Kondo Effect

In physics, the Kondo effect describes the scattering of conduction electrons in a metal due to magnetic impurities, resulting in a characteristic change in electrical resistivity with temperature.

The effect was first described by Jun Kondo, who applied third-order perturbation theory to the problem, which predicted that the scattering rate of conduction electrons of the magnetic impurity should diverge as the temperature approaches 0 K. The temperature dependence of the resistivity including the Kondo effect is written as:

${\displaystyle \rho (T)=\rho _{0}+aT^{2}+c_{m}\ln {\frac {\mu }{T}}+bT^{5},}$

where ρ₀ is the residual resistance, aT² shows the contribution from the Fermi liquid properties, and the term bT⁵ is from the lattice vibrations; a, b and c_m are constants. Jun Kondo derived the third term of the logarithmic dependence. Later calculations refined this result to produce a finite resistivity but retained the feature of a resistance minimum at a non-zero temperature. One defines the Kondo temperature as the energy scale limiting the validity of the Kondo results. The Anderson impurity model and accompanying renormalization theory were an important contribution to understanding the underlying physics of the problem.

The Kondo effect can be considered as an example of asymptotic freedom, i.e. a situation where the coupling becomes non-perturbatively strong at low temperatures and low energies. In the Kondo problem, the coupling refers to the interaction between the localized magnetic impurities and the itinerant electrons.

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