Edited by: Karl A. Gschneidner, Jr., LeRoy Eyring G.H. Lander and G.R. Choppin ISBN: 978-0-444-81502-6

The actinide concept guided the discovery of the remaining members of the actinide elements. Vallarino, Macrocycle complexes of the lanthanide (II1) yttrium (llI) and dioxouranium (VI) ions from metal template syntheses 443.

Introduction

In Section 3—the main section—we discuss results for many f electronic materials, examining where possible comparisons with LDA calculations which treat f electrons as band (f itinerant) or core (f local) and renormalized calcns. generation. In Section 4, we discuss various theories for heavy electron superconductors, including possible coupling via phonons, charge fluctuations, and spin fluctuations, and emphasize the importance that the electronic structure of the normal state will play in determining the exact theory of this most unusual phenomenon.

Formalism

Most of the materials to consider here are those where this is not the case. In the slave boson method, one usually starts with the Coqblin-Schrieffer Hamiltonian, which is the Kondo limit of the large-U Anderson model (Read and Newns 1983).

Lanthanide and actinide materials

A related proposal is that the small moment is due to Fermi surface nesting (Ozaki and Machida 1989, Miyake and K u r a m o t o 199!). Positron destruction measurements (Hoffmann et al. 1982, Waspe and West 1982) reinforced the picture of the Fermi surface. 24 we show graphs of the Fermi surface based on our f-core calculation (Norman and Min, unpublished).

Band)

CeCu ,(tore)

Superconductivity in heavy-fermion metals

Charge fluctuations

However, recent calculations in the subordinate boson scheme (Keller et al. 1990) lead to the conclusion that the net interaction is repulsive for on-site pairing, which is due to the large on-site Coulomb repulsion. Since the discovery of uranium-based heavy fermionic superconductors, spin oscillations have been suspected to be the pairing mechanism (Anderson 1984). The Q sum limit is achieved by including the f-electron form factor in the susceptibility.

The calculated gap function is of the Axu (p-wave) representation (line nodes), where the second highest Tc solution is in the Exù (p-wave) representation (point nodes), assuming that the order parameter d vector (d'S = O, where S is the spin vector of the Cooper pairs) was oriented along the c axis. In Monien and Pethick's model this is the sum used [so for the simple Putikka and Joynt model the AF correlations between planes fall outside the pair potential, i.e. this happens because the two pair potentials (corresponding to an acoustic and optical branch) are essentially a return of sensitivity to the first zone.

The isotropic part of the interaction (V~x + Vyy) enters the expression for singlet and Ms = 0 triplet (d vector along c) solutions, while the anisotropic term (Vxx- Vyy, Vxy) determines a new odd parity solution with vector d in the basal plane ( note that non-parity solutions z d along c and d in the basal plane do not mix unless there is a term Vxz or Vr z). First, they replace the complex quasiparticle matrix elements of the form (k, - kl V(r, r')[k', - k'), with the simplified V(k - k') as used above (in fact, ambiguities, discussed above on the momenta dependence of the pair potential are all due to this simple substitution).

Conclusions

Calculated symmetry of the gap function for UPt 3 from the semi-phenomenological theory of spin fluctuations assuming coupling from either high-frequency spin fluctuations (F ~ 5 meV) or low-frequency spin fluctuations [F (Q ) ~ 0.3 meV]. For example, the fact that odd parity solutions are found for AF correlations between planes may be a total artifact of the assumptions made on the matrix elements mentioned above. The successes of the renormalized band structures are a clear indication of the accuracy of the D F - L D A charge density even for these strongly enhanced materials.

As an example, for Pr or for U Pd one artificially localizes the f-electrons in the nucleus (i.e., manually suppresses the hybridization) to obtain a good representation of the Fermi surface. Gd should satisfy the requirements of the f-core model, but it is necessary to keep incorporating the f-states into the band structure to understand the minority carrier. And for Ceß6, although the topology of the Fermi surface is generally consistent with an f-core model, (1) the observed extremal regions are larger than allowed by an f-core model, and (2) one finds a mass enhancement of 50, implying f orbital involvement in the conduction bands.

Any of the improvements that could likely be incorporated into a density functional formalism would allow greater localization with reduced hybridization. It will likely remain a mystery until we get a truly rigorous understanding of the normal ground state of these metals.

H. LIU

Review of key normal state properties

Magnetic susceptibility

Theoretical approaches

3 is a plot of the specific heat 7 versus the low-temperature susceptibility Z(0) for a number of mixed-valence and heavy-fermion materials (Jones 1985). A plot of the specific heat 7 versus the low-temperature susceptibility z(O) for an Io number of mixed-valence and heavy-fermion. These experimental results drive h o m the dual nature of the f electrons in heavy-fermion m a t e r i a l s - l o c a l z e d at high temperatures and itinerant at low temperatures.

One can think of z(q, co) as the propagation or Green's function of a spin fluctuation state, then the imaginary part is the spectral density of the state.. The wave-vector dependent susceptibility Zl°)(q,0) of the free-electron gas. The wave vector q is measured in units of the Fermi momentum kv, and the susceptibility is normalized by the density of states at the Fermi level. Like other boson states in solids, paramagnons also contribute to the specific heat of the material (Doniach and Engelsberg 1966).

Schematic representation of the two hybridized bands (solid curves) for the simple two-band model. PHENOMENOLOGICAL APPROACH TO HEAVY-FERMION SYSTEMS 111 states of the unhybridized b r o a d band, then N_+(e) is for the hybridized bands.

TABLE 1 The specific heat 7 of some metals and

Summary and conclusion

This paper consists of a highly condensed review of experimental and theoretical studies of heavy fermions and mixed-valence materials. Fermi liquid models are useful at low temperatures, and whether we choose to use a one-band, two-band, or LDA model depends on the amount of detail required by the experimental situation. At very low temperatures, the experimental results can be understood in terms of spin wave theory.

Near the Curie temperature, all measurements of critical phenomena are unified by scaling theory. Between these two well-understood limits, the average properties of the system are best handled by mean-field theory, which is a rather rough approximation. As mentioned in the introduction, there is a tendency in the literature to classify mixed-valence and heavy-fermion systems as two different classes of materials.

3 clearly shows that there is no gap in the mass spectrum from the mixed-valence systems in the lower left corner to the heavy fermion systems in the upper right corner. Actinide systems, on the other hand, have many 5f electrons per atom, and the role of Hund's rule coupling between many f electrons has not been systematically studied.

S.S. BROOKS

Chemical bonding in metals t. Assignment of valence

A knowledge of the potential and some quantum mechanics is then sufficient to calculate the density. The experimental equilibrium atomic volumes of the 3d, 4d and 5d transition metals, the lanthanides and the actinides. Ratio of the equilibrium atomic volumes of the Z and Z + 1 elements for the lighter 3d, 4d and 5d transition series.

Another type of analysis directs attention not to the atomic volume but to the energy of the valence electrons in the metallic state. The first is a binding energy, the second a promotion energy, necessary to bring the free atom into the configuration of the atom in the solid. Therefore, the cohesive energies of the trivalent lanthanides should be about 100 kcal/mol relative to the trivalent atomic state (f"dsZ).

In fact not all of the multiple coupling energy is lost in the solid, as a small 5d moment remains. Free atom excitation energies are known experimentally for most of the lanthanides (Martin et al. 1978), but only for some of the actinides.

Fig. 1. The experimental equilibrium atomic volumes of the 3d, 4d and 5d transition metals, the lanthanides and the actinides

34; TETRAVALENT

Physical theory of bonding in metals

The relativistic volume effect

They can be constructed from the energy-dependent solutions of the wave equation within the atomic spheres. COHESION IN RARE EARTHS AND ACTINIDES 167 in terms of the logarithmic derivatives at the Wigner-Seitz radius, S,. They arise from the extension of the tails of the orbitals to other places in the crystal.

However, due to the centrifugal potential, the 3d density is also pushed away from the core. The H o h e n b e r g - K o h n theorem (Hohenberg and K o h n 1964) is a variation principle for the energy of a many-electron system with respect to the electron density. That is, the first-order energy change is the change in the surft of the single-electron energy eigenvalues - in a frozen potential.

In addition, the energy derivative D t in terms of the amplitude of the partial waves at the boundary of the ASA sphere is known. Therefore, R 2 is an excellent measure of the importance of the spin-orbit interaction in the ground state.

Fig. 6. T h e c a l c u l a t e d b a n d m a s s e s o f t r a n s i t i o n m e t a l s , l a n t h a n i d e s a n d a c t i n i d e s (after A n d e r s e n a n d J e p s e n 1977 a n d B r o o k s 1979)

The elemental metals

A review of the electronic structure of the trivalent lanthanides evaluated at a common Wigner-Seitz radius of 3.75 au (after Skriver 1983b). At an energy corresponding to the bottom of the 5d bands, the 5d bond density is very large, while. The 5d density is shown for the bottom (bond) and top (anti-bond) of the 5d bands.

An overview of the electronic structure of the divalent lanthanide and barium is shown in Fig. Otherwise, the energy band structure trends are similar to those of the trivalent rare earths. V(S), on the sphere, the bottom, BI, and the top, A» of the relevant bands, along with the Fermi energy.

Decomposition of the partial pressures in terms of band width and band position (lower panel) for the trivalent lanthanides. The size of the mid term is determined by the occupancy number, n» the mid position, C» and the band mass, #z.