Indirect RKKY Interaction in the Nearly Nested Fermi Liquid

TL;DR

This paper analytically evaluates the RKKY interaction in layered metals with nearly nested Fermi surfaces, revealing oscillatory behavior, sign-reversal antiferromagnetic intermediate asymptotes, and agreement with numerical results.

Contribution

It provides closed-form analytical expressions for RKKY interactions in nearly nested Fermi liquids, highlighting unique asymptotic behaviors and sign-reversal phenomena.

Findings

2k_F oscillations as far asymptote

Existence of sign-reversal antiferromagnetic intermediate asymptote

Analytical formulas agree with numerical results

Abstract

The indirect RKKY interaction in a layered metal with nearly nested (almost squared) Fermi surface is evaluated analytically. The final expressions are obtained in closed form as a combination of Bessel functions. We show that the expected ``2k_F'' oscillations occur as the far asymptote of our expressions, where a value of the effective Fermi momentum k_F depends on the direction in r-space. We demonstrate the existence of the intermediate asymptote of the interaction which is of the sign-reversal antiferromagnetic type. This part of RKKY interaction is the only term surviving in the limit of exact nesting. A good accordance of our analytical formulas with numerical findings is found until the interatomic distances.