Kondo effect in a magnetic field and the magnetoresistivity of Kondo alloys

The effect of a magnetic field on the spectral density of a $\mathrm{S}=1\mathrm{/}2$ Kondo impurity is investigated at zero and finite temperatures by using Wilson’s numerical renormalization group method. A splitting of the total spectral density is found for fields larger than a critical value $H_c(T=0)\approx 0.5T_K$, where $T_K$ is the Kondo scale. The splitting correlates with a peak in the magnetoresistivity of dilute magnetic alloys which we calculate and compare with the experiments on $\mathrm{C}{\mathrm{e}}_{\mathrm{x}}\mathrm{L}{\mathrm{a}}_{1-\mathrm{x}}\mathrm{A}{\mathrm{l}}_2,x=0.0063$. The linear magnetoconductance of quantum dots exhibiting the Kondo effect is also calculated.