Indirect RKKY interaction in any dimensionality

TL;DR

This paper introduces an analytical method to precisely determine the spatial and momentum dependence of the RKKY interaction across any dimensionality, revealing complex oscillation and sign-reversal behaviors.

Contribution

The authors develop a general analytical approach to calculate the RKKY interaction and Lindhard function for arbitrary dimensions, including layered systems.

Findings

Exact spatial dependence of RKKY interaction for any dimension

Discovery of sign-reversal in interlayer RKKY interaction

Application to layered metallic systems showing antiferromagnetic stacking

Abstract

We present an analytical method which enables one to find the exact spatial dependence of the indirect RKKY interaction between the localized moments via the conduction electrons for the arbitrary dimensionality $n$. The corresponding momentum dependence of the Lindhard function is exactly found for any $n$ as well. Demonstrating the capability of the method we find the RKKY interaction in a system of metallic layers weakly hybridized to each other. Along with usual $2k_F$ in-plane oscillations the RKKY interaction has the sign-reversal character in a direction perpendicular to layers, thus favoring the antiferromagnetic type of layers' stacking.