Coqblin-Schrieffer, model

Both the Anderson and the Kondo (or Coqblin-Schrieffer) model have been solved exactly for thermodynamic properties such as the 4f-electron valence, specific heat, static magnetic and charge susceptibilities, and the magnetization as a function of temperature and magnetic field B by means of the Bethe ansatz (see Schlottmann 1989, and references therein). This method also allows one to calculate the zero-temperature resistivity as a function of B. Non-equilibrium properties, such as the finite temperature resistivity, thermopower, heat conductivity or dynamic susceptibility, could be calculated in a self-consistent approximation (the non-crossing approximation), which works well and is based on an /N expansion where N is the degeneracy of the 4f level. 

Fig. 8. Temperature dependence of the magnetic stis-ceptibility for impurities with total angular momenta = 2,1, f, 5 and % = 1, calculated with the Belhe ansatz for the Coqblin Schrieffer model, eq. (3) (Rajan 1983).

The susceptibility x(T)/x(0) with x(0) from eq. (12) is shown in fig. 7. It is again similar for VF and HF systems, apart from a peak near 7], which is more pronounced for VF systems. This peak depends strongly on the 4f-level degeneracy N and vanishes in the Kondo model with N = 2 or effective spin S = j. Figure 8 shows this behavior for the susceptibility in the Coqblin-Schrieffer model, see eq. (3), (in which charge fluctuations are ignored) for various values of the total angular momentum j. 

For —Sf A, U A and U + 2ef = 0 the Anderson Hamiltonian, eq.(1), can be transformed into the Coqblin-Schrieffer (CS) Hamiltonian. In this Kondo limit charge fluctuations are completely suppressed and the model describes an effective 4f-electron spin j which interacts via exchange with the conduction electrons... 

For the non-symmetrical Anderson model with C/ + 2ef 0, one has in the Coqblin Schrieffer and Kondo Hamiltonians in addition to the exchange a potential scattering term. The Kondo resonance is no longer at the Fermi energy ep = 0 but is shifted. This shift leads to a smaller resistivity p(T), the maximum of which, however, is still at T = 0. The potential scattering has a dramatic effect on the thermoelectric power, which vanishes in the symmetric case C/ + 2ef = 0, but has a huge peak near 7k for C/ 4- 2ef 0. 

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