The N-Channel Kondo Model: a Possibility to Explain the System Copper-Iron

The exact solution of the n-channel Kondo model, obtained previously via Bethe-ansatz by Andrei and Destri, and Wiegmann and Tsvelick, is used to study the thermodynamic properties of several physical systems. The thermodynamic Bethe-ansatz equations are solved numerically in the presence of a magnetic field, for arbitrary n (number of orbital channels) and S (spin of impurity). The numerical method is described in chapter 1. In chapter 2 this solution is applied to study the properties of the s-d exchange model in field with arbitrary impurity spin (S <= 7/2), extending previous calculations by other authors. In chapter 3 the numerical results are compared to experimental data for the susceptibility, specific heat, magnetization and resistivity of dilute alloys of transition metal Kondo impurities in simple metals. The agreement found between theory and experiment is excellent for the typical Kondo system CuFe, and still quite good for AgFe and CuCr. The results indicate that the 4s electrons of Fe and Cr delocalize into the metal, while the 3d electrons remain localized at the impurity. The n-channel Kondo model (with n = 2, S = 1/2) has been proposed by Cox as a model for heavy-fermion systems like UBe_{13} (quadrupolar Kondo effect). The properties of the quadrupolar Kondo effect are discussed in chapter 4 using the exact numerical solution. The main features of the model are a local structural instability, large gamma-values at small quadrupolar distortions, together with a small Wilson ratio, chi/gamma, and a double-peak structure in the specific heat. In chapter 5 a relation between the low temperature behavior of metallic glasses (described by two level systems (TLS)) and the n-channel Kondo model is established for an arbitrary number of orbital channels of spinless fermions interacting with the tunneling atom (S = 1/2). When n > 1 and in the symmetric situation the susceptibility (with respect to a level splitting) diverges as T to 0 indicating that the symmetric situation is unstable to a local lattice deformation. The groundstate equilibrium situation is then asymmetric, a Fermi liquid picture with large gamma -values applies and the specific heat has a double-peak structure.