Energy-resolved inelastic electron scattering off a magnetic impurity

TL;DR

This paper investigates inelastic electron scattering off a magnetic impurity in the high-energy regime, revealing how the Kondo effect influences scattering characteristics and how magnetic fields can suppress inelastic processes.

Contribution

It provides a detailed analysis of the energy and spin dynamics dependence of inelastic scattering cross-sections in the Kondo regime, linking them to impurity spin correlations.

Findings

(E,w) varies weakly with energy E due to Kondo renormalization.

The w-dependence of (E,w) relates to impurity spin-spin correlations.

Magnetic field suppresses impurity spin dynamics, reducing inelastic scattering.

Abstract

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 T_K, then the differential inelastic cross-section \sigma (E,w), i.e., the cross-section characterizing scattering of an electron with a given energy transfer w, is well-defined. We show that \sigma (E,w) factorizes into two parts. The E-dependence of \sigma (E,w) is logarithmically weak and is due to the Kondo renormalization of the effective coupling. We are able to relate the w-dependence to the spin-spin correlation function of the magnetic impurity. Using this relation, we demonstrate that in the absence of magnetic field the dynamics of the impurity spin causes the electron scattering to be inelastic at any temperature. 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.