Theory of inelastic scattering from magnetic impurities

TL;DR

This paper employs the numerical renormalization group to analyze inelastic scattering from magnetic impurities, revealing a nearly linear frequency dependence below the Kondo temperature and a crossover to quadratic behavior at very low energies.

Contribution

It introduces a method to compute the full energy, spin, and magnetic field dependence of inelastic scattering cross sections for magnetic impurities.

Findings

Inelastic scattering cross section is nearly linear in frequency below T_K.

Crosses over to        behavior at very low energies.

Method can be applied to other quantum impurity models.

Abstract

We use the numerical renormalization group method tocalculate the single particle matrix elements $\cal T$ of the many body $T$-matrix of the conduction electrons scattered by a magnetic impurity at T=0 temperature. Since $\cal T$ determines both the total and the elastic, spin-diagonal scattering cross sections, we are able to compute the full energy-, spin- and magnetic field dependence of the inelastic scattering cross section, $\sigma_{\rm inel}(\omega)$. We find an almost linear frequency dependence of $\sigma_{\rm inel}(\omega)$ below the Kondo temperature, $T_K$, which crosses over to a $\sim \omega^2$ behavior only at extremely low energies. Our method can be generalized to other quantum impurity models.