Nonperturbative Scaling Theory of Free Magnetic Moment Phases in Disordered Metals

TL;DR

This paper investigates the transition between free magnetic moments and Kondo screening in disordered metals, revealing a phase where local pseudogaps cause free moments, with scaling behavior linked to elastic scattering.

Contribution

It introduces a nonperturbative scaling theory describing free magnetic moment phases in disordered metals, supported by numerical and analytical analysis.

Findings

Existence of a free moment phase below a critical exchange coupling J_c

Identification of a phase with free moments caused by local pseudogaps

Scaling of pseudogap width with elastic scattering rate 1/τ

Abstract

The crossover between a free magnetic moment phase and a Kondo phase in low dimensional disordered metals with dilute magnetic impurities is studied. We perform a finite size scaling analysis of the distribution of the Kondo temperature as obtained from a numerical renormalization group calculation of the local magnetic susceptibility and from the solution of the self-consistent Nagaoka-Suhl equation. We find a sizable fraction of free (unscreened) magnetic moments when the exchange coupling falls below a disorder-dependent critical value $J_{\rm c}$. Our numerical results show that between the free moment phase due to Anderson localization and the Kondo screened phase there is a phase where free moments occur due to the appearance of random local pseudogaps at the Fermi energy whose width and power scale with the elastic scattering rate $1/\tau$.