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DOE OSTI2025

Terahertz stimulated parametric downconversion of a magnon mode in an antiferromagnet

Parametric amplification, where one signal is enhanced by the action of another, offers both practical utility for boosting weak signals and fundamental insights into the nonlinear coupling between degrees of freedom. In condensed matter systems, interactions between collective modes offer avenues for nonlinear coherent manipulation of coupled excitations and quantum phases. Antiferromagnets, with inherently coupled magnon modes, provide a promising platform for nonlinear control of spin waves and magnetization. However, nonlinear magnon-magnon interactions have been only partially elaborated, leaving key gaps in the prospects for potential ultrahigh-bandwidth magnonic signal processing. Here, we excite two distinct coherent magnon modes in an antiferromagnet and find that the magnon mode with a lower frequency undergoes amplification when the higher-frequency mode is driven. We unveil the nonlinear excitation pathways of this stimulated parametric downconversion process by using polarization-selective two-dimensional terahertz spectroscopy. Our work provides fundamental insights into nonlinear magnonics in antiferromagnets, laying the groundwork for forthcoming spintronic and magnonic devices.

Science & Technology - Other Topics↗

DOE OSTI2026

A Search for Millimeter-bright Blazars as Astrophysical Neutrino Sources

The powerful jets of blazars have been historically considered as likely sites of high-energy cosmic-ray acceleration. However, the particulars of the launched jet and the locations of leptonic and hadronic jet loading remain unclear. In the case when leptonic and hadronic particle injection occur jointly, a temporal correlation between synchrotron radiation and neutrino production is expected. We use a first catalog of millimeter wavelength (95–225 GHz) blazar light curves from the Atacama Cosmology Telescope for a time-dependent correlation with 12 yr of muon neutrino events from the IceCube South Pole Neutrino Observatory. Such millimeter emission traces activity of the bright jet base, which is often self-absorbed at lower frequencies and potentially gamma-ray opaque. We perform an analysis of the population, as well as analyses of individual, selected sources. We do not observe a significant signal from the stacked population. TXS 0506+056 is found as the most significant, individual source, though this detection is not globally significant in our analysis of selected active galactic nuclei. Our results suggest that the majority of millimeter-bright blazars are neutrino dim. In general, it is possible that many blazars have lighter, leptonic jets, or that only selected blazars provide exceptional conditions for neutrino production.

Abbasi, R. [Loyola University, Chicago, IL (United↗

DOE OSTI2024

Resonance plasmonic coupling: selective enhancement of band edge emission over trap state emission of CdSe quantum dots

The photoluminescence properties of quantum dots (QDs) are often enhanced by eliminating surface trap states through chemical methods. Alternatively, a physical approach is presented here for improving photoluminescence purity in QDs by employing frequency-specific plasmon resonance coupling. Emitter-bound plasmonic hybrids are designed by electrostatically binding negatively charged QDs in water to positively charged gold nanoparticles having a thin polymer coating. Herein, two types of QDs are used: (i) bare CdSe, which exhibits both band edge and trap state emission, and (ii) CdSe overcoated with a ZnS shell (CdSe/ZnS) devoid of trap state emission. Tuning the extinction spectrum of the plasmonic system to match the band edge emission of CdSe enables the selective enhancement of band edge emission over trap state emission. Excellent match in the extinction spectrum of the gold nanoparticle with both, experimentally calculated photoluminescence enhancement factor and theoretically calculated radiative rate enhancement signifies the role of frequency-specific plasmon resonance coupling. Plasmon-coupled photoluminescence of CdSe/ZnS is further investigated by varying the number density of emitter on the surface of plasmonic nanoparticle. An enhancement in the photoluminescence is observed at a lower emitter density of CdSe/ZnS and the photoluminescence enhancement factor closely follows the plasmon resonance. However, photoluminescence quenching occurs with an increase in CdSe/ZnS due to plasmon-assisted nonradiative energy transfer between nearby QDs, as indicated by a red shift in the PL maximum. These studies establish that resonance plasmonic coupling is a convenient physical strategy for tuning the intrinsic photoluminescence properties of QDs for various optoelectronic applications.

Paul, Livin↗

DOE OSTI2025

Selecting samples of galaxies with fewer Fingers-of-God

The radial positions of galaxies inferred from their measured redshift appear distorted due to their peculiar velocities. We argue that the contribution from stochastic velocities — which gives rise to `Fingers-of-God' (FoG) anisotropy in the inferred maps — does not lend itself to perturbative modelling already on scales targeted by current experiments. To get around this limitation, we propose to remove FoG using data-driven indicators of their abundance that are local in nature and thus avoid selection biases. In particular, we show that the scale where the measured power spectrum quadrupole changes sign is tightly anti-correlated with both the satellite fraction and the velocity dispersion, and can thus be used to select galaxy samples with fewer FoG. In addition, we show that excluding galaxies in haloes more massive than a given mass threshold can help to discard many of the most problematic galaxies. Such selection could be achieved in practice using maps of the thermal Sunyaev-Zel'dovich distortion of the cosmic microwave background frequency spectrum. These techniques could potentially improve reconstructions of the large-scale velocity and displacement fields from the redshift-space positions of galaxies. They may also extend the reach of perturbative models for galaxy clustering, though in practice we find only marginal gains when fitting one-loop EFTofLSS models to simulations with mitigated FoG due to the relevance of other effects entering at two-loop order.

cosmological parameters from LSS↗

DOE OSTI2024

Infrared-Transparent Semiconductor Membranes for Electromagnetic Interference Shielding of Millimeter Waves

Here, it is demonstrated that single-crystalline and highly doped GaAs membranes are excellent candidates for realizing infrared-transparent shields of electromagnetic interference at millimeter frequencies. Measured optical transmittance spectra for the semiconductor membranes show resonant features between 750 and 2500 nm, with a 100% maximum transmittance. The shielding effectiveness of the membranes is extracted from measured scattering parameters between 65 and 85 GHz. Selected GaAs membranes and membranes/polyamide films exhibit shielding effectiveness ranging from 22 to 40 dB, which are suitable values to ensure the safe operation of infrared devices for commercial applications. Theoretical calculations based on a plane wave model show that the interplay of primary reflection and multiple internal reflections of the radio-frequency waves results in broadband shielding capabilities of the membrane between 10 and 300 GHz.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

ILLICIT TRANSIT INTERDICTION GLOBAL ANALYSIS

This study aims to enhance the security of radioactive materials during transport by analyzing commonalities in cargo thefts conducted by non-state groups such as thieves and terrorists. This research focuses on identifying patterns and trends in the methods used to steal high-value cargo, with the goal of applying these insights to improve transport security of radioactive materials. Key questions addressed include the frequency of specific tools, techniques, and insider involvement in thefts, as well as the use of weapons, electronic jamming equipment, and specialized tools. Findings will inform security design improvements and industry practices to mitigate vulnerabilities. The study involves a comprehensive review of literature and case studies, utilizing data sources from 2018 to 2023. Articles will be selected based on their relevance to thefts of valuable cargo in transit, with a focus on incidents involving non-state actors. The methodology will include statistical and inferential analysis to identify trends, with results visualized through pie charts, frequency analyses, and terrain maps. The discussion will highlight the implications of findings and provide actionable recommendations for strengthening security measures. Limitations such as data availability and reporting inconsistencies will be acknowledged. Suggestions for future improvements will be constructed using existing case studies and expert feedback. The study’s outcomes aim to raise awareness within the industry, inform policy decisions, and enhance security protocols for radioactive material transport. Metrics for impact include the potential publication of findings, presentations at conferences to raise awareness, and the subsequent actions taken by stakeholders based on the research. By identifying trends and vulnerabilities and suggesting improvements, this research contributes to preventing the illicit use of nuclear and radiological materials.

Zineddin, Dr. Z. [ORNL] (ORCID:0009000848740725)↗

DOE OSTI2024

Searching for the Highest- z Dual Active Galactic Nuclei in the Deepest Chandra Surveys

We present an analysis searching for dual active galactic nuclei (AGN) among 62 high-redshift (2.5 < z < 3.5) X-ray sources selected from the X-UDS, AEGIS-XD, CDF-S, and COSMOS-Legacy Chandra surveys. We aim to quantify the frequency of dual AGN in the high-redshift Universe, which holds implications for black hole merger timescales and low-frequency gravitational wave detection rates. We analyze each X-ray source using BAYMAX, an analysis tool that calculates the Bayes factor for whether a given archival Chandra AGN is more likely a single or dual point source. We find no strong evidence for dual AGN in any individual source in our sample. We increase our sensitivity to search for dual AGN across the sample by comparing our measured distribution of Bayes factors to that expected from a sample composed entirely of single point sources and find no evidence for dual AGN in the sample distribution. Although our analysis utilizes one of the largest Chandra catalogs of high-z X-ray point sources available to study, the findings remain limited by the modest number of sources observed at the highest spatial resolution with Chandra and the typical count rates of the detected sources. Our nondetection allows us to place an upper limit on the X-ray dual AGN fraction at 2.5 < z < 3.5 of 4.8% at the 95% confidence level. Expanding substantially on these results at X-ray wavelengths will require future surveys spanning larger sky areas and extending to fainter fluxes than has been possible with Chandra. We illustrate the potential of the AXIS mission concept in this regard.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

The Atacama Cosmology Telescope: DR6 Sunyaev-Zel'dovich Selected Galaxy Clusters Catalog

We present the results of a search for galaxy clusters in the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) microwave sky maps covering 16293 square degrees in three frequency bands, using data obtained over the lifetime of the project (2008-2022). We report redshifts and mass estimates for 10040 clusters detected via their Sunyaev-Zel'dovich (SZ) effect with signal-to-noise greater than 4 at a 2.4 arcminute filter scale. The catalog includes 1180 clusters at redshifts greater than 1, and 124 clusters at redshifts greater than 1.5. Using a relation between cluster SZ signal and mass that is consistent with recent weak-lensing measurements, we estimate that clusters detected with signal-to-noise greater than 5 form a sample which is 90% complete for clusters with masses greater than $5 \times 10^{14}$ MSun (measured within a spherical volume with mean density 500 times the critical density). El Gordo, a cluster found in an initial ACT survey of 755 square degrees, remains the most extreme cluster in mass and redshift; we find no cluster with a mass and redshift combination high enough to falsify the standard LCDM cosmology with Gaussian initial perturbations. We make public a variety of data products, including the full cluster candidate list, noise maps, and sky masks, along with our software for cluster detection and instructions for reproducing our cluster catalogs from the public ACT maps.

Aguena, M. [Trieste Observ.; LIneA, Rio de Janeiro↗

DOE OSTI2024

Convergent Concordant Mode Approach for Molecular Vibrations: CMA-2

The concordant mode approach (CMA) is a promising new scheme for dramatically increasing the system size and level of theory achievable in quantum chemical computations of molecular vibrational frequencies. Here, we achieve advances in the CMA hierarchy by computations targeting CCSD(T)/cc-pVTZ (coupled cluster singles and doubles with perturbative triples using a correlation-consistent polarized-valence triple-ζ basis set) benchmarks within the G2 molecular test set, executing a statistical analysis for 1501 frequencies from 111 compounds and then separately solving the refractory case of pyridine. First, MP2/cc-pVTZ (second-order Møller–Plesset perturbation theory with the same basis set) proves to be an excellent and preferred choice for generating the underlying (Level B) normal modes of the CMA scheme. Utilizing this Level B within the CMA-0A method reproduces the 1501 benchmark frequencies with a mean absolute error (MAE) of only 0.11 cm –1 and an attendant standard deviation of 0.49 cm –1 . Second, a convergent CMA-2 method is constituted that allows efficient computation of higher level (Level A) frequencies to any reasonable accuracy threshold by using only Hartree–Fock (HF) and MP2 or density functional theory (DFT) data to generate ξ parameters, which select the sparse off-diagonal force field elements for explicit evaluation at Level A. When Level B = MP2/cc-pVTZ, a cutoff of ξ = 0.02 provides an average maximum absolute error per molecule of only 0.17 cm –1 by incurring merely a 33% increase in average cost over CMA-0A. This CMA-2 method also eradicates the 4 problematic CMA-0A outliers of pyridine with even less effort (ξ = 0.04, 22% increase). Finally, the newly developed CMA procedures are shown to be highly successful when applied to 1-(1H-pyrrol-3-yl)ethanol, a new test molecule with diverse types of vibration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Complexity analysis of a CT injection experiment on BRB

In this work, we use Jensen–Shannon complexity and permutation entropy to analyze the magnetic field fluctuations of an astrophysically scaled plasma experiment. The experiment was intended to emulate an interplanetary coronal mass ejection event in the lab, recreating the major sections seen in satellite data. We also use a technique called “delay,” in which we use select elements, skipping one or more data points at a time, in our time series data to obtain Jensen–Shannon complexity as a function of frequency and investigate the frequency of maximized complexity. We then compare the delay frequencies to other frequencies in the plasma. We found that the frequencies for maximum complexity do not correspond to the frequencies investigated, implying that other physical mechanisms lead to an increase in complexity at these frequencies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Statistical evaluation of microscale stress conditions leading to void nucleation in the weak shock regime

Here, we investigate the heterogeneity of the stress state driven by anisotropic deformation response at the single crystal level through five statistical volume element (SVE) calculations of polycrystalline BCC tantalum. This work focuses on grain boundaries as a prominent material defect type prone to void nucleation based upon experimental observations of predominantly intergranular void nucleation in this material. The SVEs are constructed to be statistically representative of larger volumes of material and are meshed such that mean and standard deviation of grain size and orientation information is reconstructed. The computational meshes feature hexahedral (brick) elements and smooth conformal grain boundaries where significant stress concentration is known to occur, a tail effect of interest in the extreme events process of dynamic ductile damage. An existing micromechanical crystallographic plasticity model shown to capture the single crystal behavior of BCC tantalum well is used to perform the polycrystal calculations. The model includes representation of the non-Schmid effect of non-planar screw dislocation kinetics in tantalum. A three-dimensional stress state time profile predicted by damage modeling of a flyer plate impact experiment is applied as boundary conditions to each SVE. Resulting grain boundary stress state statistics are strongly non-Gaussian. Significant structural evolution is observed within the compressive hold before unloading into tension in the stress profile. Strong angular dependence of grain boundary traction magnitude with shock direction is observed. Non-Schmid effects continue to suggest their influence on propensity of microstructural defect types to nucleate voids. A general void nucleation criterion is proposed using probability theory. The general framework is specified to polycrystalline BCC tantalum in the weak shock regime to include the SVE calculations and literature molecular dynamics calculations of grain boundary void nucleation strength. Probability density functions (PDFs) are used to describe the interaction between the local stress state heterogeneity and the distributed grain boundary void nucleation strength state. A causation entropy maximization procedure removes the requirement for ad hoc selection of a PDF functional form and provides a rigorous procedure for data-based PDF determination. The resulting physically informed PDF describes the spatial appearance frequency of nucleated voids as a function of applied macroscale pressure. Lower length scale physics are thus packaged in a precise and computationally efficient way to provide computational plasticity insight to macroscale dynamic ductile damage models.

36 MATERIALS SCIENCE↗

DOE OSTI2024

MSR Transient Simulation and MSRE Transient Benchmark with SAM and SPECTRA

In recent years, there has been renewed interest in molten salt reactors (MSRs) for their potential advantages compared to reactors that rely on solid fuel. In response to such interest, many methods and codes have been developed to capture the unique features of MSRs. Among them, SPECTRA and SAM are two system analysis codes that have been enhanced to include MSR-specific modeling capabilities, including delayed neutron precursor drift and modified point kinetics equations.This paper discusses the efforts taken to verify and validate these features. A standard MSR system test problem was developed to verify and demonstrate the capability of SPECTRA and SAM on the MSR transient simulation. Sixteen transients were simulated. Further, the results obtained from SPECTRA and SAM show good agreement. The Molten Salt Reactor Experiment transient experiments were reviewed and selected to validate the SPECTRA and SAM codes. The experiments included pump startup and coastdown tests at zero power, reactivity insertion tests at different power levels, frequency tests, and a natural convection test. The simulation results from SPECTRA and SAM show good agreement with the experimental data.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Measurement of Electron Antineutrino Oscillation Amplitude and Frequency via Neutron Capture on Hydrogen at Daya Bay

This Letter reports the first measurement of the oscillation amplitude and frequency of reactor antineutrinos at Daya Bay via neutron capture on hydrogen using 1958 days of data. With over 3.6 million signal candidates, an optimized candidate selection, improved treatment of backgrounds and efficiencies, refined energy calibration, and an energy response model for the capture-on-hydrogen sensitive region, the relative ν ¯ e rates and energy spectra variation among the near and far detectors gives sin 2 2 θ 13 = 0.075 9 − 0.0049 + 0.0050 and Δ m 32 2 = ( 2.7 2 − 0.15 + 0.14 ) × 10 − 3 eV 2 assuming the normal neutrino mass ordering, and Δ m 32 2 = ( − 2.8 3 − 0.14 + 0.15 ) × 10 − 3 eV 2 for the inverted neutrino mass ordering. This estimate of sin 2 2 θ 13 is consistent with and essentially independent from the one obtained using the capture-on-gadolinium sample at Daya Bay. The combination of these two results yields sin 2 2 θ 13 = 0.0833 ± 0.0022 , which represents an 8% relative improvement in precision regarding the Daya Bay full 3158-day capture-on-gadolinium result. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Development of High-Temperature Bonding Techniques to Enable High-Temperature Static or Dynamic Strain Measurements

Current light-water nuclear reactors rely on a variety of different sensors and sensor applications to meet their structural health monitoring needs throughout the entirety of the reactor primary, secondary, and containment systems. Optical fiber–based sensor technologies could provide solutions to reduce the sensor system footprint while enhancing the measurement fidelity and spatial resolution by leveraging distributed monitoring techniques. Moreover, advanced reactors may require optical fiber–based sensors for structural health monitoring because their operating temperatures will exceed the limits of conventional transducers used to acquire dynamic strain or acoustic data in nuclear power plants. Therefore, this report describes experiments targeting the development of high-temperature bonding techniques that would allow for potentially long lengths of fibers to be bonded to metallic reactor components in advanced reactor systems. The high temperatures experienced within target application, next-generation nuclear reactors, necessitate a high-temperature resistant bond to limit the amount of tension on the fiber at the target application temperature. The primary bonding method investigated in this work is brazing; hot-rolling has also been investigated to a lesser extent. Both techniques are well-suited to bonding optical fibers to large reactor components such as primary coolant piping, pressure vessels, or heat exchangers. Optical frequency domain reflectometry was used to monitor the strain in metal-coated optical fibers before, during, and after the high-temperature bonding process. On select optical fibers that were successfully bonded, additional thermal cycling was performed to assess the extent to which the fiber remained bonded based on the expected thermal expansion of the test specimen material. The results of the various experiments yielded the following general conclusions: (1) brazing is a viable technique for bonding and allows significant compressive strain to be applied to the fiber at room temperature; (2) hot-rolling is a viable technique as well, which has been more optimized than the brazing technique for bonding, but less residual compressive strain has been observed with this technique; and (3) both techniques will need further development and optimization to demonstrate bonding of a long length of fiber that can provably operate at relevant temperatures for an advanced nuclear reactor application.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Materials Selection Principles for Designing Electro‐Thermal Neurons

Artificial neurons exhibiting volatile threshold switching and action potential‐like oscillations are crucial for brain‐inspired computing. While Complimentary Metal‐Oxide‐Semiconductor (CMOS)‐based strategies require hundreds of transistors to simulate each neuron, neuronal oscillations arise spontaneously in individual electro‐thermal devices due to nonlinearities like the Mott transition in VO 2 . Despite improved understanding of the physics, quantitative connections between neuronal performance and material properties remain under‐explored, preventing predictive neuron design and rational materials selection. In this work, a physics‐aware forward design methodology is developed for interrogating a wide palette of materials with properties varying by orders of magnitude, and their performance (high frequency, high dynamical reconfigurability and low power) under external circuit and device geometry constraints is assessed. The space of viable materials is identified to be much larger than previously recognized, with candidates from a range of materials classes, including Ge, GaP and MoS 2 . CMOS‐compatible performance (such as 100 GHz oscillating frequencies) can be achieved with CMOS‐compatible node sizes (≈10 nm). Finally, combinations of material properties yielding desired neuronal performance under uncertain design constraints are considered. This work solidifies forward design principles for electro‐thermal neuron devices, a necessary pre‐condition for inverse design from desired neuronal performance to required materials properties.

compact model↗

DOE OSTI2025

Detection of a Space Capsule Entering Earth’s Atmosphere with Distributed Acoustic Sensing (DAS)

On 24 September 2023, the Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer sample return capsule (SRC) entered Earth’s atmosphere after successfully collecting samples from an asteroid. The known trajectory and timing of this return provided a rare opportunity to strategically instrument sites to record geophysical signals produced by the capsule because it travelled at hypersonic speeds through the atmosphere. For this work, we deployed two distributed acoustic sensing (DAS) interrogators to sample over 12 km of surface-draped fiber-optic cables, as well as six collocated seismometer-infrasound sensor pairs, spread across two sites near Eureka, Nevada. This campaign-style rapid deployment is the first reported recording of an SRC re-entry with any distributed fiber-optic sensing technology. The DAS interrogators recorded an impulsive arrival with an extended coda which had features that were similar to recordings from both the seismometers and infrasound sensors. While the signal-to-noise ratio of the DAS data was lower than the seismic-infrasound data, the extremely dense spacing of fiber-optic sensors allowed for more phases to be clearly distinguished and the visualization of the continuous transformation of the wavefront as it impacted the ground. Unexpectedly, the DAS recordings contain less low-frequency content than is present in both the seismic and infrasound data. The deployment conditions strongly affected the recorded DAS data; in particular, we observed that fiber selection and placement exert strong controls on data quality.

58 GEOSCIENCES↗

DOE OSTI2026

Dynamic control of quantum phases in two-dimensional materials via Floquet engineering

The dynamical engineering of quantum states through periodic optical driving, known as Floquet engineering, has emerged as a powerful frontier in condensed matter physics, offering a pathway to realize material properties inaccessible in static equilibrium. This review provides a comprehensive overview of recent theoretical and experimental advances in the optical manipulation of two-dimensional (2D) quantum materials. We begin by systematically reviewing the evolution of the field from its pioneering applications in graphene and twisted moiré superlattices, highlighting the experimental realization of the light-induced anomalous Hall effect (AHE) to the complex spin-valley physics in transition metal dichalcogenides (TMDs). Furthermore, we briefly examine recent advances in 2D magnetic materials, demonstrating how optical driving can actively compete with intrinsic magnetism to dynamically switch magnetic orders and topological invariants. Moreover, we discuss the emerging frontiers of multi-frequency driving, quantum optimal control theory (QOCT), and ultrafast lightwave electronics. We highlight how tailored waveforms, such as bicircular light fields, and sub-cycle attosecond control can selectively break spatial symmetries to generate novel nonlinear photocurrents, mitigate dissipation, and extend the boundaries of quantum control well beyond the perturbative steady-state regime. Finally, we summarize the key experimental challenges for Floquet engineering, including effects such as heating and scattering, which limit coherent quantum control.

Wang, Wenpeng [Northeastern University, Shenyang, ↗

DOE OSTI2025

Tuning magneto-optical zero reflection via dual-channel hybrid magnonics

Multichannel coupling in hybrid systems makes an attractive testbed not only because of the distinct advantages entailed by each constituent mode but also because the opportunity to leverage interference among the various excitation pathways. Here, via combined analytical calculation and experiment, we demonstrate that the phase of the magnetization precession at the interface of a coupled yttrium iron garnet (YIG)/permalloy (Py) bilayer is collectively controlled by the microwave photon field torque and the interlayer exchange torque, manifesting a coherent, dual-channel excitation scheme that effectively tunes the magneto-optical spectrum. Furthermore, the different torque contributions vary with frequency, external bias field, and type of interlayer coupling between YIG and Py, which further results in destructive or constructive interferences between the two excitation channels, and hence selective suppression or amplification of the hybridized magnon modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗