Skyrmion crystal in the RKKY system on the two-dimensional triangular lattice

TL;DR

This study uses Monte Carlo simulations to explore how RKKY interactions on a 2D triangular lattice stabilize skyrmion crystal phases in metallic magnets, highlighting the roles of frustration and thermal fluctuations.

Contribution

It demonstrates the stabilization of skyrmion crystal phases in a 2D RKKY model without nesting or many-body interactions, emphasizing the effects of frustration and thermal fluctuations.

Findings

SkX phase stabilized under applied magnetic fields.

Absence of replica symmetry breaking in 2D model.

Thermal fluctuations and frustration are key to SkX formation.

Abstract

We study the ordering properties of the isotropic RKKY Heisenberg model on the two-dimensional (2D) triangular lattice by extensive Monte Carlo simulations to get insights into the chiral-degenerate skyrmion crystal (SkX) of metallic magnets. Our Hamiltonian contains only the spin-quadratic RKKY interaction derived from the spherical Fermi surface, containing neither the nesting nor the many-body interaction. The SkX phase is stabilized under applied fields where the frustration associated with the oscillating nature of the RKKY interaction and the emergent many-body interactions generated by thermal fluctuations play important roles. Replica symmetry breaking, reported in our recent study on the 3D RKKY model [Phys. Rev. B 104, 184432 (2021)], turns out to be absent in the present 2D model. Implications to the SkX formation mechanism are discussed.