Effects of the three-dimensional interplanar coupling on the centrosymmetric skyrmion crystal formation in the frustrated stacked-triangular Heisenberg model

Abstract

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.

Fig.4(c,d) added. Figs. 8, 12, 15, 17 modified. Some explanation and discussion added. To appear in Phys. Rev. B