Effects of the three-dimensional interplanar coupling on the centrosymmetric skyrmion crystal formation in the frustrated stacked-triangular Heisenberg model
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Effects of the three-dimensional (3D) interplanar coupling on centrosymmetric skyrmion crystal (SkX) formation is investigated via extensive Monte Carlo simulations on the frustrated isotropic Heisenberg model on a stacked-triangular lattice in both cases of the ferromagnetic (F) and the antiferromagnetic (AF) nearest-neighbor interplanar coupling $J_{1c}$. The SkX phase is stabilized at finite fields and at finite temperatures for both F and AF $J_{1c}$, although it is destabilized by modestly weak AF $J_{1c}$. The magnetic phase diagram of the 3D short-range model is more or less similar to those of the 2D short-range model and of the 2D long-range RKKY model. We find that an intriguing phenomenon of replica-symmetry breaking, popular in glass physics and recently identified in the SkX phase of the 3D long-range RKKY model [K. Mitsumoto and H. Kawamura, Phys. Rev. B {\bf 104}, 184432 (2021)], does not arise in the 3D short-range model, suggesting that the long-range nature of interaction might be necessary to realize the RSB in centrosymmetric SkX state.
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