Skyrmion Crystal Induced by Four-Spin Interactions in Itinerant Triangular Magnets

We investigate the emergence of magnetic skyrmion crystals with swirling topological spin textures in itinerant magnets with an emphasis on momentum-resolved multi-spin interactions. By performing the simulated annealing for the effective spin model with the two-spin and four-spin interactions on a two-dimensional triangular lattice, we show that various types of four-spin interactions become the microscopic origin of the magnetic skyrmion crystal with the skyrmion numbers of one and two. We find that the four-spin interactions between the different wave vectors lead to the skyrmion crystal with the skyrmion number of one, whereas those at the same wave vectors lead to the skyrmion crystals with the skyrmion number of one and two. Our results indicate that the multi-spin interactions arising from the itinerant nature of electrons provide rich topological spin textures in magnetic metals.