity in MgB2, but in this case the s-bands are extremely 2-dimensional. It is primarily the difference in dimensionality of these s-bands and their effect on optical phonon softening in diamond and MgB2 that is responsible for a factor of ten difference in their Tc’s. Consequently, within this scenario, it is unlikely that the Tc of B-doped diamond can be pushed significantly higher; although, it should increase with increasing hole concentration. With conventional values for the Coulomb pseudopotential m*Z0.1 to 0.2, the models of electron–phonon mediated superconductivity discussed above give estimates of Tc close to that found experimentally. However, the small carrier concentration in superconducting diamond implies that the Coulomb interaction is poorly screened, opening the possibility of an exotic pairing mechanism. In contrast to an analogy with MgB2, Baskaran suggests that B-doped diamond may be more like P-doped Si [7]. This different viewpoint rests, in part, on the premise that the carrier doping level in superconducting diamond is close to the Mott limit. In this case, the disordered lattice of B and associated random Coulomb potential lift the orbital degeneracy of B acceptor states, producing a single, narrow half-filled band in which superconductivity could arise through a resonating valence bond (RVB) type mechanism. Systematic study of the evolution of the superconducting and normal states as a function of hole concentration will be required to test the basic assumption and proposed pairing mechanism of this model. The limited experimental data available on this newly discovered superconductor prevent a definitive statement about the pairing mechanism, and there are several open experimental and theoretical issues that must be addressed. From an experimental point of view, these issues might be addressed most straightforwardly in thin films prepared, for example, by chemical vapor deposition. Though this method has produced B-doped diamond films with B concentrations above the Mott limit [9] and preliminary studies indicate some evidence for superconductivity in them [10], the challenge is to prepare films with even greater B concentrations and with minimal or carefully characterized concentrations of compensating nitrogen atoms. Theoretically, more realistic modeling of Coulomb interactions and consideration of non-adiabatic effects would be worthwhile. Now, we turn to the other extreme of the periodic table where superconductivity emerges in PuMGa5 (MZCo, Rh).

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Unlike the cubic structure of diamond, these superconductors crystallize [1,3] in the tetragonal HoCoGa5 (115) structure type that can be viewed as built from alternating layers of cubic HoGa3 and parallelepipeds ‘CoGa2’ that are stacked sequentially along the c-axis [11]. A series of heavy-fermion compounds CeMIn5 (MZCo, Rh, Ir) form in exactly this same crystal structure. In each of these Ce materials, unconventional superconductivity, signaled by power laws below Tc in C/T, spin-lattice relaxation rate and thermal conductivity, appears at atmospheric pressure (MZCo, Ir) or emerges as antiferromagnetic order is suppressed by applied pressure (MZRh).[4] These observations, together with superconductivity of each compound appearing in proximity to some form of magnetism and the absence of superconductivity in their non-magnetic La analogs, strongly suggest magnetically mediated pairing. Compared to the CeMIn5 superconductors, which have maximum Tc’sz2.3 K in CeCoIn5 at PZ0 and CeRhIn5 at Pz2.5 GPa [4], the isostructural Pu compounds have substantially higher transition temperatures that reach 16 K for PuRhGa5 at PZ16 GPa and over 22 K in PuCoGa5 at PZ22 GPa [12]. Because of the larger spatial extent of 5f versus 4f wavefunctions, the 5f wavefunctions of Pu should hybridize more strongly with ligand states than the 4f electron of Ce. This stronger hybridization of 5f electrons implies a higher spin-fluctuation temperature than in the Ce compounds, and, within a scenario of magnetically mediated superconductivity, provides a plausible argument for the higher Tc’s of these Pu115 materials [1]. Presently however, there is no definitive evidence for unconventional, spin-mediated superconductivity in the PuMGa5 compounds. In the following, we briefly consider possible pairing mechanisms that may be relevant to superconductivity in PuMGa5. Because the transition temperatures in PuCoGa5 and PuRhGa5 are at least a factor of four higher than in any Ceor U-based heavy fermion system but comparable to those found, for example, in transition-metal compounds with the A15 structure, an electron–phonon mechanism must be considered as a possibility. A simple estimate, using the McMillan relationship [13], TcZ(qD/1.45)exp(K1.04(1Cl)/ (lKm*(1C0.62l)), gives Tcz2.4 K for a Debye temperature qDZ240 K, extracted from specific heat measurements on PuCoGa5, a typical value of m*Z0.1, and weak electron– phonon coupling (lZ0.5). Increasing the coupling parameter to lZ1.0 produces TcZ13.8 K, not too far below the experimentally determined value. Though conventional superconductivity is not ruled out by this simple estimate, it is difficult to understand how it could coexist with magnetic moments that are inferred from the normal state magnetic susceptibility of PuMGa5. Their magnetic susceptibility follows a Curie–Weiss temperature dependence, with an effective moment meff z0.6 mB, from Tc to 300 K [1,3]. This effective moment is close to that of 0.84 mB expected for local magnetic moments, assuming Hund’s rules and Pu3C. Because magnetic moments break time-reversal symmetry of Cooper pairs in conventional superconductors and rapidly suppress Tc, the simultaneous presence of magnetic f-electrons and such

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high Tc’s in PuMGa5 are difficult to reconcile with a conventional pairing mechanism. Further, if the magnetic moments are uncoupled from the ligand electrons, they should order magnetically at some sufficiently low temperature. Recently, we have prepared PuCoGa5 with a less active Pu isotope, 242Pu, than the common isotope 239Pu that has been used in all previous samples. This new sample has allowed specific heat measurements to be extended to substantially lower temperatures than previously possible, and these experiments find no definitive evidence for magnetic order above 1 Kz0.05Tc [14], again arguing against a conventional mechanism. Band structure calculations for PuMGa5 [15] and CeMIn5 [16] compounds show that both systems for each M have very similar quasi-2 dimensional Fermi surfaces, a condition favorable to unconventional superconductivity mediated by valence or magnetic fluctuations [17]. A complication in considering these possibilities is the ambiguity in the 5f configuration of Pu’s 5f electrons. Although the effective moment above Tc in PuMGa5 is close to that expected for Pu3C, it is not exactly that expected for either L–S or J–J coupling schemes. One distinct possibility is that the magnetic susceptibility is anisotropic, and measurements to date have not captured the expected effective moment. On the other hand, photoemission studies [18] of PuCoGa5 indicate that electronic states at the Fermi energy contain some 5f character, suggesting hybridization of Pu’s 5f electrons with ligand states. With hybridization, the 5f levels broaden to a width DZp!VkfO2N(EF), where Vkf is the matrix element that mixes conduction (k) and f-electron wavefunctions and N(EF) is the density of states at the Fermi energy.[19] If the energy level of the 5f electrons is close to EF, 5f electrons spend part of their time in the conduction band. The valence of Pu is no longer integral and fluctuates between 5fn and 5fnK1 configurations on a time scale w1/D. Such valence (charge) fluctuations also induce spin fluctuations [19], both of which could play a role in superconductivity [17]. Though photoemission experiments as well as the enhanced electronic specific heat (gz70–90 mJ/mol K2) of PuMGa5 are consistent with some amount of hybridization, neither these nor any other measurement to date can make conclusive statements about the presence of valence fluctuations. Resolving the precise configuration of these 5f electrons is an urgent problem that bears directly on understanding the mechanism of superconductivity. A different perspective on superconductivity in these Pu materials is provided by a correlation between Tc and the ratio of their tetragonal lattice parameters c/a. As shown in Fig. 3, Tc increases linearly as c/a varies in PuCo1KxRhxGa5, and the same large relative rate of increase dln Tc/d(c/a)z80 is found in the isostructural family CeM1KxM 0 xIn5 [20]. Because the Fermi surface topologies of both Pu115 and Ce115 materials are very similar and depend only weakly on transition metal M [15,16], it seems unlikely that slight variations in electronic structure could account for such as strong variation in Tc with c/a, but the observation that both families show essentially the same relative dependence on c/a suggests a

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c/a Fig. 3. Superconducting transition temperatures as a function of the ratio of tetragonal lattice parameters c/a for PuCo1KxRhxGa5 (right ordinate, upper abscissa) and CeM1KxM 0 xIn5 (left ordinate, bottom abscissa). Both isostructural systems have very similar values of d ln Tc/d(c/a)z80.

common underlying mechanism. Recent studies [21,22] of the isostructural compounds UMGa5 and NpMGa5 further suggest that the mechanism may be magnetic. These experiments reveal a correlation between magnetic structures and a local distortion of the cubic AGa3 building blocks, where AZU, Np. Depending on the transition metal M, the AGa3 unit experiences a slight (few percent) tetragonal distortion away from cubic symmetry that is measured by the magnitude of (2zcKa)/a, where a and c are the tetragonal lattice parameters of the HoCoGa5 structure and z is a structural parameter locating the Ga(4i) position along the c-axis. For a given actinide, the electronic structure and Fermi-surface topology of these compounds are independent of isoelectronic transition metals M, but the magnetic structure and ordering temperature are strong functions of the weak distortion (2zcK a)/a which is set by the transition metal. These authors [21] argue that their observations result from an extreme sensitivity of hybridization and exchange interactions on the extent of the local structural distortion of AGa3. Motivated by these observations, we have found that c/a is a linear function of (2zcKa)/a in both PuCo1KxRhxGa5 and CeM1KxM 0 xIn5.[23] This linear dependence implies that the slight structural distortion of the cubic units in each may underlie the relationship between Tc and c/a. Given the correlation [21] between magnetism and (2zcKa)/a in UMGa5 and NpMGa5, a reasonable speculation is that (2zcKa)/a also tunes the ability of magnetic fluctuations to create Cooper pairs in the Ce115 and Pu115 superconductors. These same distortions also should affect crystal-field splitting and, consequently, the orbital symmetry of 5f wavefunction in the ground state. Orbital degeneracy of the G8 crystal-field ground state for purely cubic AGa3 units is lifted in the presence of a tetragonal distortion. As argued by Hotta and Ueda [24], the cooperation and competition between magnetic and orbital fluctuations arising in the lower symmetry crystal-field may

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be important for understanding the origin of superconductivity in these materials. In summary, the discovery of superconductivity in unexpected materials is a significant driving force in condensed matter physics. The cuprates, of course, are the most celebrated examples. As we have discussed, B-doped diamond superconductivity may be related to MgB2, also an unexpected candidate, but one that is now relatively well understood within conventional frameworks. The potentially important Coulomb interactions in diamond, however, make understanding its superconductivity less straightforward. The origin of superconductivity in Pu115 materials certainly is not clear but it probably is not conventional. If the dominant pairing interaction is magnetic, as NMR experiments on PuCoGa5 suggest [25], these new superconductors could be a bridge between Ce- and U-based heavy-fermion superconductors and the cuprates. The diamond and Pu superconductors present experimental and theoretical challenges that deserve additional investigation and that hold promise for new understanding of condensed matter. Acknowledgements Work at Los Alamos was performed under the auspices of the US Department of Energy Office of Science. EAE and VAS acknowledge support by the Russian Foundation for Basic Research and by the Strongly Correlated Electrons Program of the Department of Physical Sciences, Russian Academy of Sciences. The authors thank J. Rebizant and E. Colineau for helpful discussions.

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