Replica symmetry breaking in the RKKY skyrmion crystal system
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.
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