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

A century of research on magnetic phenomena had led to the view that the normal state of itinerant-electron ferromagnets such as Fe, Ni and Co could be described in terms of the standard model of the metallic state or its extension known as the nearly ferromagnetic Fermi liquid theory. In recent years, however, a large body of observations has accumulated from various complex intermetallic systems that raises the possibility that this assumption might be wrong. Here we examine this issue by means of high-precision measurements of the electrical transport and magnetic properties of pure ferromagnets-in particular, MnSi-in which the Curie temperature is tuned towards absolute zero by the application of hydrostatic pressure. With this method, it is possible for us to study the normal state over an extraordinarily large range of temperature of up to five orders of magnitude above the Curie temperature. Our results using MnSi reveal a particularly striking combination of properties-most notably a T3/2 power law for the resistivity-showing clearly that the normal state of this itinerant-electron ferromagnet cannot be described in terms of the standard model of metals.

Non-Fermi-liquid nature of the normal state of itinerant-electron ferromagnets

Only a few metallic phases have been identified in pure crystalline materials. These include normal, ferromagnetic and antiferromagnetic metals, systems with spin and charge density wave order, and superconductors. Fermi-liquid theory provides a basis for the description of all of these phases. It has been suggested that non-Fermi-liquid phases of metals may exist in some heavy-fermion compounds and oxide materials, but the discovery of a characteristic microscopic signature of such phases presents a major challenge. The transition-metal compound MnSi above a certain pressure (p(c) = 14.6 kbar) provides what may be the cleanest example of an extended non-Fermi-liquid phase in a three-dimensional metal. The bulk properties of MnSi suggest that long-range magnetic order is suppressed at p(c) (refs 7-12). Here we report neutron diffraction measurements of MnSi, revealing that sizeable quasi-static magnetic moments survive far into the non-Fermi-liquid phase. These moments are organized in an unusual pattern with partial long-range order. Our observation supports the existence of novel metallic phases with partial ordering of the conduction electrons (reminiscent of liquid crystals), as proposed for the high-temperature superconductors and heavy-fermion compounds.

Partial order in the non-Fermi-liquid phase of MnSi

Theory of itinerant electron magnetism

Paramagnetic spin fluctuations in the weak itinerant-electron ferromagnet MnSi have been measured by using both unpolarized and polarized neutron scattering, and the scattering intensity was put on an absolute value by the simultaneous measurements of phonon cross sections. The magnetic excitation spectra over the whole Brillouin zone, for a wide energy range from 0 to 20 meV (\ensuremath{\Elzxh}\ensuremath{\omega}/${\mathrm{kT}}_{c}$=7.9) and up to temperatures (T/${T}_{c}$=10) well above ${T}_{c}$, follow closely the Moriya-Kawabata self-consistent-renormalization theory for the weak itinerant-electron ferromagnet. Based on these experimental results, the origin of the increase in the amplitude of the local magnetic moment 〈${M}_{L}^{2}$〉 above ${T}_{c}$ is attributed to the thermal excitations of the high-energy spin fluctuations in the Stoner continuum.

Y. Noda

Papers

Paramagnetic spin fluctuations in the weak itinerant-electron ferromagnet MnSi