Stabilization of magnetic skyrmions by RKKY interactions

TL;DR

This paper investigates how RKKY interactions can stabilize magnetic skyrmions in monolayers on conducting substrates, revealing different stabilization mechanisms for metallic and graphene substrates through variational energy analysis.

Contribution

It introduces a novel analysis of skyrmion stabilization via RKKY interactions, contrasting with previous models based on frustrated exchange or Dzyaloshinskii-Moriya interactions.

Findings

RKKY interactions can stabilize skyrmions under specific conditions.

Metallic substrates require restrictive Fermi surface parameters for stabilization.

Graphene substrates naturally support skyrmion stabilization in various geometries.

Abstract

We study the stabilization of an isolated magnetic skyrmion in a magnetic monolayer on a nonmagnetic conducting substrate via the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction. Two different types of the substrate are considered, usual normal metal and single-layer graphene. While the full stability analysis for skyrmions in the presence of the RKKY coupling requires a separate effort that is outside the scope of this work, we are able to study the radial stability (stability of a skyrmion against collapse) using variational energy estimates obtained within first-order perturbation theory, with the unperturbed Hamiltonian describing the isotropic Heisenberg magnet, and the two perturbations being the RKKY exchange and the easy-axis anisotropy. We show that a proper treatment of the long-range nature of the RKKY interaction leads to a qualitatively different stabilization scenario compared to previous studies, where solitons were stabilized by the frustrated exchange coupling (leading to terms with the fourth power of the magnetization gradients) or by the Dzyaloshinskii-Moriya interaction (described by terms linear in the magnetization gradients). In the case of a metallic substrate, the skyrmion stabilization is possible under restrictive conditions on the Fermi surface parameters, while in the case of a graphene substrate the stabilization is naturally achieved in several geometries with a lattice-matching of graphene and magnetic layer.