Replica symmetry breaking in the RKKY skyrmion crystal system

TL;DR

This study uses Monte Carlo simulations to reveal replica-symmetry breaking in skyrmion crystal phases of a 3D RKKY Heisenberg model, showing coexistence of distinct ordered states and ergodicity breaking.

Contribution

It uncovers replica-symmetry breaking phenomena in a regular Hamiltonian system with skyrmion crystals, a novel finding in magnetic systems.

Findings

Discovery of RSB in skyrmion crystal phases.

Coexistence of multiple ordered states with degenerate free energies.

Divergence of free-energy barriers indicating ergodicity breaking.

Abstract

We study the RKKY Heisenberg model on a three-dimensional stacked-triangular lattice under magnetic fields by extensive Monte Carlo simulations to get insight into the chiral-degenerate symmetric skyrmion crystal (SkX) in centrosymmetric metallic magnets. The triple-$q$ SkX state and the double-$q$ states are realized, together with the single-$q$ state. We find an unexpected phenomenon of the replica-symmetry breaking (RSB) well-known in glassy systems, although the Hamiltonian and the ordered state are entirely regular. In the RSB SkX phase, the triple-$q$ SkX state macroscopically coexists with the single-$q$ state, in spite of the fact that these ordered states cannot be transformed via any Hamiltonian-symmetry operation. In the thermodynamic limit, the free energies of these states are degenerate whereas the free-energy barrier between the states diverges, breaking the ergodicity. A similar RSB is observed also in the RSB double-$q$ phase where the double-$q$ state macroscopically coexists with the single-$q$ state. Experimental implications are discussed.