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DOE OSTI2025

Strongly nonlinear wave propagation in elasto-plastic metamaterials: Low-order dynamic modeling

Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are often prohibitively expensive at scales of interest. Prior studies have therefore utilized low-order effective medium models, such as discrete mass-spring lattices, to capture essential properties in the long-wavelength limit. While models of this type have been successfully implemented for a wide variety of nonlinear elastic systems, they have predominantly considered dynamics depending only on the instantaneous kinematics of the lattice, neglecting history-dependent effects, such as wear and plasticity. Here, to address this limitation, the present study develops a lattice-based modeling framework for nonlinear elastic metamaterials undergoing plastic deformation. Due to the history- and rate-dependent nature of plasticity, the framework generally yields a system of differential-algebraic equations whose computational cost is significantly greater than an elastic system of comparable size. We demonstrate the method using several models inspired by classical lattice dynamics and continuum plasticity theory and explore means to obtain empirical plasticity models for general geometries, thereby gaining insight into the influence of microstructural plasticity on effective material performance, which can be used to improve the design of nonlinear mechanical metamaterials.

Dynamic simulation↗

DOE OSTI2022

Origin of ultralow phonon transport and strong anharmonicity in lead-free halide perovskites

All-inorganic lead-free halide double perovskites offer a promising avenue toward non-toxic, stable optoelectronic materials, properties that are missing in their prominent lead-containing counterparts. Their large thermopowers and high carrier mobilities also make them promising for thermoelectric applications. Here, in this work, we present a first-principles study of the lattice vibrations and thermal transport behaviors of Cs 2 SnI 6 and γ-CsSnI 3 , two prototypical compounds in this materials class. We show that conventional static zero temperature density functional theory (DFT) calculations severely underestimate the lattice thermal conductivities (κ l ) of these compounds, indicating the importance of dynamical effects. By calculating anharmonic renormalized phonon dispersions, we show that some optic phonons significantly harden with increasing temperature (T), which reduces the scattering of heat carrying phonons and enhances calculated κ l values when compared with standard zero temperature DFT. Furthermore, we demonstrate that coherence contributions to κ l , arising from wave like phonon tunneling, are important in both compounds. Overall, calculated κ l with temperature-dependent interatomic force constants, built from particle and coherence contributions, are in good agreement with available measured data, for both magnitude and temperature dependence. Large anharmonicity combined with low phonon group velocities yield ultralow values, with room temperature values of 0.26 W/m-K and 0.72 W/m-K predicted for Cs 2 SnI 6 and γ-CsSnI 3 , respectively. We further show that the lattice dynamics of these compounds are highly anharmonic, largely mediated by rotation of the SnI6 octahedra and localized modes originating from Cs rattling motion. These thermal characteristics combined with their previously computed excellent electronic properties make these perovskites promising candidates for optoelectronic and room temperature thermoelectric applications.

36 MATERIALS SCIENCE↗

NASA NTRS1984

Identification of the dynamics of a two-dimensional grid structure using least square lattice filters

The basic theory of least square lattice filters and their use in identification of structural dynamics systems is summarized. Thereafter, this theory is applied to a two-dimensional grid structure made of overlapping bars. Previously, this theory has been applied to an integral beam. System identification results are presented for both simulated and experimental tests and they are compared with those predicted using finite element modelling. The lattice filtering approach works well for simulated data based on finite element modelling. However, considerable discrepancy exists between estimates obtained from experimental data and the finite element analysis. It is believed that this discrepancy is the result of inadequacies in the finite element modelling to represent the damped motion of the laboratory apparatus.

Montgomery, R. C.↗

DOE OSTI2026

Terahertz‐Nanoscale Visualization of the Microscopic Spin‐Charge Architecture of Colossal Magnetoresistive Switching

Resolving sub-10 nm spin switching and the associated terahertz (THz) electrodynamics during the colossal magnetoresistance (CMR) transition is a definitive frontier in reaching the fundamental spatial, temporal, and energy-dissipation limits of spin-electronics. Yet, simultaneous control of high magnetic field, cryogenic environment, and nanometer resolution has remained an elusive benchmark for THz nanoscopy, leaving the local THz dynamics of these transitions largely unexplored. Here, we overcome these limitations by utilizing a custom-built cryogenic magneto-THz scattering-type scanning near-field optical microscopy (cm-THz-sSNOM) to resolve the near-field THz spectroscopic evolution of the magnetic field-driven CMR transition in a manganite single crystal. Our measurements provide a nanoscale visualization of the THz conductivity, capturing the moment that magnetic-field-induced spin switching triggers the transition from an antiferromagnetic insulator to a ferromagnetic metal. An ellipsoidal near-field model reveals a multi-scale transition initiated by 1–2 nm isolated spin-flip sites at low magnetic fields, which coalesce into ∼15 nm conducting regions as the threshold field is approached. These results provide an nano-THz view of CMR switching, establishing an analysis framework for mapping spin–charge–lattice–orbit–coupled dynamics at spatial scales that transcend the nominal sSNOM resolution.

Haeuser, Samuel [Iowa State University, Ames, IA (↗

DOE OSTI2022

Polariton Dynamics in Two-Dimensional Ruddlesden–Popper Perovskites Strongly Coupled with Plasmonic Lattices

Strong coupling between light and matter can produce hybrid eigenstates known as exciton-polaritons. Although polariton dynamics are important photophysical properties, the relaxation pathways of polaritons in different coupling regimes have seen limited attention. This paper reports the dynamics of hybridized states from 2D Ruddlesden-Popper perovskites coupled to plasmonic nanoparticle lattices. The open cavity architecture of Al lattices enables the coupling strength to be modulated by varying either the lead halide perovskite film thickness or the superstrate refractive index. Both experiments and finite-difference time-domain simulations of the optical dispersion diagrams showed avoided crossings that are a signature of strong coupling. Furthermore, our analytical model also elucidated the correlation between the exciton/plasmon mixing ratio and polariton coupling strength. Using fs-transient absorption spectroscopy, we found that both the upper and lower polaritons have shorter lifetimes than the excitons and that polaritons can show faster excited state dynamics when they have access to additional energy transfer channels.

2D perovskite↗

DOE OSTI2025

Interacting spin and charge density waves in the kagome metal FeGe

Unveiling the interplay between spin density wave (SDW) and charge density wave (CDW) orders in correlated electron materials is important in obtaining a comprehensive understanding of their electronic, structural, and magnetic properties. Kagome lattice materials are interesting because their flat electronic bands, Dirac points, and Van Hove singularities can enable a variety of exotic electronic and magnetic phenomena. The kagome metal FeGe (the B35 phase), which exhibits a CDW order deep within an A-type antiferromagnetic (AFM) phase, was found to respond dramatically to postgrowth annealing—with the ability to tune the CDW repeatedly from long-range order to negligible order. Additionally, neutron scattering studies suggest that incommensurate magnetic peaks that onset at 𝑇 Canting = 𝑇 SDW ≈ 60 K in the system arise from a SDW order instead of the AFM double-cone structure. Here, in this study, we use inelastic neutron scattering to show that two distinct spin excitations exist below 𝑇 Canting corresponding to two coexisting magnetic orders in the system in both sets of annealed samples with and without CDW. While CDW order or negligible order can dramatically affect the onset temperature of 𝑇 Canting and elastic incommensurate magnetic scattering, its impact on low-energy spin fluctuations is more limited. In both samples, a pair of gapless incommensurate spin excitations arising from the SDW order wave vector coexist with gapped commensurate spin waves from the A-type AFM order across 𝑇 Canting . The low-energy spin excitations for both samples couple dynamically to the lattice through enhanced magnetic scattering intensity on cooling below 𝑇 CDW , regardless of the status of the static long-range CDW order. The incommensurate SDW order in the long-range CDW ordered sample also induces a tiny in-plane lattice distortion of the kagome lattice that is absent in the negligible CDW ordered sample, in a way that is different from the previously known SDW and CDW ordering materials.

charge density waves↗

DOE OSTI2021

Laser-Induced Cooperative Transition in Molecular Electronic Crystal

The competing and non-equilibrium phase transitions, involving dynamic tunability of cooperative electronic and magnetic states in strongly correlated materials, show great promise in quantum sensing and information technology. To date, the stabilization of transient states is still in the preliminary stage, particularly with respect to molecular electronic solids. Here, a dynamic and cooperative phase in potassium-7,7,8,8-tetracyanoquinodimethane (K-TCNQ) with the control of pulsed electromagnetic excitation is demonstrated. Simultaneous dynamic and coherent lattice perturbation with 8 ns pulsed laser (532 nm, 15 MW cm -2 , 10 Hz) in such a molecular electronic crystal initiates a stable long-lived (over 400 days) conducting paramagnetic state (≈42 Ωcm), showing the charge–spin bistability over a broad temperature range from 2 to 360 K. Comprehensive noise spectroscopy, in situ high-pressure measurements, electron spin resonance (ESR), theoretical model, and scanning tunneling microscopy/spectroscopy (STM/STS) studies provide further evidence that such a transition is cooperative, requiring a dedicated charge–spin–lattice decoupling to activate and subsequently stabilize nonequilibrium phase. Finally, the cooperativity triggered by ultrahigh-strain-rate (above 10 6 s -1 ) pulsed excitation offers a collective control toward the generation and stabilization of strongly correlated electronic and magnetic orders in molecular electronic solids and offers unique electro-magnetic phases with technological promises.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Modeling phonons in nanomaterials

The vibrational properties of nanomaterials play fundamentally important roles in determining their stability and various functionalities, from rippling of otherwise flat two-dimensional (2D) monolayers to the extreme thermal transport behaviors observed in one-dimensional (1D) and 2D carbon-based systems. Here we discuss modeling efforts to understand how phonons in lower dimensional materials differ from those in bulk, and how these behaviors manifest in their unusual properties. In particular, this chapter gives a heavy focus to calculations of phonon dynamics, interactions, and lattice thermal transport in 1D chains and nanotubes, 2D monolayers, and van der Waals coupled bulk materials from first principles methods. This chapter will discuss important phonon calculation details related to nanomaterials with examples and discussions providing both historical and modern perspectives.

Lindsay, Lucas↗

DOE OSTI2026

Ultrafast Carrier Self-Trapping Driven by Strong Exciton–Phonon Coupling in 2D MA 3 Bi 2 I 6 Cl 3 Perovskite

Two-dimensional (2D) hybrid bismuth halide perovskites have emerged as promising lead-free materials for optoelectronic applications due to their solution processability and tunable structures. Here, in this study, we investigate 2D layered hybrid perovskite MA 3 Bi 2 I 6 Cl 3 using temperature-dependent photoluminescence (PL) and femtosecond transient absorption spectroscopy. Our results reveal strong coupling between excitons and phonons, evidenced by giant Huang–Rhys factors, coherent phonon oscillations, and ultrafast carrier self-trapping into small-polaron and self-trapped exciton (STE) states. These processes appear as time-dependent ground-state bleach and photoinduced absorption features, highlighting the influence of the lattice in carrier dynamics. Wavelength- and time-resolved measurements reveal that PL emission is dominated by STEs, while free exciton emission is weak and short-lived. By comparing 2D MA 3 Bi 2 I 6 Cl 3 with 0D MA 3 Bi 2 I 9 , which contains molecularly isolated [BiI 6 ] 3− octahedra and 2D MA 3 Bi 2 Br 9 perovskites, we demonstrate how halide composition and structural dimensionality influence the balance between free exciton populations and carrier localization. These insights uncover the intrinsic kinetic landscape of photoexcited states in MA 3 Bi 2 I 6 Cl 3 . Overall, our study contributes to a mechanistic understanding of exciton–phonon interactions in lead-free 2D perovskites.

Pradeep, Kodimana Ramakrishnan [Northwestern Univ.↗

DOE OSTI2023

Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, nonreciprocal, one-dimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly transcending conventional elasticity.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Multiphonon diffuse scattering in solids from first principles: Application to layered crystals and two-dimensional materials

Time-resolved diffuse scattering experiments have gained increasing attention due to their potential to reveal nonequilibrium dynamics of crystal lattice vibrations with full momentum resolution. Although progress has been made in interpreting experimental data on the basis of one-phonon scattering, understanding the role of individual phonons can be sometimes hindered by multiphonon excitations. In Ref. [M. Zacharias, H. Seiler, F. Caruso, D. Zahn, F. Giustino, P. C. Kelires, and R. Ernstorfer, Phys. Rev. Lett. 127, 207401 (2021)], we have introduced a rigorous approach for the calculation of the all-phonon inelastic scattering intensity of solids from first-principles. In the present work, we describe our implementation in detail and show that multiphonon interactions are captured efficiently by exploiting translational and time-reversal symmetries of the crystal. We demonstrate its predictive power by calculating the scattering patterns of monolayer molybdenum disulfide (MoS 2 ), bulk MoS 2 , and black phosphorus (bP), and we obtain excellent agreement with our measurements of thermal electron diffuse scattering. Remarkably, our results show that multiphonon excitations dominate in bP across multiple Brillouin zones, while in MoS 2 they play a less pronounced role. We expand our analysis for each system and examine the effect of individual atomic and interatomic vibrational motion on the diffuse scattering signals. We further demonstrate the high-throughput capability of our approach by reporting all-phonon scattering maps of two-dimensional MoSe 2 , WSe 2 , WS 2 , graphene, and CdI 2 , rationalizing in each case the effect of multiphonon processes. As a side point, we show that the special displacement method reproduces the thermally distorted configuration that generates precisely the all-phonon diffuse pattern. In conclusion, the present methodology opens the way for systematic calculations of the scattering intensity in crystals and the accurate interpretation of static and time-resolved inelastic scattering experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Connection between coherent phonons and electron-phonon coupling in Sb (111)

We report time- and angle-resolved photoemission spectroscopy (trARPES) measurements on the Sb(111) surface. We observe band- and momentum-dependent binding-energy oscillations in the bulk and surface bands driven by $A_{1g}$ and $E_{g}$ coherent phonons. While the bulk band shows simultaneous $A_{1g}$ and $E_{g}$ oscillations, the surface bands show either $A_{1g}$ or $E_{g}$ oscillations. The observed behavior is reproduced by frozen-phonon calculations based on density-functional theory. Furthermore, this evidences the connection between electron-phonon coupling and coherent binding energy dynamics tied to lattice vibration and confirms that band-, momentum-, and mode-dependent electron-phonon coupling can indeed be probed by trARPES in the low fluence limit.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions

Tracking the dynamics of physical systems in real time is a prime application of quantum computers. Using a trapped-ion system with up to six qubits, we simulate the real-time dynamics of a lattice gauge theory in 1+1 dimensions, i.e., the lattice Schwinger model, and demonstrate nonperturbative effects such as pair creation for times much longer than previously accessible. We study the gate requirement of two formulations of the model using the Suzuki-Trotter product formula, as well as the trade-off between errors from the ordering of the Hamiltonian terms, the Trotter step size, and experimental imperfections. To mitigate experimental errors, a recent symmetry-protection protocol for suppressing coherent errors and a symmetry-inspired postselection scheme are applied. This work demonstrates the integrated theoretical, algorithmic, and experimental approach that is essential for efficient simulation of lattice gauge theories and other complex physical systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Accounting for electron-beam-induced warping of molecular nanocrystals in MicroED structure determination

High-energy electrons induce sample damage and motion at the nanoscale to fundamentally limit the determination of molecular structures by electron diffraction. Using a fast event-based electron counting (EBEC) detector, we characterize beam-induced, dynamic, molecular crystal lattice reorientations (BIRs). These changes are sufficiently large to bring reciprocal lattice points entirely in or out of intersection with the sphere of reflection, occur as early events in the decay of diffracted signal due to radiolytic damage, and coincide with beam-induced migrations of crystal bend contours within the same fluence regime and at the same illuminated location on a crystal. These effects are observed in crystals of biotin, a series of amino acid metal chelates, and a six-residue peptide, suggesting that incident electrons inevitably warp molecular lattices. The precise orientation changes experienced by a given microcrystal are unpredictable but are measurable by indexing individual diffraction patterns during beam-induced decay. Reorientations can often tilt a crystal lattice several degrees away from its initial position before irradiation, and for an especially beam-sensitive Zn(II)-methionine chelate, are associated with dramatic crystal quakes prior to 1 e − Å −2 electron beam fluence accumulates. Since BIR coincides with the early stages of beam-induced damage, it echoes the beam-induced motion observed in single-particle cryoEM. As with motion correction for cryoEM imaging experiments, accounting for BIR-induced errors during data processing could improve the accuracy of MicroED data.

Vlahakis, Niko (ORCID:0000000250920265)↗

DOE OSTI2021

A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media

This paper presents a new deep learning data-driven model for predicting structure dependent pore-fluid velocity fields in rock. The model is based on a Convolutional Auto-Encoder (CAE) artificial neural network capable of learning from image data generated by direct numerical simulations of fluid flow through pore-structures, such as by Lattice Boltzmann or molecular dynamics methods. The main novelty of the model in comparison to previous CAE-based data-driven approaches consists of three parts. The first is a methodology for decomposing the full-domain of the porous media into sub-regions, or “sub-domains”, in order to reduce the overall size of the CAE, batch process the sub-domains in parallel, and enable the CAE to learn local and generalizable nonlinear mappings of pore-fluid velocities. The second consists of embedding the finite difference solutions of the incompressible Navier-Stokes and continuity equations into convolutional layers prior to the CAE in order to provide the CAE with knowledge of fluid dynamics physics (PhyFlow). The third main novelty is that the training of the CAE is regularized with a hierarchical loss function that encourages the learning of fluid flow patterns (in a way similar to ranked modes in principal component analysis), ranking from most to least important. This is shown to increase the stability in learning, reduce over-fitting, and promote interpretability of the CAE neural network layers (HierCAE). The comprehensive new data-driven model, which we call the PhyFlow-HierCAE model, is shown to exhibit improved accuracy and generalizability of flow field predictions over conventional CAE models, attributable to the embedded physical knowledge and the hierarchical regularization, as well as realize orders of magnitude speed-ups in computation times as a surrogate for the direct numerical simulations. Examples of training and forward predictions on unseen pore-structures are provided and evaluated for data from Lattice Boltzmann and molecular dynamics simulations of pore-fluid flow. The model is shown to be a fast and accurate emulator (or “surrogate”) for predicting effective permeability of unseen pore-structures based on learning from relatively small direct numerical simulation datasets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Quantum Spin Dynamics Due to Strong Kitaev Interactions in the Triangular-Lattice Antiferromagnet CsCeSe 2

The extraordinary properties of the Kitaev model have motivated an intense search for new physics in materials that combine geometrical and bond frustration. In this Letter, we employ inelastic neutron scattering, spin wave theory, and exact diagonalization to study the spin dynamics in the perfect triangular-lattice antiferromagnet (TLAF) CsCeSe 2 . This material orders into a stripe phase, which is demonstrated to arise as a consequence of the off-diagonal bond-dependent terms in the spin Hamiltonian. By studying the spin dynamics at intermediate fields, we identify an interaction between the single-magnon state and the two-magnon continuum that causes decay of coherent magnon excitations, level repulsion, and transfer of spectral weight to the continuum that are controlled by the strength of the magnetic field. Our results provide a microscopic mechanism for the stabilization of the stripe phase in TLAF and show how complex many-body physics can be present in the spin dynamics in a magnet with strong Kitaev coupling even in an ordered ground state. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Impact of dynamic Jahn-Teller effect on magnetic excitations, lattice vibration, and thermal conductivity in U 𝑥 ⁢T⁢h 1−𝑥 ⁡O 2 system

Vibrational and magnetic properties of single-crystal uranium-thorium dioxide (U 𝑥 ⁢T⁢h 1−𝑥⁡ O 2 ) with a full range of 0 < 𝑥 < 1 are investigated. Thorium dioxide is a diamagnet whose thermal properties are governed by lattice vibration. The addition of paramagnetic uranium ions leads to the emergence of magnetic effects that alter the thermophysical properties noticeably even at room temperature. The interaction of phonons with magnetic moments of uranium 5⁢𝑓 electrons mediated by magnetoelastic coupling results in an anomalous low-temperature thermal conductivity profile. Analysis of the magnetic susceptibility measurements indicates a departure from the Curie-Weiss relationship characteristic of noninteracting paramagnetic ions, previously associated with the dynamic Jahn-Teller (DJT) effect characterized by coupling between spin and the oxygen sublattice. The T 2⁢g Raman peak position follows a nonlinear trend as a function of uranium concentration and hints that these Raman active optical modes play a role in either DJT or in mediating quadrupole-quadrupole interactions. A first-principle-based thermal transport model is implemented to explain the low-temperature transport measurements, where the anomalous reduction is attributed to phonon-spin resonant scattering. The interplay between spins and phonons is also captured using high-resolution inelastic x-ray scattering (IXS) measurements of phonon linewidths. Our results provide insights into the phonon interactions with the magnetic excitations governing DJT effect and impacting the low-temperature thermal transport processes in this material system. Furthermore, these findings have implications for understanding low-temperature thermal transport and magnetic properties in advanced materials for information processing and energy applications.

36 - MATERIALS SCIENCE↗

DOE OSTI2025

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 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 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 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 Co 0.325 ⁢TaS 2 further establishes it as a prominent material platform for exploring topological spin textures in the genuine 2D limit.

Park, Pyeongjae [Oak Ridge National Laboratory (OR↗