Introduction

Our main concern so far has been with theories of a single magnetic impurity in a simple host metal. These theories have been developed over a period of more than thirty years and most of the models put forward for explaining these systems are now well understood. The concepts for understanding their behaviour in terms of scaling trajectories, fixed points, spin compensation, quasi-particles, Fermi liquid theory and Kondo resonances have been developed and there are exact solutions for the thermodynamic behaviour of many of the models as well as good approximations for their dynamic response (for the reader who has skipped the details of chapters 4–8 the important single impurity results are summarized in appendix K). As we saw in the previous chapter there is still much to be done in the way of detailed predictions for specific systems to compare with experiment. There is also the possibility of new types of experiments to probe the theory further (for example, the possibility of probing the Kondo resonance by resonant tunnelling has recently been discussed by Hershfield, Davies and Wilkins, 1991). These may throw up new puzzles to be answered. The general belief, however, is that if these occur they will be relatively minor and will not require a fundamental reworking of the theory. With these provisos it may be claimed the single impurity problem has been ‘solved’.