Properties of the skyrmion crystal SkX-2 in the Heisenberg triangular lattice with scalar chirality
Skyrmion crystals have been primarily discovered under a magnetic field for materials with non-centrosymmetric interactions. More recent developments have investigated the stability of skyrmion crystals in itinerant magnets without magnetic field. In this study, we find that a type of skyrmion crystal with two topological charges per unit cell and no magnetization at the ferromagnetic point in reciprocal space, SkX-2, is naturally stabilized in an $SO(3)$-symmetric model with short-range interactions realized by the Heisenberg model on the triangular lattice with scalar chirality. We complement our numerical results with a theoretical analysis that quantitatively describes the transition from the ferromagnetic ground state to the SkX-2 and the evolution of the topological charge density. Despite the constraints given by the Mermin-Wagner theorem at finite temperature, the SkX-2 exhibits both a first-order phase transition associated with translation symmetry breaking and a continuous transition to a floating solid, depending on the charge density controlled by the model parameters. Finally, the tetrahedral phase supported by an antiferromagnetic interaction in our model is found to host $\mathbb{Z}_2$-vortices at finite temperature, suggesting the existence of an additional vortex topological transition.