Magnetic fluctuations and possible formation of a spin-singlet cluster under pressure in the heavy-fermion spinel\({\mathrm{LiV}}_{2}{\mathrm{O}}_{4}\)probed by\({}^{7}\mathrm{Li}\)and$ {}^{51}\mathrm{V}$NMR

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.

Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. Heavy fermion metals have in recent years emerged as prototypical systems to study quantum critical points. There have been considerable efforts, both experimental and theoretical, which use these magnetic systems to address problems that are central to the broad understanding of strongly correlated quantum matter. Here, we summarize some of the basic issues, including i) the extent to which the quantum criticality in heavy fermion metals goes beyond the standard theory of order-parameter fluctuations, ii) the nature of the Kondo effect in the quantum critical regime, iii) the non-Fermi liquid phenomena that accompany quantum criticality, and iv) the interplay between quantum criticality and unconventional superconductivity.