Transitions from Coplanar Double-Q to Noncoplanar Triple-Q States Induced by High-Harmonic Wave-Vector Interaction

We theoretically investigate topological transitions between coplanar and noncoplanar magnetic states in centrosymmetric itinerant magnets on a square lattice. A canonical effective spin model incorporating bilinear and biquadratic exchange interactions at finite wave vectors is analyzed to elucidate the emergence of multiple-Q magnetic orders. By taking into account high-harmonic wave-vector interactions, we demonstrate that a coplanar double-Q spin texture continuously evolves into a noncoplanar triple-Q state carrying a finite scalar spin chirality. The stability of these multiple-Q states is examined using simulated annealing as a function of the relative strengths of the high-harmonic coupling, the biquadratic interaction, and the external magnetic field. The resulting phase diagrams reveal a competition between double-Q and triple-Q states, where the noncoplanar triple-Q phase is stabilized through the cooperative effect of the high-harmonic and biquadratic interactions. Real-space spin textures, spin structure factors, and scalar spin chirality distributions are analyzed to characterize the distinct magnetic phases and the topological transitions connecting them. These findings provide a microscopic framework for understanding the emergence of noncoplanar magnetic textures driven by the interplay between two- and four-spin interactions in centrosymmetric itinerant magnets.