Fermi-liquid instabilities at magnetic quantum phase transitions

TL;DR

This review examines the instabilities of Fermi-liquid states at magnetic quantum critical points, comparing theoretical models with experimental data on heavy-fermion and transition-metal systems to assess current understanding.

Contribution

It provides a comprehensive analysis of Fermi-liquid instabilities at magnetic quantum phase transitions, highlighting limitations of existing theories and integrating experimental findings.

Findings

Breakdown of Hertz-Millis-Moriya theory in certain cases

Experimental data challenge existing quantum critical models

Identification of conditions leading to non-Fermi-liquid behavior

Abstract

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.