RKKY interactions in the regime of strong localization

TL;DR

This paper investigates how strong disorder and Anderson localization suppress and alter the distribution of RKKY interactions between magnetic moments in metals, revealing a transition from long-range to localized behavior.

Contribution

It introduces a new understanding of RKKY interactions under strong localization, highlighting the non-Gaussian distribution and the exponential suppression of typical interaction strength.

Findings

RKKY interactions have non-Gaussian distributions with long tails.

Localization suppresses the typical RKKY interaction exponentially.

Anderson localization effectively eliminates long-range RKKY interactions.

Abstract

We study the influence of strong nonmagnetic disorder on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between diluted magnetic moments in metals. We find that the probability distribution for the RKKY interactions assumes strongly non-Gaussian form featuring long tails. Since such distributions cannot be characterized by its moments, we define a \textit{typical} value of the interaction amplitude, which we find to be exponentially suppressed in presence of Anderson localization. Our results present a plausible and physically transparent picture describing how Anderson localization effectively eliminates the long range nature of the RKKY interactions.