Spin dynamics of triple-Q magnetic orderings in a triangular lattice: Implications for multi-Q orderings in general two-dimensional lattices

Multi-Q magnetic structures on two-dimensional (2D) lattices provide a key route to realizing topological physics in 2D magnetism. A major experimental challenge is to unambiguously confirm their formation by excluding the possibility of topologically trivial multi-domain single- or double-Q magnetic orders, which cannot be distinguished using conventional diffraction techniques. Here, we propose that long-wavelength spin dynamics offers a universal diagnostic for triangular lattices: triple-Q orders that preserve rotational symmetry and single- or double-Q orders that break it exhibit qualitatively distinct anisotropies in their Goldstone mode velocities, stemming from fundamental differences in their underlying spin configurations. We validate this concept using the metallic triangular lattice antiferromagnet Co$_{0.325}$TaS$_{2}$, which hosts both a stripe-type single-Q state and a triple-Q tetrahedral ordering at different temperatures. Using inelastic neutron scattering (INS) and spin dynamics simulations, we first refine the spin Hamiltonian by fitting the paramagnetic excitation spectra, allowing us to develop an unbiased model independent of magnetic ordering. We then show that the observed velocity profiles of the Goldstone modes agree with the high-temperature model's predictions: markedly anisotropic for the single-Q phase and near isotropic for the triple-Q phase. Importantly, this contrast persists across various exchange parameters, highlighting its model-independent nature and suggesting potential applicability to other 2D lattice systems. This work provides universal insight into the dynamical properties of topological multi-Q magnetic orderings in 2D lattice structures, offering a broadly applicable diagnostic to distinguishing them from topologically trivial single- or double-Q counterparts. (For the full abstract, please refer to the manuscript)