Kondo Effect in a Magnetic Field and the Magnetoresistivity of Kondo Alloys

The effect of a magnetic field on the spectral density of a $S=1\mathrm{}/2$ 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 $H_c(T=0\mathrm{})\approx {0.5T}_K$, 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 ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{Al}}_2,x=0.0063\mathrm{}$. The linear magnetoconductance of quantum dots exhibiting the Kondo effect is also calculated.