Introduction to the Kondo Effect
Conduction measurements of magnetic systems at low temperature, like the present study of 3d transition metal MePc on Ag(100) are closely intertwined with a phenomenon known as the Kondo effect. Essentially it is a coupling of the conduction electrons of
- PDF / 796,803 Bytes
- 20 Pages / 439.37 x 666.142 pts Page_size
- 5 Downloads / 184 Views
Introduction to the Kondo Effect
Conduction measurements of magnetic systems at low temperature, like the present study of 3d transition metal MePc on Ag(100) are closely intertwined with a phenomenon known as the Kondo effect. Essentially it is a coupling of the conduction electrons of a metal to a magnetic impurity. Below a critical temperature, the so-called Kondo temperature, the coupling leads to a screening of the spin of the magnetic impurity due to the creation of a many-body singlet state. This gives rise to a typical sharp resonance in the DOS at the Fermi level, which can be accessed experimentally by STS measurements. This Kondo resonance is characteristic of magnetic impurities on a non-magnetic surface. Hereby it provides a method for STM measurements to probe the magnetic properties of adatoms or molecules. As the Kondo effect is intrinsically a many-body problem, its mathematical description is necessarily complex. Since its first explanation in the 1960, many advanced mathematical tools such as the Numerical Renormalization Group (NRG), and the Bethe ansatz have been applied to solve the problem. In this chapter we present an outline of the basic concepts in a descriptive manner, in order to understand the mechanisms involved. For a more complete treatment the reader is referred to the specific literature [1–4].
3.1 The Kondo Problem In the 1930s measurements of the electrical resistivity of certain metals revealed an effect that would puzzle physicists for 30 years [6]: as the temperature of the sample is lowered, the resistivity reaches a minimum and then increases again as −ln(T ), for even lower temperature (see Fig. 3.1). Later it was found that this effect only occurs if the metal contains dilute magnetic impurities, such as iron or cobalt atoms. In metals, the electric resistivity is caused by the scattering of conduction electrons. They can scatter off crystal lattice vibrations (phonons) or off static defects in the lattice itself such as vacancies or substitutions.
C. Krull, Electronic Structure of Metal Phthalocyanines on Ag(100), Springer Theses, DOI: 10.1007/978-3-319-02660-2_3, © Springer International Publishing Switzerland 2014
31
32
3 Introduction to the Kondo Effect
Fig. 3.1 Resistivity of a copper crystal, with different percentages of Fe impurities. Figure adapted from [5]
As the temperature decreases, lattice vibrations become less pronounced, hence the effect of phonon scattering on the resistivity goes down (∝T 5 ). The contribution of the static impurities remains unchanged, and the resistivity saturates at a minimum caused by these defects. The increase in resistivity observed for the dilute magnetic alloys was explained by J. Kondo in 1964 [7], by introducing another scattering mechanism for the conduction electrons. The spin flip interaction between the magnetic impurities and the spin of the conduction electrons. He described this in the s-d exchange model or Kondo model: H = H Bloch + HK HK = −J S · s(r )
(3.1) (3.2)
The Hamiltonian consists of a H Bloch pa
Data Loading...
