Magnetic-field effects in energy relaxation mediated by Kondo impurities in mesoscopic wires

We study the energy distribution function of quasiparticles in short voltage biased mesoscopic wires in the presence of magnetic impurities and applied magnetic field. The system is described by a Boltzmann equation where the collision integral is determined by coupling to spin-$\frac{1}{2}$ impurities. We develop a theory of the coupling of nonequilibrium electrons to dissipative spins. This theory is valid as long as the characteristic smearing of the steps in the energy distribution function, which depends both on the bias voltage and the location of the probe, exceeds the Kondo temperature. We further address the renormalization of coupling constants by nonequilibrium electrons. Magnetic-field dependence of the energy relaxation rate turns out to be nonmonotonic. For low magnetic field an enhancement of energy relaxation is found, whereas for larger magnetic fields the energy relaxation decreases again meeting qualitatively the experimental findings by Anthore et al. (cond-mat/0109297). This gives a strong indication that magnetic impurities are in fact responsible for the enhanced energy relaxation in copper wires. Our theoretical results are in good agreement with the experiment at large bias voltages where the theory is applicable. At the same time, at small bias voltages there are substantial quantitative deviations. Furthermore, the concentration of the spins, which follows from the energy relaxation for Cu, seems to to be substantially higher than the concentration estimated from weak localization (dephasing rate) measurements. Since the approach presented is valid only above Kondo temperature, it does not apply to the related problem of weak localization at low temperature in equilibrium.