Scaling the Kondo lattice

The origin of magnetic order in metals has two extremes: an instability in a liquid of local magnetic moments interacting through conduction electrons, and a spin-density wave instability in a Fermi liquid of itinerant electrons. This dichotomy between 'local-moment' magnetism and 'itinerant-electron' magnetism is reminiscent of the valence bond/molecular orbital dichotomy present in studies of chemical bonding. The class of heavy-electron intermetallic compounds of cerium, ytterbium and various 5f elements bridges the extremes, with itinerant-electron magnetic characteristics at low temperatures that grow out of a high-temperature local-moment state. Describing this transition quantitatively has proved difficult, and one of the main unsolved problems is finding what determines the temperature scale for the evolution of this behaviour. Here we present a simple, semi-quantitative solution to this problem that provides a basic framework for interpreting the physics of heavy-electron materials and offers the prospect of a quantitative determination of the physical origin of their magnetic ordering and superconductivity. It also reveals the difference between the temperature scales that distinguish the conduction electrons' response to a single magnetic impurity and their response to a lattice of local moments, and provides an updated version of the well-known Doniach diagram