The Kondo effect

In addition, there are certain metals involving 4f- or 5f-states, formerly called Kondo metals and now described as heavy-fermion materials, which have a very large electronic specific heat and may be described as crystals in which every rare-earth metal is envisaged, coherently, in a Kondo-type spin flip. 

Many papers have been published on the theory of die Kondo effect, including some exact solutions. We recommend the 260 page review by Tsvelich and Weigmann (1983). Our aim in giving a simple non-mathematical account is to point out the similarity between the enhancement of the effective mass that occurs in crystalline metallic systems near to the conditions for a Mott transition (Chapter 4), and also to address the possible effects of free spins in doped semiconductors near the transition (Chapter 5). 

Our first point is that, in a material containing per unit volume N magnetic impurities with s=, the proportion rj that are doubly occupied is given by 

We now assert that the range of energies that give a peak in 2, originally of width A, is narrowed by a factor rj. Thus the contribution of each magnetic 

Caplin and Rizzuto (1968) used this argument to describe their observation that in dilute alloys of Mn and Cr in Al Cr the resistance has the form 

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Park J, Pasupathy AN, Goldsmith JI, Chang C, Yaish Y, Petta JR, Rinkoski M, Sethna JP, Abruna HD, McEuen PL, Ralph DC (2002) Coulomb blockade and the Kondo effect in single-atom transistors. Nature 417(6890) 722-725... 

In a heavy fermion compound Yb MnSbn, the dephasing rate of the coherent optical phonons decreased with lowering temperature above Curie temperature Tc, but increased below Tc- The results were attributed to the coupling between an optical phonon mode and the Kondo effect [100]. 

Cgo single molecules between electrodes fabricated by electromigration [103] to create single Cgo molecule transistors were measured at a temperature of 40 mK. The results showed the coexistence and competition of the effects of Coulomb repulsion, Kondo correlations and superconductivity [104]. The Kondo effect had been previously observed in similar devices [105]. Recently a SAM of a tricarboxylic acid fullerene derivative was used to fabricate a transistor. The SAM was created by allowing the fullerene compound to self assemble on top of an AI2O3 layer just above the aluminum drain electrode the source lead was created by... 

An P, Bialczak RC, Martinek J, Grose JE, Donev LAK, McEuen PL, Ralph DC (2004) The Kondo effect in the presence of ferromagnetism. Science 306 86-89... 

We use this formula in Chapter 3 in a discussion of the Kondo effect. 

Formulae similar to (6) have wide application to the movement of a system through an activated intermediate state, and will be applied to a simplified description of the Kondo effect in Chapter 3. For polarons the effect is to allow band motion at low temperatures with well-defined wavenumber k but enhanced effective mass mp given by... 

The model of a degenerate gas of spin polarons suggests that if the direct or RKKY interaction between moments is weak and EF too great to allow ferromagnetism then the moments might all resonate between their various orientations. This would mean that it is possible in principle to have a heavily doped magnetic semiconductor or rare-earth metal in which there is no magnetic order, even at absolute zero. This possibility is discussed further in Section 8 in connection with the Kondo effect. 

The question of the existence of the Kondo effect in amorphous systems is of interest for the considerations of Chapter 5. There is no theoretical reason to suppose that the Kondo temperature will be greatly affected on the other hand, the short mean free path l should cut down the RKKY interaction, which, for distances r greater than / should fall off as e-r/ (de Gennes 1962). In alloys... 

In the case of a single site junction with two (spin-up and spin-down) states and Coulomb interaction between these states (Anderson impurity model), the linear conductance properties have been successfully studied by means of the EOM approach in the cases related to Coulomb blockade [203, 204] and the Kondo effect [205]. Later the same method was applied to some two-site models [206-209], Multi-level systems were started to be considered only recently [210,211], Besides, there are some difficulties in building the lesser GF in the nonequilibrium case (at finite bias voltages) by means of the EOM method [212-214],... 

CeAl3 is a very interesting case where the superposition of the Kondo effect on crystal field interaction gives rise to anomalous heat capacity (7(5) and resistivity behavior (46, 77, 78) at low temperatures. The heat capacity measurements of Mahoney (75) showed that the full entropy of R In 6 was recovered under the excess... 

Contents H.Matsuda Atoms as Constituents of Matter. - T. Tsuneto System of Protons and Electrons. - T. Tsuneto Helium. - T. Tsuneto Superfluid Helium 3. - T.Matsubara Metals. - T.Matsubara Non-metals. - T.Matsubara Localized Electron Approximation. - T.Murao Magnetism. - T.Murao Magnetic Properties of Dilute Alloys - the Kondo Effect. - H.Matsuda Random Systems. - F. Yonezawa Coherent Potential Approximation (CPA).- References.- Subject Index. 

Delfs et al. (1975) have obtained quench-condensed PbCe (0-10 at% Ce) films to examine the connection between the superconductivity and the Kondo effect. They have studied the superconducting transition (between 0-7 K) versus the Ce content and shown that the transition temperatures are sensitive to the degree of structural disorder. The samples exhibit changes of the transition temperature and Kondo resistance by annealing at 77 and 20 K, respectively. 

One topic has not been included in this article. Many authors have made a thorough study of dilute pseudobinary alloys containing low concentrations of magnetic rare earth atoms. We feel that these investigations, many of which are related to the Kondo effect, belong properly to the field of dilute magnetic alloys and they are therefore reported there. An excellent review of this topic has been... 

Cornut and Coqblin (1972) derived an expression for the resistivity taking into account the influence of both the crystal field and the Kondo effect. A fit of this... 

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