Skyrmion and vortex crystals in the Hubbard model

Mutual interaction between the charge and spin degrees of freedom in electrons leads to the instability towards various topological magnetic orderings such as magnetic skyrmion and vortex crystals [1], whose structures are characterized by the multiple-Q state. In centrosymmetric itinerant magnets, the stabilization mechanism has been extensively studied in the Kondo lattice model consisting of itinerant electrons and localized spins, where the contribution from the charge degrees of freedom of localized electrons is disregarded. In this study, we investigate a realization of the skyrmion crystal (SkX) with the Hubbard model on a centrosymmetric triangular lattice, in which electrons show the itinerant nature rather than the localized one. Based on the self-consistent Hartree-Fock mean-field calculations, we find two types of the SkX as the ground state even without the external magnetic field, one of which corresponds to the findings in the Kondo lattice model [2]. Furthermore, we obtain another noncoplanar vortex crystal phase, and observe the topological phase transition from the vortex crystal to a different SkX in a magnetic field. Our results provide a further possibility to search for exotic topological magnetism in itinerant magnets.

[1] T. Kurumaji et al., Science 365, 914 (2019). [2] R. Ozawa et al., Phys. Rev. Lett. 118, 147205 (2017).