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Spin Dynamics of Triple-Q Magnetic Orderings in a Triangular Lattice: Implications for Multi-Q Orderings in General Two-Dimensional Lattices

Pyeongjae Park1,2,3,*, Woonghee Cho2,3, Chaebin Kim2,3, Yeochan An2,3, Kazuki Iida4, Ryoichi Kajimoto5, Sakib Matin6,7, Shang-Shun Zhang8, Cristian D. Batista8,9 et al.

Je-Geun Park2,3,10,†

  • *Contact author: parkp@ornl.gov
  • †Contact author: jgpark10@snu.ac.kr
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Phys. Rev. X 15, 031032 – Published 30 July, 2025

DOI: https://doi.org/10.1103/y9ly-4kld

Abstract

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 multidomain 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 Co0.325TaS2, which hosts both a stripe-type single-Q state and a triple-Q tetrahedral ordering at different temperatures. Using inelastic neutron-scattering 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. Beyond the long-wavelength regime, we present a substantial discrepancy between the measured and simulated magnon spectra exclusively in the triple-Q phase. We attribute this discrepancy to magnon energy renormalization arising from order-of-magnitude-enhanced magnon-magnon interactions in the triple-Q phase, due to its noncollinear configuration. 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. The unequivocal confirmation of the triple-Q structure in Co0.325TaS2 further establishes it as a prominent material platform for exploring topological spin textures in the genuine 2D limit.

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Special Collection on 2D Materials

PRX launches this collection to showcase articles in the exciting field of 2D materials and van der Waals heterostructures to constitute an emblematic example of the diversity of physics in this very active scientific domain.

Popular Summary

Two-dimensional magnets are promising candidates for future spintronic technologies, especially when they exhibit complex “multi-Q” spin textures—intricate arrangements of magnetic moments that can lead to topological states such as skyrmions. However, identifying these topological states is challenging, as they often appear similar to more conventional magnetic orders in standard diffraction experiments. In this study, we propose a new and general method to distinguish between topological and trivial magnetic orders by examining how spin waves—collective excitations of spins—propagate through the material.

We focus on triangular-lattice magnets, a common host for multi-Q textures, and investigate how their low-energy spin waves behave. Our calculations reveal a clear distinction: In topological triple-Q phases, spin waves spread isotropically, moving at nearly the same speed in all directions. In contrast, in conventional single- or double-Q phases, the spin-wave speed is anisotropic, varying with direction.

We confirm this behavior experimentally in a layered triangular-lattice magnet that naturally transitions between topological and conventional phases as temperature changes. Using inelastic neutron scattering, we directly observe the predicted differences in spin-wave propagation. This distinction is rooted in general symmetry and long-wavelength behavior, making it widely applicable across different materials.

Our approach offers a powerful, material-independent way to identify topological spin textures in 2D magnets. Looking ahead, it could guide the discovery of new topological magnetic phases and support the development of advanced spintronic devices based on robust, topologically protected states.

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Phys. Rev. X 15, 031032– Published 30 July, 2025
  • Received 2 October 2024
  • Revised 9 May 2025
  • Accepted 8 July 2025
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