On the Kondo problem and thermodynamics of dilute magnetic alloys

TL;DR

This paper extends Kondo's theory for dilute magnetic alloys by introducing an effective temperature to account for Coulomb attraction, successfully matching experimental resistivity and thermodynamic data at low temperatures.

Contribution

It proposes a novel effective temperature approach to extend Kondo's theory, accurately modeling resistivity and thermodynamics without rescaling, and explains nonlinear heat capacity dependence.

Findings

Extended Kondo formula matches low-temperature resistivity data.

Thermodynamic functions agree with experimental measurements.

Accounts for nonlinear impurity concentration effects on heat capacity.

Abstract

An argument is given showing that Coulomb attraction between conduction electrons and impurity ions in a dilute magnetic alloy (DMA) can be disregarded, provided the system's inverse temperature beta is replaced by an effective inverse temperature t < beta. This replacement allows to remove the singularity in Kondo's expression for DMA impurity resistivity and extend his theory to 0 K. The extended Kondo formula agrees with experimental data on resistivity of CuFe in the range of low temperatures and in the neighbourhood of the resistivity minimum. Using an asymptotic solution of the thermodynamics of a dilute s-d system at inverse temperature t, the impurity thermodynamic functions are derived and shown to provide good agreement with experimental data on CuFe, CuCr and (LaCe)Al_2 alloys in the low-temperature range. The magnitude of these functions agrees with experiment and does not require rescaling as in previous s-d theories. Nonlinear dependence of CuFe heat capacity on impurity concentration has been accounted for the first time.