Energy-resolved inelastic electron scattering off a magnetic impurity

We study inelastic scattering of energetic electrons off a Kondo impurity. If the energy E of the incoming electron (measured from the Fermi level) exceeds significantly the Kondo temperature TK, then the differential inelastic cross section σ(E,ω), i.e., the cross section characterizing scattering of an electron with a given energy transfer ω, is well defined. We show that σ(E,ω) factorizes into two parts. The E dependence of σ(E,ω) is logarithmically weak and is due to the Kondo renormalization of the effective coupling. We are able to relate the ω dependence to the spin-spin correlation function of the magnetic impurity. Using this relation, we demonstrate that in the absence of the magnetic field, the dynamics of the impurity spin causes the electron scattering to be inelastic at any temperature. At temperatures T low compared to the Kondo temperature TK, the cross section is strongly asymmetric in ω and has a well-pronounced maximum at ω~TK. At T⪢TK, the dependence σ vs ω has a maximum at ω=0; the width of the maximum exceeds TK∕ and is determined by the Korringa relaxation time of the magnetic impurity. Quenching of the spin dynamics by an applied magnetic field results in a finite elastic component of the electron scattering cross section. The differential scattering cross section may be extracted from the measurements of relaxation of hot electrons injected in conductors containing localized spins.