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

The effect of a magnetic field on the spectral density of a $\rm{S=1/2}$ 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 $H_{c}(T=0)\approx 0.5 T_{K}$, 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 $\rm{Ce_{x}La_{1-x}Al_{2}}, x=0.0063$. The linear magnetoconductance of quantum dots exhibiting the Kondo effect is also calculated.