Multiple-Q States in Bilayer Triangular-Lattice Systems with Bond-Dependent Anisotropic Interaction

We investigate magnetic instabilities toward multiple-Q states in centrosymmetric bilayer triangular-lattice systems. By focusing on the interplay between the layer-dependent Dzyaloshinskii–Moriya interaction and layer-independent bond-dependent anisotropic interaction, both of which originate from the relativistic spin-orbit coupling, we construct a low-temperature phase diagram based on an effective spin model that also includes frustrated isotropic exchange interactions. Employing simulated annealing, we reveal the stabilization of three distinct double-Q phases in the absence of an external magnetic field, each characterized by noncoplanar spin textures with spatially modulated local scalar spin chirality. Under applied magnetic fields, we identify field-induced phase transitions among single-Q, double-Q, and triple-Q states, some of which exhibit a finite net scalar spin chirality indicative of topologically nontrivial order. These findings highlight centrosymmetric systems with sublattice-dependent Dzyaloshinskii–Moriya interactions as promising platforms for realizing a variety of multiple-Q spin textures.