Noncoplanar spin configurations in itinerant magnets have been attracting much interest because they act as a huge effective magnetic field for itinerant electrons through the spin Berry phase mechanism and bring about peculiar quantum transport phenomena. Chiral magnets with the spin-orbit coupling (SOC) are good platforms of stabilizing noncoplanar spin configurations, such as skyrmion crystals. Recently, however, several noncoplanar spin configurations induced by Fermi surface instabilities have been discovered in itinerant magnets for certain electron filling fractions even in the absence of the SOC [1-6]. Here, we demonstrate that noncoplanar ordering is a generic property of a class of frustrated itinerant magnets in their weak-coupling limit and unveil the origin of the multi-modulated structures induced by Fermi surface instabilites.
By performing large-scale Langevin dynamics simulations  of the square Kondo lattice model, we find double- Q noncoplanar vortex-antivortex crystals . We study the stabilization mechanism by two complementary approaches: perturbative expansion with respect to the spin-charge coupling and degree of noncoplanarity and direct diagonalization of the full Hamiltonian. These studies consistently clarify the origin of the double- Q vortex crystals. Our results indicate that the key ingredient is “frustration” arising from multiple peaks of the bare magnetic susceptibility, which is a generic property of high-symmetry itinerant helimagnets.
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