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Multiple-$Q$ spin textures induced by spiral--staggered interference in one-dimensional itinerant magnets

We theoretically investigate multiple-$Q$ magnetic states emerging from the interference between finite-$Q$ spiral and staggered spin modulations in a one-dimensional itinerant electron system. The multiple-$Q$ spin textures are characterized by a superposition of symmetry-unrelated ordering wave vectors in the same direction with distinct periodicities rather than rotationally symmetry-related ones. Motivated by recent experimental observations of broken helix magnetic structures in EuIn$_2$As$_2$, we focus on the microscopic interaction conditions in stabilizing such multiple-$Q$ states.We employ two effective spin models: One is the momentum-space-based model, and the other is the real-space-based model, both of which include bilinear and biquadratic easy-plane anisotropic interactions. By analyzing their ground state via simulated annealing, we find that a superposition of a spiral and a staggered modulation yields a robust double-$Q$ magnetic structure. Moreover, we demonstrate that the obtained double-$Q$ spin configuration exhibits an antisymmetric spin-split band structure even without the relativistic Dzyaloshinskii-Moriya interaction, and further reveals asymmetric band modulations when the magnetic field is applied along the out-of-plane direction. Our results provide a theoretical framework for understanding unconventional multiple-$Q$ magnetic textures in one-dimensional systems.