# RKKY coupling in Weyl semimetal thin films

## TL;DR

This paper investigates the RKKY interaction between impurity spins on the surfaces of Weyl semimetal thin films, revealing anisotropic surface coupling and thickness-dependent bulk-mediated interactions.

## Contribution

It provides analytical and numerical analysis of surface and bulk-mediated RKKY coupling in Weyl semimetal thin films, highlighting the strong, thickness-dependent interactions.

## Key findings

- Surface spin coupling reflects Fermi arc anisotropy and spin-momentum locking.
- Opposite surface coupling is mediated by both Fermi arcs and bulk states.
- Coupling strength varies with film thickness, peaking at an optimal thickness.

## Abstract

We consider the effective coupling between impurity spins on surfaces of a thin-film Weyl semimetal within Ruderman-Kittel-Kasuya-Yoshida (RKKY) theory. If the spins are on the same surface, their coupling reflects the anisotropy and the spin-momentum locking of the Fermi arcs. By contrast when the spins are on opposite surfaces, their coupling is mediated by the Fermi arcs as well as by bulk states. In this case the coupling is both surprisingly strong and strongly thickness dependent, with a maximum at an optimum thickness. We demonstrate our results using analytical solutions of states in the thin-film geometry, as well using a two-surface recursive Green's function analysis of the tight-binding model.