The Static and Dynamic Impurity Spin Susceptibility of Kondo Alloys

Abstract

In this lecture we want to discuss some properties of a single magnetic impurity imbedded in a metal matrix. We assume that the impurity is described completely by its spin operators S _z, S _± = (S _x ± S _y)/ $sqrt 2$. For the sake of simplicity we assume the spin to be ½. The metal we will approximate as a free Fermi gas of conduction electrons, and as the interaction between impurity and matrix we will use a simplified exchange contact Hamiltonian. Such a model presents a reasonable description of simple metals like copper or gold containing a small fraction of magnetic ions like Fe, Mn or Cr. Direct measurements of magnetic properties can be performed by determining the spin polarization in an external static magnetic field, or by measuring hyperfine splittings for the impurity nucleus. Hyperfine techniques also provide information about the dynamical behaviour of the impurity spin. In the following we will focus our attention on the static zero field susceptibility and on the zero field excitation spectrum of the impurity.