This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

http://export.arxiv.org/pdf/cond-mat/0606317

Fermi-liquid instabilities at magnetic quantum phase transitions

In a conventional superconductor, the binding of electrons into the paired states that collectively carry the supercurrent is mediated by phonons — vibrations of the crystal lattice. Here we argue that, in the case of the heavy fermion superconductors CePd2Si2 and CeIn3, the charge carriers are bound together in pairs by magnetic spin–spin interactions. The existence of magnetically mediated superconductivity in these compounds could help shed light on the question of whether magnetic interactions are relevant for describing the superconducting and normal-state properties of other strongly correlated electron systems, perhaps including the high-temperature copper oxide superconductors.

Magnetically mediated superconductivity in heavy fermion compounds

Intermetallic compounds containing $f$-electron elements display a wealth of superconducting phases, which are prime candidates for unconventional pairing with complex order parameter symmetries. For instance, superconductivity has been found at the border of magnetic order as well as deep within ferromagnetically and antiferromagnetically ordered states, suggesting that magnetism may promote rather than destroy superconductivity. Superconducting phases near valence transitions or in the vicinity of magnetopolar order are candidates for new superconductive pairing interactions such as fluctuations of the conduction electron density or the crystal electric field, respectively. The experimental status of the study of the superconducting phases of $f$-electron compounds is reviewed.

Superconducting phases of f -electron compounds

This review considers the experimental and theoretical studies of concentrated Kondo systems (CKS), Kondo lattices, substitutional solid solutions and their transition from Kondo impurity to Kondo lattice, and ‘intermediate valence compounds’ which are, in fact, high T K CKS (T K is the Kondo temperature). The anomalous low temperature properties of CKS are related to the formation of the narrow (∼k B T K) high-amplitude Abrikosov-Suhl resonance E R in the vicinity of the Fermi level E F. This resonance is situated exactly at E F in low T K CKS with T K ΔCF (ΔCF is the crystal field splitting). In low T K ‘j=1/2’ CKS the condition E R=E F leads to an increase of the density of states at E F, which is large enough to induce heavy fermion superconductivity in CeCu2Si2, UBe13. We demonstrate that the transition from low T K (E R=E F) to high T K CKS (E R≠E F) might be what was formerly considered as a ‘Kondo-lattice-intermediate valence state’ transition...

Concentrated Kondo systems

Pressure induced heavy fermion superconductivity of CeCu2Ge2

We report the results of neutron-diffraction experiments on CeM/sub 2/Si/sub 2/ (M = Ag,Au,Pd,Rh) which were performed to explore the role of valence fluctuations and 4f hybridization in the magnetic ordering of cerium compounds. All four order antiferromagnetically, the first three exhibiting structures consisting of ferromagnetic layers with moments perpendicular to the layers, which are believed to be characteristic of 4f-4f interactions mediated through hybridization with conduction electrons. CePd/sub 2/Si/sub 2/ has an anomalously small moment (0.62..mu../sub B/) in the ordered state. CeAg/sub 2/Si/sub 2/ exhibits an incommensurate longitudinal, static magnetization wave with moment and propagation direction along the a axis. The fourth compound, CeRh/sub 2/Si/sub 2/, has the highest known transition temperature (39 K) reported for cerium ordering; it exhibits another second-order transition at 27 K to a complex commensurate structure with modulated moments. The results are discussed in terms of the effects that 4f hybridization can have on ordering.

B.H. Grier

Papers

Magnetic ordering in CeM/sub 2/Si/sub 2/ (M = Ag,Au,Pd,Rh) compounds as studied by neutron diffraction